Importance Sampling Squared for Bayesian Inference in Latent Variable Models

By Minh-Ngoc Tran, Marcel Scharth, Michael K. Pitt, Robert Kohn. 2013

57 citations recorded by the source corpus.

We consider Bayesian inference by importance sampling when the likelihood is analytically intractable but can be unbiasedly estimated. We refer to this procedure as importance sampling squared (IS2), as we can often estimate the likelihood itself by importance sampling. We provide a formal justification for importance sampling when working with an estimate of the likelihood and study its convergence properties. We analyze the effect of estimating the likelihood on the resulting inference and provide guidelines on how to set up the precision of the likelihood estimate in order to obtain an optimal tradeoff between computational cost and accuracy for posterior inference on the model parameters. We illustrate the procedure in empirical applications for a generalized multinomial logit model and a stochastic volatility model. The results show that the IS2 method can lead to fast and accurate posterior inference under the optimal implementation.

Subfields: Finance, Statistics and Probability

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Citations in the corpus

Kernel Sequential Monte Carlo (2015, background): “…kernel then Set X t to end if end for return X 1 , . . . , X T and W 1 , . . . , W T KSMC framework is particularly useful in combination with importance sampling frameworks such as SMC 2 [5] and IS 2 [23] for sampling from doubly intractable targets, where gradient information is unavailable.”
Nested Sequential Monte Carlo Methods (2015, methodology): “RELATION TO IS Here we will show how IS, proposed by Tran et al. (2013), can be viewed as a special case of Nested SIS.”