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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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