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#reading

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#reading

Typically, estimators can be divided into two types called: point estimators and set estimators.

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Typically, estimators can be divided into two types: point estimators and set estimators. A point estimator which maps from the sample space X to a point in the parameter space Θ. A set estimator which maps from X to a set in Θ.

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Question

Answer

Sufficient statistic

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Sufficient statistic: A statistic S = s(X) is sufficient for θ if the conditional distribution of X, given the value of s(X) (and θ), fX|S(x | s, θ), does not depend upon θ.

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Question

Answer

the conditional distribution of *X*, given the value of *s(X)* (and *θ*), *f*_{X|S}(x | s, θ), does not depend upon *θ*.

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Sufficient statistic: A statistic S = s(X) is sufficient for θ if the conditional distribution of X, given the value of s(X) (and θ), fX|S(x | s, θ), does not depend upon θ.

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#reading

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Following Section 2.2(iii) of Cox and Hinkley (1974), we may interpret sufficiency as follows.

- Consider two individuals who both assert the model E = {X, Θ, f
_{X}(x |θ)}. - The first individual observes x directly.
- The second individual also observes x but in a two stage process:
- They first observe a value s(x) of a sufficient statistic S with distribution f
_{S}(s |θ). - They then observe the value x of the random variable X with distribution f
_{X|S}(x |s) which does not depend upon θ.

- They first observe a value s(x) of a sufficient statistic S with distribution f

It may well then be reasonable to argue that, as the final distribution for X for the two individuals are identical, the conclusions drawn from the observation of a given x should be identical for the two individuals. That is, they should make the same inference about θ.

For the second individual, when sampling from f_{X|S}(x |s) they are sampling from a fixed distribution and so, assuming the correctness of the model, only the first stage is informative: all of the knowledge about θ is contained in s(x).

If one takes these two statements together then the inference to be made about θ depends only on the value s(x) and not the individual values x i contained in x.

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The MLE satisfies the invariance property [Theorem 7.2.10, Casella and Berger (2002)] that if is the MLE of θ then for any function g(θ), the MLE of g(θ) is g().

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Hastie and Efron (2016) consider that there are three ages of statistical inference:

- the pre-computer age (essentially the period from 1763 and the publication of Bayes’ rule up until the 1950s),
- the early-computer age (from the 1950s to the 1990s),
- and the current age (a period of computer-dependence with enormously ambitious algorithms and model complexity).

With these developments in mind, it is clear that there exist a hierarchy of statistical models.

- Models where f
_{X}(x |θ) has a known analytic form. - Models where f
_{X}(x |θ) can be evaluated. - Models where we can simulate X from f
_{X}(x |θ).

Between the first case and the second case exist models where f_{X}(x |θ) can be evaluated up to an unknown constant, which may or may not depend upon θ. In the first case, we might be able to derive an analytic expression for θ or to prove that f_{X}(x |θ) has a unique maximum so that any numerical maximisation will converge to θ(x).

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ter is legendary or even fictitious. (93) Scholars continually debate whether such stories should rightly be called "Naru literature" or "fictitious autobiography" but, whichever term one uses, <span>the works purposefully represent themselves as first-person accounts of an event of significance from which an audience is supposed to learn some important information, whether the "truth" of historical events, a religious moral, or simply some lesson which was thought useful to those hearing the tales. The term "Naru literature" comes from "naru", which is explained by scholar Gerdien Jonker: The word naru is used as a name for various objects, originally boundary stones, memorial st

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events, a religious moral, or simply some lesson which was thought useful to those hearing the tales. The term "Naru literature" comes from "naru", which is explained by scholar Gerdien Jonker: <span>The word naru is used as a name for various objects, originally boundary stones, memorial stones and monuments. Two sorts of inscribed objects received the designation naru at the dawn of the second millennium: tablets accompanying presents and tablets used for building inscriptions. At the end of the third millennium the naru chiefly played a part in religious transactions; at the beginning of the second millennium it was to become not only actually but also symbo

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tones and monuments. Two sorts of inscribed objects received the designation naru at the dawn of the second millennium: tablets accompanying presents and tablets used for building inscriptions. <span>At the end of the third millennium the naru chiefly played a part in religious transactions; at the beginning of the second millennium it was to become not only actually but also symbolically the bearer of memory. (90) As the bearers of actual memory, Naru literature carried enormous significance for those who heard the tales, and this was especially true of those stories concerning the great kings of

