Title | Inflated Density Ratio and Its Variation and Generalization for Computing Marginal Likelihoods. |
Publication Type | Journal Article |
Year of Publication | 2020 |
Authors | Wang, Yu-Bo, Ming-Hui Chen, Wei Shi, Paul Lewis, and Lynn Kuo |
Journal | J Korean Stat Soc |
Volume | 49 |
Issue | 1 |
Pagination | 244-263 |
Date Published | 2020 Mar |
ISSN | 1226-3192 |
Abstract | In the Bayesian framework, the marginal likelihood plays an important role in variable selection and model comparison. The marginal likelihood is the marginal density of the data after integrating out the parameters over the parameter space. However, this quantity is often analytically intractable due to the complexity of the model. In this paper, we first examine the properties of the inflated density ratio (IDR) method, which is a Monte Carlo method for computing the marginal likelihood using a single MC or Markov chain Monte Carlo (MCMC) sample. We then develop a variation of the IDR estimator, called the dimension reduced inflated density ratio (Dr.IDR) estimator. We further propose a more general identity and then obtain a general dimension reduced (GDr) estimator. Simulation studies are conducted to examine empirical performance of the IDR estimator as well as the Dr.IDR and GDr estimators. We further demonstrate the usefulness of the GDr estimator for computing the normalizing constants in a case study on the inequality-constrained analysis of variance. |
DOI | 10.1007/s42952-019-00013-z |
Alternate Journal | J Korean Stat Soc |
Original Publication | Inflated density ratio and its variation and generalization for computing marginal likelihoods. |
PubMed ID | 33071541 |
PubMed Central ID | PMC7560979 |
Grant List | P01 CA142538 / CA / NCI NIH HHS / United States R01 GM070335 / GM / NIGMS NIH HHS / United States |