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Overview page. Subjects: Architecture.

[Ge]

Structural division in the length of a building or roof. The unit within a building between a pair of piers or buttresses; the division of a roof marked by its main trusses.

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Bayes's theorem

in A Dictionary of Statistics

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Probability and Statistics. 182 words.

A simple form of Bayes's theorem is P(A|B)=P(A)P(

Bayes’ Theorem

in Bayesian Statistics for Beginners

May 2019; p ublished online July 2019 .

Chapter. Subjects: Biomathematics and Statistics. 2622 words.

This chapter focuses on Bayes’ Theorem. The chapter first gives a brief introduction to Thomas Bayes, who first formulated the theorem. It then builds on the content presented in Chapters 1...

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Bayes factor

Overview page. Subjects: Probability and Statistics.

A measure of the evidence provided by the data, D, in favour of model M 1 as opposed to model M 2. The Bayes factor is B, given by . The value of B may be assessed...

Bayes theorem

Overview page. Subjects: Mathematics — Psychology.

A simple form of Bayes's theorem is , where A′ denotes the complementary event (see sample space) to the event A. For example, suppose a man has two coins in his pocket. One is unbiased,...

Bayes linear kinematics and Bayes linear Bayes graphical models

in Biometrika

June 2004; p ublished online June 2004 .

Journal Article. Subjects: Probability and Statistics. 0 words.

Probability kinematics (Jeffrey, 1965, 1983) furnishes a method for revising a prior probability specification based upon new probabilities over a partition. We develop a corresponding Bayes...

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Bayes’s theorem

in A Dictionary of Statistics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Probability and Statistics. 92 words.

A simple form of Bayes’s theorem iswhere A′ denotes the complementary event (see sample space) to the event ...

Empirical Bayes Gibbs sampling

in Biostatistics

December 2001; p ublished online December 2001 .

Journal Article. Subjects: Probability and Statistics. 0 words.

The wide applicability of Gibbs sampling has increased the use of more complex and multi‐level hierarchical models. To use these models entails dealing with hyperparameters in the deeper...

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Bayes and empirical Bayes: do they merge?

in Biometrika

June 2014; p ublished online April 2014 .

Journal Article. Subjects: Biomathematics and Statistics; Probability and Statistics. 0 words.

Bayesian inference is attractive due to its internal coherence and for often having good frequentist properties. However, eliciting an honest prior may be difficult, and common practice is...

Influence functions and robust Bayes and empirical Bayes small area estimation

in Biometrika

September 2008; p ublished online September 2008 .

Journal Article. Subjects: Probability and Statistics. 0 words.

We introduce new robust small area estimation procedures based on area-level models. We first find influence functions corresponding to each individual area-level observation by measuring...

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Flexible Bayes regression of epidemiologic data

in The Oxford Handbook of Applied Bayesian Analysis

October 2013; p ublished online August 2018 .

Article. Subjects: Mathematics. 9002 words.

This article focuses on flexible Bayes regression of epidemiologic data involving pregnancy outcomes. It first provides an overview of finite mixture models and nonparametric Bayes methods...

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Bayes, Reverend Thomas (1701–61)

in A Dictionary of Statistics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Probability and Statistics. 90 words.

Nonconformist minister in Tunbridge Wells, England. Bayes was elected FRS in 1742. The eponymous theorem has led to the development of an approach to Statistics that runs parallel to the...

Calibration and empirical Bayes variable selection

in Biometrika

December 2000; p ublished online December 2000 .

Journal Article. Subjects: Probability and Statistics. 0 words.

For the problem of variable selection for the normal linear model, selection criteria such as aic, Cp , bic and ric have fixed dimensionality penalties. Such criteria are shown...

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Miscellanea. Bayes factors for Fieller's problem

in Biometrika

September 2000; p ublished online September 2000 .

Journal Article. Subjects: Probability and Statistics. 0 words.

This paper considers point null hypothesis testing when the sampling distribution belongs to a particular class, defined in Gleser & Hwang (1987). We discuss the drawbacks of frequentist and...

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Nonparametric Bayes modelling of count processes

in Biometrika

December 2013; p ublished online October 2013 .

Journal Article. Subjects: Probability and Statistics. 0 words.

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent...

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Nonparametric Bayes inference on conditional independence

in Biometrika

March 2016; p ublished online January 2016 .

Journal Article. Subjects: Biomathematics and Statistics; Probability and Statistics. 6773 words.

In many application areas, a primary focus is on assessing evidence in the data refuting the assumption of independence of [math] and [math] conditionally on [math], with [math] response...

Objective Bayes and conditional inference in exponential families

in Biometrika

June 2010; p ublished online April 2010 .

Journal Article. Subjects: Probability and Statistics. 0 words.

Objective Bayes methodology is considered for conditional frequentist inference about a canonical parameter in a multi-parameter exponential family. A condition is derived under which...

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Empirical Bayes estimation for additive hazards regression models

in Biometrika

September 2009; p ublished online June 2009 .

Journal Article. Subjects: Probability and Statistics. 0 words.

We develop a novel empirical Bayesian framework for the semiparametric additive hazards regression model. The integrated likelihood, obtained by integration over the unknown prior of the...

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A family of Bayes multiple testing procedures

in Biometrika

June 2008; p ublished online June 2008 .

Journal Article. Subjects: Probability and Statistics. 0 words.

Under the model of independent test statistics, we propose a two-parameter family of Bayes multiple testing procedures. The two parameters can be viewed as tuning parameters. Using the...

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Thomas Bayes

Overview page. Subjects: Mathematics.

(1702–61)

English mathematician remembered for his work in probability, which led to a method of statistical inference based on the theorem that bears his name. His paper on the...

Bayes, Thomas (1701?–1761), mathematician and Presbyterian minister

in Oxford Dictionary of National Biography

September 2004; p ublished online September 2004 .

Reference Entry. Subjects: Mathematics; Protestantism and Protestant Churches. 850 words.

Bayes, Thomas (1701?–1761), mathematician and Presbyterian minister, was probably born in Hertfordshire, the eldest in the family of four sons and three daughters of the Revd Joshua Bayes...