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count first given out in an effort to win the hearts and minds of the lower-class Sumerian populace Sargon wanted support from in conquering Sumer. Akkadian Ruler by Sumerophile (Public Domain) <span>He presents himself as having been born the illegitimate son of a priestess, set adrift on the Euphrates River soon after his birth, rescued by a gardener and then, through the help of the goddess Inanna, rising to become king of Akkad. At the time Sargon came to power in 2334 BCE, Sumer was a region which had only recently been united under the king of Umma (and later of Uruk), Lugalzagesi and, even then, it was not

#history

Huntington divided the world into the "major civilizations" in his thesis as such: Western civilization, comprising the United States and Canada, Western and Central Europe, Australia, Oceania and most of the Philippines. Whether Latin America and the former member states of the Soviet Union are included, or are instead their own separate civilizations, will be an important future consideration for those regions, according to Huntington. The traditional Western viewpoint identified Western Civilization with the Western Christian (Catholic-Protestant) countries and culture.[12] Latin American. Includes Central America, South America (excluding Guyana, Suriname and French Guiana), Cuba, the Dominican Republic, and Mexico. May be considered a part of Western civilization. Many people in South America and Mexico regard themselves as full members of Western civilization. The Orthodox world of the former Soviet Union, the former Yugoslavia, Bulgaria, Cyprus, Greece and Romania. Countries with a non-Orthodox

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illegitimate son of a priestess, set adrift on the Euphrates River soon after his birth, rescued by a gardener and then, through the help of the goddess Inanna, rising to become king of Akkad. <span>At the time Sargon came to power in 2334 BCE, Sumer was a region which had only recently been united under the king of Umma (and later of Uruk), Lugalzagesi and, even then, it was not a cohesive union. Prior to Lugalzagesi's conquest, Sumerian cities were frequently at war with each other vying for resources such as water and land rights. F

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tween the rich and the poor. The historian Susan Wise Bauer writes on this, commenting: Sargon's relatively speedy conquest of the entire Mesopotamian plain is startling, given the inability of <span>Sumerian kings to control any area much larger than two or three cities [but the Sumerians] were suffering from an increased gap between elite leadership and poor laborers. [The rich] used their combined religious and secular power to claim as much as three-quarters of the land in any given city for themselves. Sargon's relatively easy conquest of the area (not to mention his constant carping on his own non-aristocratic background) may reveal a successful appeal to the downtrodden members of Sumerian society to come over to his side. (99) By presenting himself as a "man of the people" he was able to garner support for his cause and took Sumer with relative ease. Once the south of Mesopotamia was under his control, he wen

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model a random variable X as the triple E = {X, Θ, f_{X}(x |θ)} where only the finite dimensional parameter θ ∈ Θ is unknown

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Parametric model: model a random variable X as the triple E = {X, Θ, fX(x |θ)} where only the finite dimensional parameter θ ∈ Θ is unknown.

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Answer

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Parametric model: model a random variable X as the triple E = {X, Θ, fX(x |θ)} where only the finite dimensional parameter θ ∈ Θ is unknown.

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Question

A [...] is termed an estimator.

Answer

statistic designed to estimate θ

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A statistic designed to estimate θ is termed an estimator.

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Question

A statistic designed to estimate θ is termed an [...].

Answer

estimator

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A statistic designed to estimate θ is termed an estimator.

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Question

Typically, estimators can be divided into two types called: [...].

Answer

point estimators and set estimators

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Typically, estimators can be divided into two types called: point estimators and set estimators.

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Question

if S is sufficient then so is any [...]

Answer

one-to-one function of S

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if S is sufficient then so is any one-to-one function of S

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Question

Answer

Fisher-Neyman Factorization Theorem

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Fisher-Neyman Factorization Theorem: The statistic S = s(X) is sufficient for θ if and only if, for all x and θ, fX(x |θ) = g(s(x), θ)h(x) for some pair of functions g(s(x), θ) and h(x).

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Fisher-Neyman Factorization Theorem: The statistic S = s(X) is sufficient for θ if and only if, for all x and θ, fX(x |θ) = g(s(x), θ)h(x) for some pair of functions g(s(x), θ) and h(x).

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Answer

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The sufficiency principle: If S = s(X) is a sufficient statistic for θ and x and y are two observations such that s(x) = s(y), then the inference about θ should be the same irrespective of whether X = x or Y = y

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Answer

the inference about *θ* should be the same irrespective of whether *X = x* or *Y = y* was observed

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The sufficiency principle: If S = s(X) is a sufficient statistic for θ, and x and y are two observations such that s(x) = s(y), then the inference about θ should be the same irrespective of whether X = x or Y = y was observed.

