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#probability

In probability theory and statistics, the **negative binomial distribution** is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted *r*) occurs.

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) 2 ( p ) {\displaystyle {\frac {r}{(1-p)^{2}(p)}}} <span>In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs. For example, if we define a 1 as failure, all non-1s as successes, and we throw a dice repeatedly until the third time 1 appears (r = three failures), then the probability distribution

#probability

The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution. That is, we can view the negative binomial as a Poisson(*λ*) distribution, where *λ* is itself a random variable, distributed as a gamma distribution with shape = *r* and scale θ = *p*/(1 − *p*) or correspondingly rate β = (1 − *p*)/*p* .

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) . {\displaystyle \operatorname {Poisson} (\lambda )=\lim _{r\to \infty }\operatorname {NB} \left(r,{\frac {\lambda }{\lambda +r}}\right).} Gamma–Poisson mixture[edit source] <span>The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution. That is, we can view the negative binomial as a Poisson(λ) distribution, where λ is itself a random variable, distributed as a gamma distribution with shape = r and scale θ = p/(1 − p) or correspondingly rate β = (1 − p)/p. To display the intuition behind this statement, consider two independent Poisson processes, “Success” and “Failure”, with intensities p and 1 − p. Together, the Success and Failure pr

#probability

The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution.

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The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution. That is, we can view the negative binomial as a Poisson(λ) distribution, where λ is itself a random variable, distributed as a gamma distribution with shape = r and scale θ = p/(1 − p)

) . {\displaystyle \operatorname {Poisson} (\lambda )=\lim _{r\to \infty }\operatorname {NB} \left(r,{\frac {\lambda }{\lambda +r}}\right).} Gamma–Poisson mixture[edit source] <span>The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution. That is, we can view the negative binomial as a Poisson(λ) distribution, where λ is itself a random variable, distributed as a gamma distribution with shape = r and scale θ = p/(1 − p) or correspondingly rate β = (1 − p)/p. To display the intuition behind this statement, consider two independent Poisson processes, “Success” and “Failure”, with intensities p and 1 − p. Together, the Success and Failure pr

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#probability

Question

The negative binomial distribution also arises as a [...] of Poisson distributions

Answer

continuous mixture

*Can be used to model over dispersed count observations, known as Gamma-Poisson distribution.*

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The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution.

) . {\displaystyle \operatorname {Poisson} (\lambda )=\lim _{r\to \infty }\operatorname {NB} \left(r,{\frac {\lambda }{\lambda +r}}\right).} Gamma–Poisson mixture[edit source] <span>The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution. That is, we can view the negative binomial as a Poisson(λ) distribution, where λ is itself a random variable, distributed as a gamma distribution with shape = r and scale θ = p/(1 − p) or correspondingly rate β = (1 − p)/p. To display the intuition behind this statement, consider two independent Poisson processes, “Success” and “Failure”, with intensities p and 1 − p. Together, the Success and Failure pr

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#probability

Question

Answer

The negative binomial distribution

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The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution. </spa

) . {\displaystyle \operatorname {Poisson} (\lambda )=\lim _{r\to \infty }\operatorname {NB} \left(r,{\frac {\lambda }{\lambda +r}}\right).} Gamma–Poisson mixture[edit source] <span>The negative binomial distribution also arises as a continuous mixture of Poisson distributions (i.e. a compound probability distribution) where the mixing distribution of the Poisson rate is a gamma distribution. That is, we can view the negative binomial as a Poisson(λ) distribution, where λ is itself a random variable, distributed as a gamma distribution with shape = r and scale θ = p/(1 − p) or correspondingly rate β = (1 − p)/p. To display the intuition behind this statement, consider two independent Poisson processes, “Success” and “Failure”, with intensities p and 1 − p. Together, the Success and Failure pr

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#probability

Question

Answer

negative binomial distribution

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In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of fai

) 2 ( p ) {\displaystyle {\frac {r}{(1-p)^{2}(p)}}} <span>In probability theory and statistics, the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs. For example, if we define a 1 as failure, all non-1s as successes, and we throw a dice repeatedly until the third time 1 appears (r = three failures), then the probability distribution

#computer-science #mathematics

In mathematics and computer science, a **canonical**, **normal**, or **standard** **form** of a mathematical object is a standard way of presenting that object as a mathematical expression.

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strings " madam curie " and " radium came " are given as C arrays. Each one is converted into a canonical form by sorting. Since both sorted strings literally agree, the original strings were anagrams of each other. <span>In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. The distinction between "canonical" and "normal" forms varies by subfield. In most fields, a canonical form specifies a unique representation for every object, while

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#computer-science #mathematics

Question

a **[...]** form of a mathematical object is a standard way of presenting that object as a mathematical expression.

Answer

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In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.

strings " madam curie " and " radium came " are given as C arrays. Each one is converted into a canonical form by sorting. Since both sorted strings literally agree, the original strings were anagrams of each other. <span>In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. The distinction between "canonical" and "normal" forms varies by subfield. In most fields, a canonical form specifies a unique representation for every object, while

#linear-state-space-models

The objects in play are:

- An \( n \times 1\) vector \(x_t\) denoting the
**state**at time \(t = 0, 1, 2, \ldots\) - An iid sequence of \(m \times 1\) random vectors \(w_t \sim N(0,I)\)
- A \(k \times 1\) vector \(y_t\) of
**observations**at time \( t = 0, 1, 2, \ldots\) - An \(n \times n\) matrix A called the
**transition matrix** - An \(n \times m\) matrix C called the
**volatility matrix** - A \(k \times n\) matrix G sometimes called the
**output matrix**

Here is the linear state-space system\(\) \begin{aligned} x_{t+1} & = A x_t + C w_{t+1} \\ y_t & = G x_t \nonumber \\ x_0 & \sim N(\mu_0, \Sigma_0) \nonumber \end{aligned}

.

