| Item type: | Article | ||||
|---|---|---|---|---|---|
| Journal or Publication Title: | Comp. Stats. & Data An. | ||||
| Publisher: | ELSEVIER SCIENCE BV | ||||
| Place of Publication: | AMSTERDAM | ||||
| Volume: | 72 | ||||
| Page Range: | pp. 252-272 | ||||
| Date: | 2014 | ||||
| Institutions: | Medicine > Institut für Funktionelle Genomik > Lehrstuhl für Statistische Bioinformatik (Prof. Spang) Informatics and Data Science > Department Computational Life Science > Lehrstuhl für Statistische Bioinformatik (Prof. Spang) Physics > Institute of Theroretical Physics | ||||
| Identification Number: |
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| Keywords: | MAXIMUM-LIKELIHOOD-ESTIMATION; MARKOV-CHAIN; BAYESIAN-ANALYSIS; PARAMETER EXPANSION; ALGORITHM; BINARY; SIMULATION; INFERENCE; MATRIX; Maximum likelihood; Multivariate probit; Monte Carlo EM; Adaptive sequential Monte Carlo | ||||
| Dewey Decimal Classification: | 500 Science > 530 Physics 600 Technology > 610 Medical sciences Medicine | ||||
| Status: | Published | ||||
| Refereed: | Yes, this version has been refereed | ||||
| Created at the University of Regensburg: | Partially | ||||
| Item ID: | 21577 |
Abstract
Multivariate probit models have the appealing feature of capturing some of the dependence structure between the components of multidimensional binary responses. The key for the dependence modelling is the covariance matrix of an underlying latent multivariate Gaussian. Most approaches to maximum likelihood estimation in multivariate probit regression rely on Monte Carlo EM algorithms to avoid ...
Abstract
Multivariate probit models have the appealing feature of capturing some of the dependence structure between the components of multidimensional binary responses. The key for the dependence modelling is the covariance matrix of an underlying latent multivariate Gaussian. Most approaches to maximum likelihood estimation in multivariate probit regression rely on Monte Carlo EM algorithms to avoid computationally intensive evaluations of multivariate normal orthant probabilities. As an alternative to the much used Gibbs sampler a new sequential Monte Carlo (SMC) sampler for truncated multivariate normals is proposed. The algorithm proceeds in two stages where samples are first drawn from truncated multivariate Student t distributions and then further evolved towards a Gaussian. The sampler is then embedded in a Monte Carlo EM algorithm. The sequential nature of SMC methods can be exploited to design a fully sequential version of the EM, where the samples are simply updated from one iteration to the next rather than resampled from scratch. Recycling the samples in this manner significantly reduces the computational cost. An alternative view of the standard conditional maximisation step provides the basis for an iterative procedure to fully perform the maximisation needed in the EM algorithm. The identifiability of multivariate probit models is also thoroughly discussed. In particular, the likelihood invariance can be embedded in the EM algorithm to ensure that constrained and unconstrairied maximisations are equivalent. A simple iterative procedure is then derived for either maximisation which takes effectively no computational time. The method is validated by applying it to the widely analysed Six Cities dataset and on a higher dimensional simulated example. Previous approaches to the Six Cities dataset overly restrict the parameter space but, by considering the correct invariance, the maximum likelihood is quite naturally improved when treating the full unrestricted model. (C) 2013 Elsevier B.V. All rights reserved.
Metadata last modified: 29 Sep 2021 07:38
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