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Answer

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The sufficiency principle: If S = s(X) is a sufficient statistic for θ, and x and y are two observations such that s(x) = s(y), then the inference about θ should be the same irrespective of whether X = x or Y = y was observed.

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Answer

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The sufficiency principle: If S = s(X) is a sufficient statistic for θ, and x and y are two observations such that s(x) = s(y), then the inference about θ should be the same irrespective of whether X = x or Y = y was observed.

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Question

Intuitively, the [...] is a reasonable choice for an estimator: it’s the value of θ which makes the observed sample most likely

Answer

MLE

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Intuitively, the MLE is a reasonable choice for an estimator: it’s the value of θ which makes the observed sample most likely

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Question

Intuitively, the MLE is a reasonable choice for an estimator: it’s the value of θ which makes [...]

Answer

the observed sample most likely

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Intuitively, the MLE is a reasonable choice for an estimator: it’s the value of θ which makes the observed sample most likely

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Question

The MLE satisfies the invariance property [Theorem 7.2.10, Casella and Berger (2002)] that if is the MLE of θ then [...].

Answer

for any function g(θ), the MLE of g(θ) is g(\({\boldsymbol {\hat {\theta }}}\))

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The MLE satisfies the invariance property [Theorem 7.2.10, Casella and Berger (2002)] that if is the MLE of θ then for any function g(θ), the MLE of g(θ) is g().

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Question

The MLE satisfies the [...] that if is the MLE of θ then for any function g(θ), the MLE of g(θ) is g().

Answer

invariance property [Theorem 7.2.10, Casella and Berger (2002)]

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The MLE satisfies the invariance property [Theorem 7.2.10, Casella and Berger (2002)] that if is the MLE of θ then for any function g(θ), the MLE of g(θ) is g().

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Question

The assessment of whether T is a good estimator is made not for the observed data x but [...]

Answer

based on the distributional properties of X

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The assessment of whether T is a good estimator is made not for the observed data x but based on the distributional properties of X

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the uncertainty surrounding assumptions about the distributions of the latent and infectious periods should be incorporated into quantitative predictions made from epidemiological models, especially since this may well be greater than any uncertainty that arises from noise in the data

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Question

In the case of count data, [...] which means the PIT is no longer uniform under the hypothesis of an ideal forecast

Answer

the predictive distribution is discrete

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In the case of count data, the predictive distribution is discrete which means the PIT is no longer uniform under the hypothesis of an ideal forecast

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Question

In the case of count data, the predictive distribution is discrete which means the PIT [...] under the hypothesis of an ideal forecast

Answer

is no longer uniform

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In the case of count data, the predictive distribution is discrete which means the PIT is no longer uniform under the hypothesis of an ideal forecast

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reasing dimensionality of the target distribution, however, the weights degenerate: a small number of particles are assigned relatively large weights and most of the particles have weight zero. <span>To overcome weight degeneracy, resampling steps can be inserted in order to rejuvenate the sequential sample <span>

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With increasing dimensionality of the target distribution, however, the weights degenerate: a small number of particles are assigned relatively large weights and most of the particles have weight zero. To overcome weight degeneracy, resampling steps can be inserted in order to rejuvenate the sequential sample

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Question

SMC [...]: a small number of particles are assigned relatively large weights and most of the particles have weight zero

Answer

weight degeneration

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SMC weight degeneration: a small number of particles are assigned relatively large weights and most of the particles have weight zero

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Question

SMC weight degeneration: [...]

Answer

a small number of particles are assigned relatively large weights and most of the particles have weight zero

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SMC weight degeneration: a small number of particles are assigned relatively large weights and most of the particles have weight zero

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#2018_Adalja_etal_pandemic_potential_pathogens #reading

Question

Attributes likely to be essential components of any GCBR-level pathogen include:

- [...] human-to-human transmissibility,
- an appreciable case fatality rate,
- the absence of an effective or widely available medical countermeasure,
- an immunologically naïve population,
- virulence factors enabling immune system evasion, and
- respiratory mode of spread.

Additionally, the ability to transmit during incubation periods and/or the occurrence of mild illnesses would further augment spread.

