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Easily Computed Marginal Likelihoods from Posterior Simulation Using the THAMES Estimator

Published in Bayesian Analysis, 2024

We propose an easily computed estimator of the marginal likelihood from posterior simulation output, via reciprocal importance sampling, combining earlier proposals of DiCiccio et al (1997) and Robert and Wraith (2009).

Recommended citation: Martin Metodiev, Marie Perrot-Dockès, Sarah Ouadah, Nicholas J. Irons, Pierre Latouche, Adrian E. Raftery. "Easily Computed Marginal Likelihoods from Posterior Simulation Using the THAMES Estimator." Bayesian Analysis, 20(3) 1003-1030 September 2025.
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A Structured Estimator for large Covariance Matrices in the Presence of Pairwise and Spatial Covariates

Published in arXiv, 2024

We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure.

Recommended citation: Metodiev, M., Perrot-Dockès, M., Ouadah, S., Fosdick, B. K., Robin, S., Latouche, P., & Raftery, A. E. (2024). A Structured Estimator for large Covariance Matrices in the Presence of Pairwise and Spatial Covariates. arXiv preprint arXiv:2411.04520.
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The Principle of Redundant Reflection

Published in arXiv, 2025

The fact that redundant information does not change a rational belief after Bayesian updating implies uniqueness of Bayes rule.

Recommended citation: Metodiev, M., Marsman, M., Waldorp, L., Gronau, Q. F., & Wagenmakers, E. J. (2025). The Principle of Redundant Reflection. arXiv preprint arXiv:2503.21719.
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Easily Computed Marginal Likelihoods for Multivariate Mixture Models Using the THAMES Estimator

Published in arXiv, 2025

We present a new version of the truncated harmonic mean estimator (THAMES) for univariate or multivariate mixture models.

Recommended citation: Martin Metodiev, Nicholas J. Irons, Marie Perrot-Dockès, Pierre Latouche, Adrian E. Raftery. "Easily Computed Marginal Likelihoods for Multivariate Mixture Models Using the THAMES Estimator." arXiv preprint arXiv:2504.21812.
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thames (R package): Truncated Harmonic Mean Estimator of the Marginal Likelihood

Published in CRAN, 2025

Implements the truncated harmonic mean estimator (THAMES) of the reciprocal marginal likelihood using posterior samples and unnormalized log posterior values via reciprocal importance sampling.

Recommended citation: Irons N, Perrot-Dockès M, Metodiev M (2025). _thames: Truncated Harmonic Mean Estimator of the Marginal Likelihood_. doi:10.32614/CRAN.package.thames , R package version 0.1.2,
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thamesmix (R package): Truncated Harmonic Mean Estimator of the Marginal Likelihood for Mixtures

Published in CRAN, 2025

Implements the truncated harmonic mean estimator (THAMES) of the reciprocal marginal likelihood for uni- and multivariate mixture models using posterior samples and unnormalized log posterior values via reciprocal importance sampling.

Recommended citation: Metodiev M, Irons N, Perrot-Dockès M (2025). _thamesmix: Truncated Harmonic Mean Estimator of the Marginal Likelihood for Mixtures_. R package version 0.1.2, commit 5bf05daec1f8922589f6cb53eec54b0c8cb07716, .
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talks

teaching

Outils Mathématiques 2 (22.5 hours of teaching)

Undergraduate Course, Université Clermont Auvergne, laboratoire de mathématiques Blaise Pascal, 2024

An introduction to the basic concepts of mathematics, such as ordinary differential equations.

The Variational EM Algorithm (10 hours of teaching)

Graduate Project, Polytech, 2026

The goal was to replicate the results of the following article: Daudin, J. J., Picard, F., & Robin, S. (2008). A mixture model for random graphs. Statistics and computing, 18(2), 173-183.