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#linear-state-space-models

A martingale difference sequence is a sequence that is zero mean when conditioned on past information

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Martingale difference shocks¶ We’ve made the common assumption that the shocks are independent standardized normal vectors But some of what we say will be valid under the assumption that {wt+1}{wt+1} is a martingale difference sequence <span>A martingale difference sequence is a sequence that is zero mean when conditioned on past information In the present case, since {xt}{xt} is our state sequence, this means that it satisfies 𝔼[wt+1|xt,xt−1,…]=0E[wt+1|xt,xt−1,…]=0 This is a weaker condition than that {wt}{wt} is i

#linear-state-space-models

The primitives of the model are

- the matrices A , C , G A,C,G A, C, G
- shock distribution, which we have specialized to N ( 0 , I ) N(0,I) N(0,I)
- the distribution of the initial condition x 0 x0 x_0 , which we have set to N ( μ 0 , Σ 0 )

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#linear-state-space-models

In state space models, finding the state is an art

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N(0,I) Examples¶ By appropriate choice of the primitives, a variety of dynamics can be represented in terms of the linear state space model The following examples help to highlight this point They also illustrate the wise dictum <span>finding the state is an art Second-order difference equation¶ Let {yt}{yt} be a deterministic sequence that satifies (2)¶ yt+1=ϕ0+ϕ1yt+ϕ2yt−1s.t.y0,y−1 givenyt+1=ϕ0+ϕ1yt+ϕ2yt−1s.t.y0,y−1 given To map (2

#linear-state-space-models

Sufficient statistics form a list of objects that characterize a population distribution

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full distribution However, there are some situations where these moments alone tell us all we need to know These are situations in which the mean vector and covariance matrix are sufficient statistics for the population distribution (<span>Sufficient statistics form a list of objects that characterize a population distribution) One such situation is when the vector in question is Gaussian (i.e., normally distributed) This is the case here, given our Gaussian assumptions on the primitives the fact that n

#linear-state-space-models

In linear state space models, we can generate independent draws of y_T by repeatedly simulating the evolution of the system up to time T , using an independent set of shocks each time

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#linear-state-space-models

The difference equation \( \mu_{t+1} = A \mu_t \) is known to have *unique* fixed point \( \mu_{\infty} = 0 \) if all eigenvalues of A have moduli strictly less than unity.

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#linear-state-space-models

However, global stability is more than we need for stationary solutions, and often more than we want

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o has a unique fixed point in this case, and, moreover μt→μ∞=0andΣt→Σ∞ast→∞μt→μ∞=0andΣt→Σ∞ast→∞ regardless of the initial conditions μ0μ0 and Σ0Σ0 This is the globally stable case — see these notes for more a theoretical treatment <span>However, global stability is more than we need for stationary solutions, and often more than we want To illustrate, consider our second order difference equation example Here the state is xt=[1ytyt−1]′xt=[1ytyt−1]′ Because of the constant first component in the state vector, we w

#linear-state-space-models

Ergodicity is the property that time series and ensemble averages coincide

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verages x¯:=1T∑t=1Txtandy¯:=1T∑t=1Tytx¯:=1T∑t=1Txtandy¯:=1T∑t=1Tyt Do these time series averages converge to something interpretable in terms of our basic state-space representation? The answer depends on something called ergodicity <span>Ergodicity is the property that time series and ensemble averages coincide More formally, ergodicity implies that time series sample averages converge to their expectation under the stationary distribution In particular, 1T∑Tt=1xt→μ∞1T∑t=1Txt→μ∞ 1T∑Tt=1(

#linear-state-space-models

More formally, ergodicity implies that time series sample averages converge to their expectation under the stationary distribution

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hese time series averages converge to something interpretable in terms of our basic state-space representation? The answer depends on something called ergodicity Ergodicity is the property that time series and ensemble averages coincide <span>More formally, ergodicity implies that time series sample averages converge to their expectation under the stationary distribution In particular, 1T∑Tt=1xt→μ∞1T∑t=1Txt→μ∞ 1T∑Tt=1(xt−x¯T)(xt−x¯T)′→Σ∞1T∑t=1T(xt−x¯T)(xt−x¯T)′→Σ∞ 1T∑Tt=1(xt+j−x¯T)(xt−x¯T)′→AjΣ∞1T∑t=1T(xt+j−x¯T)(xt−x¯T)′→AjΣ∞ In our linear Gaussia

#linear-state-space-models

In our linear Gaussian setting, any covariance stationary process is also ergodic

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ample averages converge to their expectation under the stationary distribution In particular, 1T∑Tt=1xt→μ∞1T∑t=1Txt→μ∞ 1T∑Tt=1(xt−x¯T)(xt−x¯T)′→Σ∞1T∑t=1T(xt−x¯T)(xt−x¯T)′→Σ∞ 1T∑Tt=1(xt+j−x¯T)(xt−x¯T)′→AjΣ∞1T∑t=1T(xt+j−x¯T)(xt−x¯T)′→AjΣ∞ <span>In our linear Gaussian setting, any covariance stationary process is also ergodic Noisy Observations¶ In some settings the observation equation yt=Gxtyt=Gxt is modified to include an error term Often this error term represents the idea that the true sta