Answer

efficient

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Attributes likely to be essential components of any GCBR-level pathogen include: efficient human-to-human transmissibility, an appreciable case fatality rate, the absence of an effective or widely available medical countermeasure, an immunologically naïve population, virulenc

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Question

Attributes likely to be essential components of any GCBR-level pathogen include:

- efficient human-to-human transmissibility,
- [...] case fatality rate,
- the absence of an effective or widely available medical countermeasure,
- an immunologically naïve population,
- virulence factors enabling immune system evasion, and
- respiratory mode of spread.

Additionally, the ability to transmit during incubation periods and/or the occurrence of mild illnesses would further augment spread.

Answer

an appreciable

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Attributes likely to be essential components of any GCBR-level pathogen include: efficient human-to-human transmissibility, an appreciable case fatality rate, the absence of an effective or widely available medical countermeasure, an immunologically naïve population, virulence factors enabling immune system evasion, and re

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Question

Attributes likely to be essential components of any GCBR-level pathogen include:

- efficient human-to-human transmissibility,
- an appreciable case fatality rate,
- [...] medical countermeasure,
- an immunologically naïve population,
- virulence factors enabling immune system evasion, and
- respiratory mode of spread.

Additionally, the ability to transmit during incubation periods and/or the occurrence of mild illnesses would further augment spread.

Answer

the absence of an effective or widely available

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Attributes likely to be essential components of any GCBR-level pathogen include: efficient human-to-human transmissibility, an appreciable case fatality rate, the absence of an effective or widely available medical countermeasure, an immunologically naïve population, virulence factors enabling immune system evasion, and respiratory mode of spread. Additionally, the ability to transmit duri

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Question

Attributes likely to be essential components of any GCBR-level pathogen include:

- efficient human-to-human transmissibility,
- an appreciable case fatality rate,
- the absence of an effective or widely available medical countermeasure,
- an immunologically [...],
- virulence factors enabling immune system evasion, and
- respiratory mode of spread.

Answer

naïve population

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-level pathogen include: efficient human-to-human transmissibility, an appreciable case fatality rate, the absence of an effective or widely available medical countermeasure, an immunologically <span>naïve population, virulence factors enabling immune system evasion, and respiratory mode of spread. Additionally, the ability to transmit during incubation periods and/or the occurrence of mild illnesse

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Question

Attributes likely to be essential components of any GCBR-level pathogen include:

- efficient human-to-human transmissibility,
- an appreciable case fatality rate,
- the absence of an effective or widely available medical countermeasure,
- an immunologically naïve population,
- virulence factors enabling [...], and
- respiratory mode of spread.

Answer

immune system evasion

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uman transmissibility, an appreciable case fatality rate, the absence of an effective or widely available medical countermeasure, an immunologically naïve population, virulence factors enabling <span>immune system evasion, and respiratory mode of spread. Additionally, the ability to transmit during incubation periods and/or the occurrence of mild illnesses would further augment spread. <span>

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Question

Attributes likely to be essential components of any GCBR-level pathogen include:

- efficient human-to-human transmissibility,
- an appreciable case fatality rate,
- the absence of an effective or widely available medical countermeasure,
- an immunologically naïve population,
- virulence factors enabling immune system evasion, and
- [...] mode of spread.

Answer

respiratory

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ppreciable case fatality rate, the absence of an effective or widely available medical countermeasure, an immunologically naïve population, virulence factors enabling immune system evasion, and <span>respiratory mode of spread. Additionally, the ability to transmit during incubation periods and/or the occurrence of mild illnesses would further augment spread. <span>

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Question

Attributes likely to be essential components of any GCBR-level pathogen include:

- efficient human-to-human transmissibility,
- an appreciable case fatality rate,
- the absence of an effective or widely available medical countermeasure,
- an immunologically naïve population,
- virulence factors enabling immune system evasion, and
- respiratory mode of spread.

Additionally, the ability to transmit during [...] periods and/or the occurrence of mild illnesses would further augment spread.

Answer

incubation

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lable medical countermeasure, an immunologically naïve population, virulence factors enabling immune system evasion, and respiratory mode of spread. Additionally, the ability to transmit during <span>incubation periods and/or the occurrence of mild illnesses would further augment spread. <span>

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Tags

#2018_Adalja_etal_pandemic_potential_pathogens #reading

Question

Attributes likely to be essential components of any GCBR-level pathogen include:

- efficient human-to-human transmissibility,
- an appreciable case fatality rate,
- the absence of an effective or widely available medical countermeasure,
- an immunologically naïve population,
- virulence factors enabling immune system evasion, and
- respiratory mode of spread.

