*Griffin Jim E and Stephens David A*

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199695607
- eISBN:
- 9780191744167
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199695607.003.0007
- Subject:
- Mathematics, Probability / Statistics

This chapter traces some of the key developments that further developed the underpinning theory and potential applications of Markov chain Monte Carlo (MCMC) since the mid 1990s. In particular, it ...
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This chapter traces some of the key developments that further developed the underpinning theory and potential applications of Markov chain Monte Carlo (MCMC) since the mid 1990s. In particular, it reviews three main developments: reversible jump or transdimensional MCMC, population MCMC methods, and adaptive MCMC.Less

This chapter traces some of the key developments that further developed the underpinning theory and potential applications of Markov chain Monte Carlo (MCMC) since the mid 1990s. In particular, it reviews three main developments: reversible jump or transdimensional MCMC, population MCMC methods, and adaptive MCMC.

*Chib Siddhartha*

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199695607
- eISBN:
- 9780191744167
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199695607.003.0006
- Subject:
- Mathematics, Probability / Statistics

This chapter provides a brief summary of Markov chain Monte Carlo (MCMC) methods. The chapter is organized as follows. Section 6.2 describes the Metropolis–Hastings algorithm and its generalized ...
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This chapter provides a brief summary of Markov chain Monte Carlo (MCMC) methods. The chapter is organized as follows. Section 6.2 describes the Metropolis–Hastings algorithm and its generalized version. Section 6.3 considers the Gibbs sampling algorithm while additional topics of importance, such as sampling with latent data and calculation of the marginal likelihood, are discussed in Section 6.4. Section 6.5 has concluding remarks.Less

This chapter provides a brief summary of Markov chain Monte Carlo (MCMC) methods. The chapter is organized as follows. Section 6.2 describes the Metropolis–Hastings algorithm and its generalized version. Section 6.3 considers the Gibbs sampling algorithm while additional topics of importance, such as sampling with latent data and calculation of the marginal likelihood, are discussed in Section 6.4. Section 6.5 has concluding remarks.

*Edward P. Herbst and Frank Schorfheide*

- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691161082
- eISBN:
- 9781400873739
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161082.003.0009
- Subject:
- Economics and Finance, Econometrics

This chapter argues that in order to conduct Bayesian inference, the approximate likelihood function has to be embedded into a posterior sampler. It begins by combining the particle filtering methods ...
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This chapter argues that in order to conduct Bayesian inference, the approximate likelihood function has to be embedded into a posterior sampler. It begins by combining the particle filtering methods with the MCMC methods, replacing the actual likelihood functions that appear in the formula for the acceptance probability in Algorithm 5 with particle filter approximations. The chapter refers to the resulting algorithm as PFMH algorithm. It is a special case of a larger class of algorithms called particle Markov chain Monte Carlo (PMCMC). The theoretical properties of PMCMC methods were established in Andrieu, Doucet, and Holenstein (2010). Applications of PFMH algorithms in other areas of econometrics are discussed in Flury and Shephard (2011).Less

This chapter argues that in order to conduct Bayesian inference, the approximate likelihood function has to be embedded into a posterior sampler. It begins by combining the particle filtering methods with the MCMC methods, replacing the actual likelihood functions that appear in the formula for the acceptance probability in Algorithm 5 with particle filter approximations. The chapter refers to the resulting algorithm as PFMH algorithm. It is a special case of a larger class of algorithms called particle Markov chain Monte Carlo (PMCMC). The theoretical properties of PMCMC methods were established in Andrieu, Doucet, and Holenstein (2010). Applications of PFMH algorithms in other areas of econometrics are discussed in Flury and Shephard (2011).