#linear-state-space-models

The theory of prediction for linear state space systems is elegant and simple

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t]=Gμt The variance-covariance matrix of ytyt is easily shown to be (19)¶ Var[yt]=Var[Gxt+Hvt]=GΣtG′+HH′Var[yt]=Var[Gxt+Hvt]=GΣtG′+HH′ The distribution of ytyt is therefore yt∼N(Gμt,GΣtG′+HH′)yt∼N(Gμt,GΣtG′+HH′) Prediction¶ <span>The theory of prediction for linear state space systems is elegant and simple Forecasting Formulas – Conditional Means¶ The natural way to predict variables is to use conditional distributions For example, the optimal forecast of xt+1xt+1 given informatio

#linear-state-space-models

The natural way to predict variables is to use conditional distributions

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vt]=GΣtG′+HH′ The distribution of ytyt is therefore yt∼N(Gμt,GΣtG′+HH′)yt∼N(Gμt,GΣtG′+HH′) Prediction¶ The theory of prediction for linear state space systems is elegant and simple Forecasting Formulas – Conditional Means¶ <span>The natural way to predict variables is to use conditional distributions For example, the optimal forecast of xt+1xt+1 given information known at time tt is 𝔼t[xt+1]:=𝔼[xt+1∣xt,xt−1,…,x0]=AxtEt[xt+1]:=E[xt+1∣xt,xt−1,…,x0]=Axt The right-hand side foll

#linear-state-space-models

if \( \{y_t\}\) is a stream of dividends, then \( \mathbb{E} \left[\sum_{j=0}^\infty \beta^j y_{t+j} | x_t \right]\) is a model of a stock price

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#linear-state-space-models

Question

In state space models, finding [...] is an art

Answer

the state

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In state space models, finding the state is an art

N(0,I) Examples¶ By appropriate choice of the primitives, a variety of dynamics can be represented in terms of the linear state space model The following examples help to highlight this point They also illustrate the wise dictum <span>finding the state is an art Second-order difference equation¶ Let {yt}{yt} be a deterministic sequence that satifies (2)¶ yt+1=ϕ0+ϕ1yt+ϕ2yt−1s.t.y0,y−1 givenyt+1=ϕ0+ϕ1yt+ϕ2yt−1s.t.y0,y−1 given To map (2

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#linear-state-space-models

Question

if \( \{y_t\}\) is [...], then \( \mathbb{E} \left[\sum_{j=0}^\infty \beta^j y_{t+j} | x_t \right]\) is a model of a stock price

Answer

a stream of dividends

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if \( \{y_t\}\) is a stream of dividends, then \( \mathbb{E} \left[\sum_{j=0}^\infty \beta^j y_{t+j} | x_t \right]\) is a model of a stock price

Tags

#linear-state-space-models

Question

if \( \{y_t\}\) is a stream of dividends, then \( \mathbb{E} \left[\sum_{j=0}^\infty \beta^j y_{t+j} | x_t \right]\) is a model of [...]

Answer

a stock price

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if \( \{y_t\}\) is a stream of dividends, then \( \mathbb{E} \left[\sum_{j=0}^\infty \beta^j y_{t+j} | x_t \right]\) is a model of a stock price

Tags

#linear-state-space-models

Question

if \( \{y_t\}\) is a stream of dividends, then [...] is a model of a stock price

Answer

\( \mathbb{E} \left[\sum_{j=0}^\infty \beta^j y_{t+j} | x_t \right]\)

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if \( \{y_t\}\) is a stream of dividends, then \( \mathbb{E} \left[\sum_{j=0}^\infty \beta^j y_{t+j} | x_t \right]\) is a model of a stock price

Tags

#linear-state-space-models

Question

The natural way to predict variables is to use

[...]Answer

conditional distributions

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The natural way to predict variables is to use conditional distributions

vt]=GΣtG′+HH′ The distribution of ytyt is therefore yt∼N(Gμt,GΣtG′+HH′)yt∼N(Gμt,GΣtG′+HH′) Prediction¶ The theory of prediction for linear state space systems is elegant and simple Forecasting Formulas – Conditional Means¶ <span>The natural way to predict variables is to use conditional distributions For example, the optimal forecast of xt+1xt+1 given information known at time tt is 𝔼t[xt+1]:=𝔼[xt+1∣xt,xt−1,…,x0]=AxtEt[xt+1]:=E[xt+1∣xt,xt−1,…,x0]=Axt The right-hand side foll

Tags

#linear-state-space-models

Question

In our linear Gaussian setting, any covariance stationary process is also [...]

