The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference
This paper presents the R package MitISEM (mixture of t by importance sampling weighted expectation maximization) which provides an automatic and flexible two-stage method to approximate a non-elliptical target density kernel - typically a posterior density kernel - using an adaptive mixture of...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Foundation for Open Access Statistics
2017-07-01
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| Series: | Journal of Statistical Software |
| Subjects: | |
| Online Access: | https://www.jstatsoft.org/index.php/jss/article/view/3200 |
| _version_ | 1819178162887589888 |
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| author | Nalan Baştürk Stefano Grassi Lennart Hoogerheide Anne Opschoor Herman K. van Dijk |
| author_facet | Nalan Baştürk Stefano Grassi Lennart Hoogerheide Anne Opschoor Herman K. van Dijk |
| author_sort | Nalan Baştürk |
| collection | DOAJ |
| description | This paper presents the R package MitISEM (mixture of t by importance sampling weighted expectation maximization) which provides an automatic and flexible two-stage method to approximate a non-elliptical target density kernel - typically a posterior density kernel - using an adaptive mixture of Student t densities as approximating density. In the first stage a mixture of Student t densities is fitted to the target using an expectation maximization algorithm where each step of the optimization procedure is weighted using importance sampling. In the second stage this mixture density is a candidate density for efficient and robust application of importance sampling or the Metropolis-Hastings (MH) method to estimate properties of the target distribution. The package enables Bayesian inference and prediction on model parameters and probabilities, in particular, for models where densities have multi-modal or other non-elliptical shapes like curved ridges. These shapes occur in research topics in several scientific fields. For instance, analysis of DNA data in bio-informatics, obtaining loans in the banking sector by heterogeneous groups in financial economics and analysis of education's effect on earned income in labor economics. The package MitISEM provides also an extended algorithm, 'sequential MitISEM', which substantially decreases computation time when the target density has to be approximated for increasing data samples. This occurs when the posterior or predictive density is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that MH using the candidate density obtained by MitISEM outperforms, in terms of numerical efficiency, MH using a simpler candidate, as well as the Gibbs sampler. The MitISEM approach is also used for Bayesian model comparison using predictive likelihoods. |
| first_indexed | 2024-12-22T21:38:10Z |
| format | Article |
| id | doaj.art-174bec722c8d4a58a5241b4d6b2ae20c |
| institution | Directory Open Access Journal |
| issn | 1548-7660 |
| language | English |
| last_indexed | 2024-12-22T21:38:10Z |
| publishDate | 2017-07-01 |
| publisher | Foundation for Open Access Statistics |
| record_format | Article |
| series | Journal of Statistical Software |
| spelling | doaj.art-174bec722c8d4a58a5241b4d6b2ae20c2022-12-21T18:11:41ZengFoundation for Open Access StatisticsJournal of Statistical Software1548-76602017-07-0179114010.18637/jss.v079.i011125The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian InferenceNalan BaştürkStefano GrassiLennart HoogerheideAnne OpschoorHerman K. van DijkThis paper presents the R package MitISEM (mixture of t by importance sampling weighted expectation maximization) which provides an automatic and flexible two-stage method to approximate a non-elliptical target density kernel - typically a posterior density kernel - using an adaptive mixture of Student t densities as approximating density. In the first stage a mixture of Student t densities is fitted to the target using an expectation maximization algorithm where each step of the optimization procedure is weighted using importance sampling. In the second stage this mixture density is a candidate density for efficient and robust application of importance sampling or the Metropolis-Hastings (MH) method to estimate properties of the target distribution. The package enables Bayesian inference and prediction on model parameters and probabilities, in particular, for models where densities have multi-modal or other non-elliptical shapes like curved ridges. These shapes occur in research topics in several scientific fields. For instance, analysis of DNA data in bio-informatics, obtaining loans in the banking sector by heterogeneous groups in financial economics and analysis of education's effect on earned income in labor economics. The package MitISEM provides also an extended algorithm, 'sequential MitISEM', which substantially decreases computation time when the target density has to be approximated for increasing data samples. This occurs when the posterior or predictive density is updated with new observations and/or when one computes model probabilities using predictive likelihoods. We illustrate the MitISEM algorithm using three canonical statistical and econometric models that are characterized by several types of non-elliptical posterior shapes and that describe well-known data patterns in econometrics and finance. We show that MH using the candidate density obtained by MitISEM outperforms, in terms of numerical efficiency, MH using a simpler candidate, as well as the Gibbs sampler. The MitISEM approach is also used for Bayesian model comparison using predictive likelihoods.https://www.jstatsoft.org/index.php/jss/article/view/3200finite mixturesStudent t densitiesimportance samplingMCMCMetropolis-Hastings algorithmexpectation maximizationBayesian inferenceR software |
| spellingShingle | Nalan Baştürk Stefano Grassi Lennart Hoogerheide Anne Opschoor Herman K. van Dijk The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference Journal of Statistical Software finite mixtures Student t densities importance sampling MCMC Metropolis-Hastings algorithm expectation maximization Bayesian inference R software |
| title | The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference |
| title_full | The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference |
| title_fullStr | The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference |
| title_full_unstemmed | The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference |
| title_short | The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference |
| title_sort | r package mitisem efficient and robust simulation procedures for bayesian inference |
| topic | finite mixtures Student t densities importance sampling MCMC Metropolis-Hastings algorithm expectation maximization Bayesian inference R software |
| url | https://www.jstatsoft.org/index.php/jss/article/view/3200 |
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