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Markov Chain Monte Carlo

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.003.0007
Subject:
Biology, Ecology

This chapter explains how to implement Bayesian analyses using the Markov chain Monte Carlo (MCMC) algorithm, a set of methods for Bayesian analysis made popular by the seminal paper of Gelfand and ... More


Inference from a Single Model

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.003.0008
Subject:
Biology, Ecology

This chapter shows how to make inferences using MCMC samples. Here, the process of inference begins on the assumption that a single model is being analyzed. The objective is to estimate parameters, ... More


Hierarchical Bayesian Models

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.003.0006
Subject:
Biology, Ecology

This chapter seeks to explain hierarchical models and how they differ from simple Bayesian models and to illustrate building hierarchical models using mathematically correct expressions. It begins ... More


Inference from Multiple Models

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.003.0009
Subject:
Biology, Ecology

This chapter describes how to evaluate alternative models with data. There are two broad ways to formally use multiple models: model selection and model averaging. In model selection, models are ... More


Solutions

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.003.0012
Subject:
Biology, Ecology

This chapter provides solutions to the problems presented in the preceding chapter. It presents the diagrams for each problem as well as some explanations on how the solutions are arrived at. As has ... More


Metropolis-Hastings Algorithms for DSGE Models

Edward P. Herbst and Frank Schorfheide

in Bayesian Estimation of DSGE Models

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691161082
eISBN:
9781400873739
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161082.003.0004
Subject:
Economics and Finance, Econometrics

This chapter talks about the most widely used method to generate draws from posterior distributions of a DSGE model: the random walk MH (RWMH) algorithm. The DSGE model likelihood function in ... More


A Crash Course in Bayesian Inference

Edward P. Herbst and Frank Schorfheide

in Bayesian Estimation of DSGE Models

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691161082
eISBN:
9781400873739
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161082.003.0003
Subject:
Economics and Finance, Econometrics

This chapter provides a self-contained review of Bayesian inference and decision making. It begins with a discussion of Bayesian inference for a simple autoregressive (AR) model, which takes the form ... More


Trends and Breaking Points of the Bayesian Econometric Literature

Luc Bauwens and Michel Lubrano

in Economics Beyond the Millennium

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198292111
eISBN:
9780191596537
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198292112.003.0016
Subject:
Economics and Finance, Macro- and Monetary Economics, Microeconomics

The authors recall the basic differences of view between classical and Bayesian analysis and note that the dispute among statisticians has not been exactly reflected in econometrics. Starting with a ... More


Problems

N. Thompson Hobbs and Mevin B. Hooten

in Bayesian Models: A Statistical Primer for Ecologists

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691159287
eISBN:
9781400866557
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159287.003.0011
Subject:
Biology, Ecology

This chapter provides a set of structured problems to hone the reader's skills in model building. Each problem requires the reader to draw a Bayesian network and write the posterior and joint ... More


Bayesian estimation and inference

M. D. Edge

in Statistical Thinking from Scratch: A Primer for Scientists

Published in print:
2019
Published Online:
October 2019
ISBN:
9780198827627
eISBN:
9780191866463
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198827627.003.0012
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

Bayesian methods allow researchers to combine precise descriptions of prior beliefs with new data in a principled way. The main object of interest in Bayesian statistics is the posterior ... More


The Survivor Problem: Simple Linear Regression with MCMC

Therese M. Donovan and Ruth M. Mickey

in Bayesian Statistics for Beginners: a step-by-step approach

Published in print:
2019
Published Online:
July 2019
ISBN:
9780198841296
eISBN:
9780191876820
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198841296.003.0017
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

While one of the most common uses of Bayes’ Theorem is in the statistical analysis of a dataset (i.e., statistical modeling), this chapter examines another application of Gibbs sampling: parameter ... More


Finite Mixture Examples; MAPIS Details

Russell Cheng

in Non-Standard Parametric Statistical Inference

Published in print:
2017
Published Online:
September 2017
ISBN:
9780198505044
eISBN:
9780191746390
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198505044.003.0018
Subject:
Mathematics, Probability / Statistics

Two detailed numerical examples are given in this chapter illustrating and comparing mainly the reversible jump Markov chain Monte Carlo (RJMCMC) and the maximum a posteriori/importance sampling ... More


The Author Problem: Bayesian Inference with Two Hypotheses

Therese M. Donovan and Ruth M. Mickey

in Bayesian Statistics for Beginners: a step-by-step approach

Published in print:
2019
Published Online:
July 2019
ISBN:
9780198841296
eISBN:
9780191876820
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198841296.003.0005
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

The “Author Problem” provides a concrete example of Bayesian inference. This chapter draws on work by Frederick Mosteller and David Wallace, who used Bayesian inference to assign authorship for ... More


Bayesian Statistics for Beginners: a step-by-step approach

Therese Donovan and Ruth M. Mickey

Published in print:
2019
Published Online:
July 2019
ISBN:
9780198841296
eISBN:
9780191876820
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198841296.001.0001
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

Bayesian Statistics for Beginners is an entry-level book on Bayesian statistics. It is like no other math book you’ve read. It is written for readers who do not have advanced degrees in mathematics ... More


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