Answer

ergodic

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In our linear Gaussian setting, any covariance stationary process is also ergodic

ample averages converge to their expectation under the stationary distribution In particular, 1T∑Tt=1xt→μ∞1T∑t=1Txt→μ∞ 1T∑Tt=1(xt−x¯T)(xt−x¯T)′→Σ∞1T∑t=1T(xt−x¯T)(xt−x¯T)′→Σ∞ 1T∑Tt=1(xt+j−x¯T)(xt−x¯T)′→AjΣ∞1T∑t=1T(xt+j−x¯T)(xt−x¯T)′→AjΣ∞ <span>In our linear Gaussian setting, any covariance stationary process is also ergodic Noisy Observations¶ In some settings the observation equation yt=Gxtyt=Gxt is modified to include an error term Often this error term represents the idea that the true sta

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#linear-state-space-models

Question

In our linear Gaussian setting, any [...] process is also ergodic

Answer

covariance stationary

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In our linear Gaussian setting, any covariance stationary process is also ergodic

ample averages converge to their expectation under the stationary distribution In particular, 1T∑Tt=1xt→μ∞1T∑t=1Txt→μ∞ 1T∑Tt=1(xt−x¯T)(xt−x¯T)′→Σ∞1T∑t=1T(xt−x¯T)(xt−x¯T)′→Σ∞ 1T∑Tt=1(xt+j−x¯T)(xt−x¯T)′→AjΣ∞1T∑t=1T(xt+j−x¯T)(xt−x¯T)′→AjΣ∞ <span>In our linear Gaussian setting, any covariance stationary process is also ergodic Noisy Observations¶ In some settings the observation equation yt=Gxtyt=Gxt is modified to include an error term Often this error term represents the idea that the true sta

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#linear-state-space-models

Question

In [...] setting, any covariance stationary process is also ergodic

Answer

our linear Gaussian

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In our linear Gaussian setting, any covariance stationary process is also ergodic

ample averages converge to their expectation under the stationary distribution In particular, 1T∑Tt=1xt→μ∞1T∑t=1Txt→μ∞ 1T∑Tt=1(xt−x¯T)(xt−x¯T)′→Σ∞1T∑t=1T(xt−x¯T)(xt−x¯T)′→Σ∞ 1T∑Tt=1(xt+j−x¯T)(xt−x¯T)′→AjΣ∞1T∑t=1T(xt+j−x¯T)(xt−x¯T)′→AjΣ∞ <span>In our linear Gaussian setting, any covariance stationary process is also ergodic Noisy Observations¶ In some settings the observation equation yt=Gxtyt=Gxt is modified to include an error term Often this error term represents the idea that the true sta

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#linear-state-space-models

Question

More formally, ergodicity implies that [...] converge to their expectation under the stationary distribution

Answer

time series sample averages

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More formally, ergodicity implies that time series sample averages converge to their expectation under the stationary distribution

hese time series averages converge to something interpretable in terms of our basic state-space representation? The answer depends on something called ergodicity Ergodicity is the property that time series and ensemble averages coincide <span>More formally, ergodicity implies that time series sample averages converge to their expectation under the stationary distribution In particular, 1T∑Tt=1xt→μ∞1T∑t=1Txt→μ∞ 1T∑Tt=1(xt−x¯T)(xt−x¯T)′→Σ∞1T∑t=1T(xt−x¯T)(xt−x¯T)′→Σ∞ 1T∑Tt=1(xt+j−x¯T)(xt−x¯T)′→AjΣ∞1T∑t=1T(xt+j−x¯T)(xt−x¯T)′→AjΣ∞ In our linear Gaussia

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#linear-state-space-models

Question

More formally, ergodicity implies that time series sample averages converge to

[...]Answer

their
expectation under the stationary distribution

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More formally, ergodicity implies that time series sample averages converge to their expectation under the stationary distribution

hese time series averages converge to something interpretable in terms of our basic state-space representation? The answer depends on something called ergodicity Ergodicity is the property that time series and ensemble averages coincide <span>More formally, ergodicity implies that time series sample averages converge to their expectation under the stationary distribution In particular, 1T∑Tt=1xt→μ∞1T∑t=1Txt→μ∞ 1T∑Tt=1(xt−x¯T)(xt−x¯T)′→Σ∞1T∑t=1T(xt−x¯T)(xt−x¯T)′→Σ∞ 1T∑Tt=1(xt+j−x¯T)(xt−x¯T)′→AjΣ∞1T∑t=1T(xt+j−x¯T)(xt−x¯T)′→AjΣ∞ In our linear Gaussia

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#linear-state-space-models

Question

Ergodicity is the property that averages of **[...]** and **[...]** coincide

Answer

time series and ensemble

*The ensemble is the samples from the stationary distribution*

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scheduled repetition interval | last repetition or drill |

Ergodicity is the property that time series and ensemble averages coincide

verages x¯:=1T∑t=1Txtandy¯:=1T∑t=1Tytx¯:=1T∑t=1Txtandy¯:=1T∑t=1Tyt Do these time series averages converge to something interpretable in terms of our basic state-space representation? The answer depends on something called ergodicity <span>Ergodicity is the property that time series and ensemble averages coincide More formally, ergodicity implies that time series sample averages converge to their expectation under the stationary distribution In particular, 1T∑Tt=1xt→μ∞1T∑t=1Txt→μ∞ 1T∑Tt=1(

Tags

#linear-state-space-models

Question

However, [...] is more than we need for stationary solutions, and often more than we want

Answer

global stability

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However, global stability is more than we need for stationary solutions, and often more than we want

o has a unique fixed point in this case, and, moreover μt→μ∞=0andΣt→Σ∞ast→∞μt→μ∞=0andΣt→Σ∞ast→∞ regardless of the initial conditions μ0μ0 and Σ0Σ0 This is the globally stable case — see these notes for more a theoretical treatment <span>However, global stability is more than we need for stationary solutions, and often more than we want To illustrate, consider our second order difference equation example Here the state is xt=[1ytyt−1]′xt=[1ytyt−1]′ Because of the constant first component in the state vector, we w

Tags

#linear-state-space-models

Question

In linear state space models, we can generate independent draws of y_T by [...] , using an independent set of shocks each time

Answer

repeatedly simulating the evolution of the system up to time T

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

In linear state space models, we can generate independent draws of y_T by repeatedly simulating the evolution of the system up to time T , using an independent set of shocks each time

Tags

#linear-state-space-models

Question

In linear state space models, we can generate independent draws of y_T by repeatedly simulating the evolution of the system up to time T , using [...]

