Improvement and comparison of likelihood functions for model calibration and parameter uncertainty analysis within a Markov chain Monte Carlo scheme

2014 ◽  
Vol 519 ◽  
pp. 2202-2214 ◽  
Author(s):  
Qin-Bo Cheng ◽  
Xi Chen ◽  
Chong-Yu Xu ◽  
Christian Reinhardt-Imjela ◽  
Achim Schulte
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Uncertainty Analysis ◽  
Parameter Uncertainty ◽  
Model Calibration ◽  
Likelihood Functions ◽  
Parameter Uncertainty Analysis

Combining Particle Filters with MH Samplers

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Particle Filtering ◽  
Likelihood Function ◽  
Mcmc Methods ◽  
Acceptance Probability ◽  
Likelihood Functions ◽  
Approximate Likelihood ◽  
Special Case

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).

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