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Sequential Monte Carlo EM for Multivariate Probit Models

Moffa, Giusi and Kuipers, Jack. (2014) Sequential Monte Carlo EM for Multivariate Probit Models. Computational Statistics & Data Analysis, 72. pp. 252-272.

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Official URL: https://edoc.unibas.ch/81034/

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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 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 unconstrained 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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Statistik (Moffa)
UniBasel Contributors:Moffa, Giusi
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Elsevier
ISSN:0167-9473
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:13 Apr 2021 14:02
Deposited On:13 Apr 2021 14:02

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