Answer

an independent set of shocks each time

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

In linear state space models, we can generate independent draws of y_T by repeatedly simulating the evolution of the system up to time T , using an independent set of shocks each time

Tags

#linear-state-space-models

Question

[...] form a list of objects that characterize a population distribution

Answer

Sufficient statistics

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Sufficient statistics form a list of objects that characterize a population distribution

full distribution However, there are some situations where these moments alone tell us all we need to know These are situations in which the mean vector and covariance matrix are sufficient statistics for the population distribution (<span>Sufficient statistics form a list of objects that characterize a population distribution) One such situation is when the vector in question is Gaussian (i.e., normally distributed) This is the case here, given our Gaussian assumptions on the primitives the fact that n

Tags

#linear-state-space-models

Question

In the linear state-space system\(\)

\begin{aligned} x_{t+1} & = A x_t + C w_{t+1} \\ y_t & = G x_t \nonumber \\ x_0 & \sim N(\mu_0, \Sigma_0) \nonumber \end{aligned}

C is called the **[...]**

Answer

volatility matrix

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An n×1 vector xt denoting the state at time t=0,1,2,… An iid sequence of m×1 random vectors wt∼N(0,I) A k×1 vector yt of observations at time t=0,1,2,… An n×n matrix A called the transition matrix An n×m matrix C called the <span>volatility matrix A k×n matrix G sometimes called the output matrix Here is the linear state-space system xt+1ytx0=Axt+Cwt+1=Gxt∼N(μ0,Σ0) . .

Tags

#linear-state-space-models

Question

The difference equation \( \mu_{t+1} = A \mu_t \) is known to have *unique* fixed point \( \mu_{\infty} = 0 \) if [...].

Answer

all eigenvalues of A have moduli strictly less than unity

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

The difference equation μt+1=Aμt is known to have unique fixed point μ∞=0 if all eigenvalues of A have moduli strictly less than unity.

Tags

#linear-state-space-models

Question

the **[...]** distribution is specialized to \(N(0,I)\)

Answer

shock

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

The primitives of the model are the matrices A , C , G A,C,G A, C, G shock distribution, which we have specialized to N ( 0 , I ) N(0,I) N(0,I) the distribution of the initial condition x 0 x0 x_0 , which we have set to N ( μ 0 , Σ 0 )

Tags

#linear-state-space-models

Question

The theory of [...] for linear state space systems is elegant and simple

Answer

prediction

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The theory of prediction for linear state space systems is elegant and simple

t]=Gμt The variance-covariance matrix of ytyt is easily shown to be (19)¶ Var[yt]=Var[Gxt+Hvt]=GΣtG′+HH′Var[yt]=Var[Gxt+Hvt]=GΣtG′+HH′ The distribution of ytyt is therefore yt∼N(Gμt,GΣtG′+HH′)yt∼N(Gμt,GΣtG′+HH′) Prediction¶ <span>The theory of prediction for linear state space systems is elegant and simple Forecasting Formulas – Conditional Means¶ The natural way to predict variables is to use conditional distributions For example, the optimal forecast of xt+1xt+1 given informatio

[unknown IMAGE 1799065308428]

Tags

#has-images #jaynes #plausible-reasoning

Question

Given

A ≡ it will start to rain by 10 am at the latest;

B ≡ the sky will become cloudy before 10 am.

The weaker syllogism (B is true) takes the form**[...]**

A ≡ it will start to rain by 10 am at the latest;

B ≡ the sky will become cloudy before 10 am.

The weaker syllogism (B is true) takes the form

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Question

Reflecting on the history of logic forces us to reflect on what it means to be a [...], to think properly.

Answer

reasonable cognitive agent

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Reflecting on the history of logic forces us to reflect on what it means to be a reasonable cognitive agent, to think properly.

dgeman The history of logic should be of interest to anyone with aspirations to thinking that is correct, or at least reasonable. This story illustrates different approaches to intellectual enquiry and human cognition more generally. <span>Reflecting on the history of logic forces us to reflect on what it means to be a reasonable cognitive agent, to think properly. Is it to engage in discussions with others? Is it to think for ourselves? Is it to perform calculations? In the Critique of Pure Reason (1781), Immanuel Kant stated that no progress in