Additionally, the ability to transmit during incubation periods and/or [...] would further augment spread.

Answer

the occurrence of mild illnesses

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re, an immunologically naïve population, virulence factors enabling immune system evasion, and respiratory mode of spread. Additionally, the ability to transmit during incubation periods and/or <span>the occurrence of mild illnesses would further augment spread. <span>

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Question

ILI is a medical diagnosis of possible influenza with a set of common symptoms: [...] and measured or reported fever >38˚C, with onset within the last 10 days [21]

Answer

cough

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ILI is a medical diagnosis of possible influenza with a set of common symptoms: cough and measured or reported fever >38˚C, with onset within the last 10 days [21]

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Question

ILI is a medical diagnosis of possible influenza with a set of common symptoms: cough and [...], with onset within the last 10 days [21]

Answer

measured or reported fever >38˚C

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

scheduled repetition interval | last repetition or drill |

ILI is a medical diagnosis of possible influenza with a set of common symptoms: cough and measured or reported fever >38˚C, with onset within the last 10 days [21]

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ILI is a medical diagnosis of possible influenza

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ILI is a medical diagnosis of possible influenza with a set of common symptoms: cough and measured or reported fever >38˚C, with onset within the last 10 days [21]

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Question

ILI is a medical diagnosis of possible influenza with a set of common symptoms: cough and measured or reported fever >38˚C, with onset [...] [21]

Answer

within the last 10 days

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ILI is a medical diagnosis of possible influenza with a set of common symptoms: cough and measured or reported fever >38˚C, with onset within the last 10 days [21]

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Early in any outbreak, estimates of the case-fatality ratio can suffer from imprecise information on both the numerator (if not all deaths due to the infection are identified as such; for example, because health services are overwhelmed caring for the sick) and the denominator (if cases are not reported or, conversely, noncases get reported as cases if they are not laboratory-confirmed).

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rom imprecise information on both the numerator (if not all deaths due to the infection are identified as such; for example, because health services are overwhelmed caring for the sick) and the <span>denominator (if cases are not reported or, conversely, noncases get reported as cases if they are not laboratory-confirmed). <span>

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Early in any outbreak, estimates of the case-fatality ratio can suffer from imprecise information on both the numerator (if not all deaths due to the infection are identified as such; for example, because health services are overwhelmed caring for the sick) and the denominator (if cases are not reported or, conversely, noncases get reported as cases if they are not laboratory-confirmed).

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Question

[...] refers to the concentration of the predictive distributions, and is a property of the forecasts only

Answer

Sharpness

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Sharpness refers to the concentration of the predictive distributions, and is a property of the forecasts only

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Question

Sharpness refers to the [...], and is a property of the forecasts only

Answer

concentration of the predictive distributions

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Sharpness refers to the concentration of the predictive distributions, and is a property of the forecasts only

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Question

Sharpness refers to the concentration of the predictive distributions, and is a property of [...]

Answer

the forecasts only

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Sharpness refers to the concentration of the predictive distributions, and is a property of the forecasts only

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imates of R0 from the exponentially distributed and gamma-distributed ﬁts reiterate the importance of accurately determining the precise distributions of latent and infectious periods. Although <span>the data required for such a task are often available from post hoc analyses of epidemics they are certainly lacking for a novel emerging infection. Instead, the uncertainty surrounding assumptions about the distributions should be incorporated into quantitative predictions made from epidemiological models, especially since this ma

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Question

Multiple agents infecting the same host individual have been shown to influence each other by [...], thereby influencing the population dynamics of these agents in ways that we have yet to explore and understand (34, 35)

Answer

increasing or decreasing susceptibility and/or infectivity of that individual

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Multiple agents infecting the same host individual have been shown to influence each other by increasing or decreasing susceptibility and/or infectivity of that individual, thereby influencing the population dynamics of these agents in ways that we have yet to explore and understand (34, 35)

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us period has no qualitative effects on the asymptotic values or properties of the system [21,24], though perturbations to the endemic equilibrium take longer to die out as n increases [22,26]. <span>When contact rates vary seasonally, for example, to mimic the aggregation of children in schools [28,29], changes in p(t) are known to have important consequences for the persistence likelihood of infections [25,26,30]. An issue that has received surprisingly little attention, despite its obvious applicability to emerging infections and possible ‘‘ deliberate exposure,’’ is the inﬂuence of latent and i