on 24-Apr-2018 (Tue)

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.

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 .

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.

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

The primitives of the model are

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

In state space models, finding the state is an art

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

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

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.

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

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

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

The natural way to predict variables is to use conditional distributions

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

语料库的地址是： http：// corpus.byu.edu/coca/

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").

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.).

Aspect expresses how an action, event extends over time.

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

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

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

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

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

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

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.

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.

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

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

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

smart contract

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.

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

E-procurement

Prossima tappa: la creazione di un osservatorio sulla blockchain e una call for action sulle aziende.

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.