语料库的地址是： http：// corpus.byu.edu/coca/

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英语 话题 的优秀回答者 564人赞了该文章 美国当代英语语料库（Corpus of Contemporary American English，简称COCA）是目前最大的免费英语语言库，它由包含5.2亿词的文本构成，这些文本由口语，小说，流行杂志，报纸以及学术文章五种不同的文体构成。从1990年至2015年年间语料库以每年增加两千万词的速度进行扩充，以保证语料库内容的时效性。因此，美国当代英语语料库被认为是用来观察美国英语当前发展变化的最合适的英语语料库。 <span>语料库的地址是： http：// corpus.byu.edu/coca/ 与传统词典相比，COCA具有以下几点优势： （1）语料库的文本实时性比较强，类似生活满意度，社交媒体这样的词很多传统词典都没有收录，但在语料库中都可以查到。 （2）语料库可以提供单词的词频信息，这有助于我们了解该单词在实际应用中的出现频率，有助于实现准确用词。 （3）语料库还能提供模糊搜索和单词搭配等功能。 。实际使用时可以将语料库作为词典的补充工具，在词典里面无法确

#linguistics #verbs

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started reading on | finished reading on |

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

#linguistics #verbs

status | not read | reprioritisations | ||
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last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>In linguistics, grammatical mood (also mode) is a grammatical feature of verbs, used for signaling modality. [2] [3] :p.181; [4] That is, it is the use of verbal inflections that allow speakers to express their attitude toward what they are saying (e.g. a statement of fact, of desire, of command, etc.). The term is also used more broadly to describe the syntactic expression of modality, that is, the use of verb phrases that do not involve inflexion of the verb itself. Mood is distinc

Tags

#linguistics #verbs

Question

Answer

verbal inflections

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

mood is the use of verbal inflections that allow speakers to express their attitude toward what they are saying (e.g. a statement of fact, of desire, of command, etc.).

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>In linguistics, grammatical mood (also mode) is a grammatical feature of verbs, used for signaling modality. [2] [3] :p.181; [4] That is, it is the use of verbal inflections that allow speakers to express their attitude toward what they are saying (e.g. a statement of fact, of desire, of command, etc.). The term is also used more broadly to describe the syntactic expression of modality, that is, the use of verb phrases that do not involve inflexion of the verb itself. Mood is distinc

Tags

#linguistics #verbs

Question

Answer

mood

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

mood is the use of verbal inflections that allow speakers to express their attitude toward what they are saying (e.g. a statement of fact, of desire, of command, etc.).

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>In linguistics, grammatical mood (also mode) is a grammatical feature of verbs, used for signaling modality. [2] [3] :p.181; [4] That is, it is the use of verbal inflections that allow speakers to express their attitude toward what they are saying (e.g. a statement of fact, of desire, of command, etc.). The term is also used more broadly to describe the syntactic expression of modality, that is, the use of verb phrases that do not involve inflexion of the verb itself. Mood is distinc

#linguistics #verbs

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started reading on | finished reading on |

Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

#linguistics #verbs

Perfective aspect refers to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him")

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people").

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

#linguistics #verbs

Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people").

status | not read | reprioritisations | ||
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last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). <span>Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). <span><body><html>

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

Tags

#linguistics #verbs

Question

Answer

Aspect

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Aspect expresses how an action, event extends over time.

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

Tags

#linguistics #verbs

Question

Answer

time

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Aspect expresses how an action, event extends over time.

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

Tags

#linguistics #verbs

Question

Perfective aspect refers to an event conceived as **[...]**

Answer

bounded and unitary

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Perfective aspect refers to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him")

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

Tags

#linguistics #verbs

Question

Perfective aspect doesn't refer to any [...]

Answer

duration of time

*("I helped him")*

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Perfective aspect refers to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him")

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

Tags

#linguistics #verbs

Question

Answer

Perfective aspect

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Perfective aspect refers to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him")

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

Tags

#linguistics #verbs

Question

Imperfective aspect is used for situations conceived as existing [...or...] as time flows

Answer

continuously or repetitively

*("I was helping him"; "I used to help people")*

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people").

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

Tags

#linguistics #verbs

Question

Answer

Imperfective aspect

*("I was helping him"; "I used to help people")*

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). </htm

onstruction Singulative-Collective-Pluractive Specificity Subject/Object Suffixaufnahme (Case stacking) Tense Tense–aspect–mood Telicity Transitivity Topic and Comment Thematic relation (Agent/Patient) Valency Voice Volition v t e <span>Aspect is a grammatical category that expresses how an action, event, or state, denoted by a verb, extends over time. Perfective aspect is used in referring to an event conceived as bounded and unitary, without reference to any flow of time during ("I helped him"). Imperfective aspect is used for situations conceived as existing continuously or repetitively as time flows ("I was helping him"; "I used to help people"). Further distinctions can be made, for example, to distinguish states and ongoing actions (continuous and progressive aspects) from repetitive actions (habitual aspect). Certain aspe

[unknown IMAGE 1803053042956]

Tags

#has-images #jaynes #plausible-reasoning

Question

Given

A ≡ it will start to rain by 10 am at the latest;

B ≡ the sky will become cloudy before 10 am.

The second weaker syllogism (A is false) takes the form**[...]**

A ≡ it will start to rain by 10 am at the latest;

B ≡ the sky will become cloudy before 10 am.

The second weaker syllogism (A is false) takes the form

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

[unknown IMAGE 1803054615820]

Tags

#has-images #jaynes #plausible-reasoning

Question

Given

A ≡ man is a burglar;

B ≡ man behave weird.

The still weaker syllogism takes the form**[...]**

A ≡ man is a burglar;

B ≡ man behave weird.

The still weaker syllogism takes the form

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

#jaynes #plausible-reasoning

we conceal how complicated our daily reasoning process really is by calling it common sense

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#jaynes #plausible-reasoning

in the burglar/police case, our reasoning depends very much on prior information to help us in evaluating the degree of plausibility

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#jaynes #plausible-reasoning

In trying to understand common sense, we make progress by constructing idealized mathematical models which reproduce a few of its features

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started reading on | finished reading on |

#jaynes #plausible-reasoning

Often, the things which are most familiar to us turn out to be the hardest to understand. Phenomena whose very existence is unknown to the vast majority of the human race (such as the differ- ence in ultraviolet spectra of iron and nickel) can be explained in exhaustive mathematical detail – but all of modern science is practically helpless when faced with the complications of such a commonplace fact as growth of a blade of grass

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#jaynes #plausible-reasoning

advance in knowledge often leads to consequences of great practical value, but of an unpredictable nature

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#jaynes #plausible-reasoning

In principle, the only operations which a machine cannot perform for us are those which we cannot describe in detail, or which could not be completed in a finite number of steps.

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#jaynes #plausible-reasoning

a mathematical model reproduces a part of common sense by prescribing a definite set of operations, this shows us how to ‘build a machine’, (i.e. write a computer program) which operates on incomplete information and, by applying quantitative versions of the above weak syllogisms, does plausible reasoning instead of deductive reasoning.

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#jaynes #plausible-reasoning

Our unaided common sense can decide between a few distinctive hypotheses, but not many similar ones.

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Tags

#jaynes #plausible-reasoning

Question

in the burglar/police case, our reasoning depends very much on [...] to help us in evaluating the degree of plausibility

Answer

prior information

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

in the burglar/police case, our reasoning depends very much on prior information to help us in evaluating the degree of plausibility

Tags

#jaynes #plausible-reasoning

Question

in the burglar/police case, our reasoning depends very much on prior information to help us in evaluating the [...]

Answer

degree of plausibility

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

in the burglar/police case, our reasoning depends very much on prior information to help us in evaluating the degree of plausibility

Tags

#jaynes #plausible-reasoning

Question

we conceal how complicated our [...] really is by calling it common sense

Answer

daily reasoning process

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

we conceal how complicated our daily reasoning process really is by calling it common sense

Tags

#jaynes #plausible-reasoning

Question

we conceal how complicated our daily reasoning process really is by calling it [...]

Answer

common sense

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

we conceal how complicated our daily reasoning process really is by calling it common sense

Tags

#jaynes #plausible-reasoning

Question

advance in knowledge often leads to consequences of great practical value, but of [...] nature

Answer

an unpredictable

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

advance in knowledge often leads to consequences of great practical value, but of an unpredictable nature

Tags

#jaynes #plausible-reasoning

Question

advance in knowledge often leads to consequences of [...] value, but of an unpredictable nature

Answer

great practical

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

advance in knowledge often leads to consequences of great practical value, but of an unpredictable nature

Tags

#jaynes #plausible-reasoning

Question

In principle, the only operations which a machine cannot perform for us are those which [...], or which could not be completed in a finite number of steps.

Answer

we cannot describe in detail

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

In principle, the only operations which a machine cannot perform for us are those which we cannot describe in detail, or which could not be completed in a finite number of steps.

Tags

#jaynes #plausible-reasoning

Question

In principle, the only operations which a machine cannot perform for us are those which we cannot describe in detail, or which [...].

Answer

could not be completed in a finite number of steps

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

In principle, the only operations which a machine cannot perform for us are those which we cannot describe in detail, or which could not be completed in a finite number of steps.

#jaynes #plausible-reasoning

a mathematical model reproduces a part of common sense by prescribing a definite set of operations

status | not read | reprioritisations | ||
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last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

a mathematical model reproduces a part of common sense by prescribing a definite set of operations, this shows us how to ‘build a machine’, (i.e. write a computer program) which operates on incomplete information and, by applying quantitative versions of the above weak syllogisms, do

#jaynes #plausible-reasoning

A model operates on incomplete information and, by applying quantitative versions of the above weak syllogisms, does plausible reasoning instead of deductive reasoning.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

a mathematical model reproduces a part of common sense by prescribing a definite set of operations, this shows us how to ‘build a machine’, (i.e. write a computer program) which operates on incomplete information and, by applying quantitative versions of the above weak syllogisms, does plausible reasoning instead of deductive reasoning.

Tags

#jaynes #plausible-reasoning

Question

[...] reproduces a part of common sense by prescribing a definite set of operations

Answer

a mathematical model

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

a mathematical model reproduces a part of common sense by prescribing a definite set of operations

Tags

#jaynes #plausible-reasoning

Question

a mathematical model reproduces [...] by prescribing a definite set of operations

Answer

a part of common sense

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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

a mathematical model reproduces a part of common sense by prescribing a definite set of operations

Tags

#jaynes #plausible-reasoning

Question

a mathematical model reproduces a part of common sense by prescribing [...]

Answer

a definite set of operations

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

a mathematical model reproduces a part of common sense by prescribing a definite set of operations

Tags

#jaynes #plausible-reasoning

Question

A model operates on [...how much...] information

Answer

incomplete

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

A model operates on incomplete information and, by applying quantitative versions of the above weak syllogisms, does plausible reasoning instead of deductive reasoning.

Tags

#jaynes #plausible-reasoning

Question

A model does [...] instead of deductive reasoning.

Answer

plausible reasoning

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

A model operates on incomplete information and, by applying quantitative versions of the above weak syllogisms, does plausible reasoning instead of deductive reasoning.

Tags

#jaynes #plausible-reasoning

Question

A model does plausible reasoning by applying [...]

Answer

quantitative versions of the weak syllogisms

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

A model operates on incomplete information and, by applying quantitative versions of the above weak syllogisms, does plausible reasoning instead of deductive reasoning.

Tags

#jaynes #plausible-reasoning

Question

Our unaided common sense can decide between [...] but not **[...]**

Answer

a few distinctive hypotheses, many similar ones

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Our unaided common sense can decide between a few distinctive hypotheses, but not many similar ones.

smart contract

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saustiva panoramica su potenzialità, limiti e situazione attuale della tecnologia, e approfondimenti mirati su utilizzi specifici quali disintermediazione dei processi di autenticazione, autorizzazione e audit, token, transazioni multi-firma, <span>smart contract. Questi ultimi, rappresentano un’enorme risorsa per il futuro, andando a rafforzare o addirittura a sostituire il sistema dei contratti tradizionali, con un abbattimento dei costi, de

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Questi ultimi, rappresentano un’enorme risorsa per il futuro, andando a rafforzare o addirittura a sostituire il sistema dei contratti tradizionali, con un abbattimento dei costi, dei tempi e dei rischi di inadempienza. Punto di forza degli <span>smart contract è il fatto che sono eseguiti automaticamente, senza bisogno di intermediari e, allo stesso tempo, proprio per il meccanismo di verifica reciproca dei blocchi, possono consentire anche a soggetti che non si conoscono e non si fidano reciprocamente di interagire e concludere una transazione. Il secondo giorno si è stato chiesto agli attori di proporre possibili servizi, disposizioni di legge o processi amministrativi (in ambito Pubblica Amministrazione) per le quali l’app

token sociale (riconoscere, tracciare e incentivare l’impegno civile)

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12 possibili progetti oggetto di studio e per ognuno di essi sono stati analizzati punti di forza, debolezze, rischi e opportunitá. Fra quelli che hanno ottenuto più consensi, l’utilizzo della blockchain per identità digitale multilivello, <span>token sociale (riconoscere, tracciare e incentivare l’impegno civile), sovranità e riconducibilità del dato, E-procurement (gestione gare, tracciabilità degli acquisti PA, registro fornitori trasparente) e tracciabilità e conservazione delle ricevute tele

E-procurement

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, rischi e opportunitá. Fra quelli che hanno ottenuto più consensi, l’utilizzo della blockchain per identità digitale multilivello, token sociale (riconoscere, tracciare e incentivare l’impegno civile), sovranità e riconducibilità del dato, <span>E-procurement (gestione gare, tracciabilità degli acquisti PA, registro fornitori trasparente) e tracciabilità e conservazione delle ricevute telematiche Pago PA. Una delle riflessioni più interess

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i innovazione, ossia non solamente mettere in pratica l’utilizzo della tecnologia nella Pubblica Amministrazione, ma anche far sì che il territorio diventi attrattivo e luogo privilegiato per aziende e start-up che utilizzano la blockchain. <span>Prossima tappa: la creazione di un osservatorio sulla blockchain e una call for action sulle aziende. TAGS featured Condividi Facebook Twitter Articolo precedenteLa Nuova Zelanda vieta le trivellazioni offshore Prossimo articoloSensazione di tatto sul braccio d

Il 15 dicembre 2017 al fine di accrescere e divulgare sul territorio la conoscenza della Blockchain, Città di Torino, Università degli Studi di Torino e Nesta Italia, in collaborazione con numerosi altri partner, hanno organizzato “Blockchain for Social Good”, primo evento in Italia sulla blockchain e le sue applicazioni in ambito non finanziario, a cui hanno partecipato relatori nazionali e internazionali provenienti da pubblica amministrazione, mondo universitario, imprese private, no-profit ed enti di ricerca.

Nell’occasione è stato lanciato un premio di 5 milioni di euro promosso dalla Commissione Europea, un concorso aperto a privati, enti giuridici e organizzazioni internazionali per sviluppare soluzioni innovative, efficienti e ad alto impatto sociale utilizzando la tecnologia della blockchain.

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condono uno o più informatici, pubblicò il protocollo Bitcoin. Nata come infrastruttura per gli scambi in criptovalute, solo in un secondo momento il suo utilizzo è stato allargato come impianto su cui eseguire altri tipi di applicazione. <span>Il 15 dicembre 2017 al fine di accrescere e divulgare sul territorio la conoscenza della Blockchain, Città di Torino, Università degli Studi di Torino e Nesta Italia, in collaborazione con numerosi altri partner, hanno organizzato “Blockchain for Social Good”, primo evento in Italia sulla blockchain e le sue applicazioni in ambito non finanziario, a cui hanno partecipato relatori nazionali e internazionali provenienti da pubblica amministrazione, mondo universitario, imprese private, no-profit ed enti di ricerca. Nell’occasione è stato lanciato un premio di 5 milioni di euro promosso dalla Commissione Europea, un concorso aperto a privati, enti giuridici e organizzazioni internazionali per sviluppare soluzioni innovative, efficienti e ad alto impatto sociale utilizzando la tecnologia della blockchain. I primi progetti in cui è stata avviata un’applicazione sperimentale di blockchain nella nostra città sono CRIO (Strumenti per la Lotta al Cyberbullismo sui social network nell’ambit