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Jean-Michel Marin

Publications and source records attributed to Jean-Michel Marin.

At least 19 recordsLinked to original sources
arXiv2025

Estimating Marginal Likelihoods in Likelihood-Free Inference via Neural Density Estimation

The marginal likelihood, or evidence, plays a central role in Bayesian model selection, yet remains notoriously challenging to compute in likelihood-free settings. While Simulation-Based Inference (SBI) techniques such as Sequential Neural Likelihood Estimation (SNLE) offer powerful tools to approximate posteriors using neural density estimators, they typically do not provide estimates of the evidence. In this technical report presented at BayesComp 2025, we present a simple and general methodology to estimate the marginal likelihood using the output of SNLE.

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arXiv2025

Goodness of Fit for Bayesian Generative Models with Applications in Population Genetics

In population genetics and other application fields, models with intractable likelihood are common. Approximate Bayesian Computation (ABC) or more generally Simulation-Based Inference (SBI) methods work by simulating instrumental data sets from the models under study and comparing them with the observed data set, using advanced machine learning tools for tasks such as model selection and parameter inference. The present work focuses on model criticism, and more specifically on Goodness of fit (GoF) tests, for intractable likelihood models. We introduce two new GoF tests: the pre-inference \gof tests whether the observed dataset is distributed from the prior predictive distribution, while the post-inference GoF tests whether there is a parameter value such that the observed dataset is distributed from the likelihood with that value. The pre-inference test can be used to prune a large set of models using a limited amount of simulations, while the post-inference test is used to assess the fit of a selected model. Both tests are based on the Local Outlier Factor (LOF, Breunig et al., 2000). This indicator was initially defined for outlier and novelty detection. It is able to quantify local density deviations, capturing subtleties that a more traditional k-NN-based approach may miss. We evaluated the performance of our two GoF tests on simulated datasets from three different model settings of varying complexity. We then illustrate the utility of these approaches on a dataset of single nucleotide polymorphism (SNP) markers for the evaluation of complex evolutionary scenarios of modern human populations. Our dual-test GoF approach highlights the flexibility of our method: the pre-inference \gof test provides insight into model validity from a Bayesian perspective, while the post-inference test provides a more general and traditional view of assessing goodness of fit

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arXiv2018

Computational Solutions for Bayesian Inference in Mixture Models

This chapter surveys the most standard Monte Carlo methods available for simulating from a posterior distribution associated with a mixture and conducts some experiments about the robustness of the Gibbs sampler in high dimensional Gaussian settings. This is a chapter prepared for the forthcoming 'Handbook of Mixture Analysis'.

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arXiv2018

ABC random forests for Bayesian parameter inference

This preprint has been reviewed and recommended by Peer Community In Evolutionary Biology (http://dx.doi.org/10.24072/pci.evolbiol.100036). Approximate Bayesian computation (ABC) has grown into a standard methodology that manages Bayesian inference for models associated with intractable likelihood functions. Most ABC implementations require the preliminary selection of a vector of informative statistics summarizing raw data. Furthermore, in almost all existing implementations, the tolerance level that separates acceptance from rejection of simulated parameter values needs to be calibrated. We propose to conduct likelihood-free Bayesian inferences about parameters with no prior selection of the relevant components of the summary statistics and bypassing the derivation of the associated tolerance level. The approach relies on the random forest methodology of Breiman (2001) applied in a (non parametric) regression setting. We advocate the derivation of a new random forest for each component of the parameter vector of interest. When compared with earlier ABC solutions, this method offers significant gains in terms of robustness to the choice of the summary statistics, does not depend on any type of tolerance level, and is a good trade-off in term of quality of point estimator precision and credible interval estimations for a given computing time. We illustrate the performance of our methodological proposal and compare it with earlier ABC methods on a Normal toy example and a population genetics example dealing with human population evolution. All methods designed here have been incorporated in the R package abcrf (version 1.7) available on CRAN.

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arXiv2016

A fully objective Bayesian approach for the Behrens-Fisher problem using historical studies

For in vivo research experiments with small sample sizes and available historical data, we propose a sequential Bayesian method for the Behrens-Fisher problem. We consider it as a model choice question with two models in competition: one for which the two expectations are equal and one for which they are different. The choice between the two models is performed through a Bayesian analysis, based on a robust choice of combined objective and subjective priors, set on the parameters space and on the models space. Three steps are necessary to evaluate the posterior probability of each model using two historical datasets similar to the one of interest. Starting from the Jeffreys prior, a posterior using a first historical dataset is deduced and allows to calibrate the Normal-Gamma informative priors for the second historical dataset analysis, in addition to a uniform prior on the model space. From this second step, a new posterior on the parameter space and the models space can be used as the objective informative prior for the last Bayesian analysis. Bayesian and frequentist methods have been compared on simulated and real data. In accordance with FDA recommendations, control of type I and type II error rates has been evaluated. The proposed method controls them even if the historical experiments are not completely similar to the one of interest.

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arXiv2016

Likelihood-free Model Choice

This document is an invited chapter covering the specificities of ABC model choice, intended for the incoming Handbook of ABC by Sisson, Fan, and Beaumont (2017). Beyond exposing the potential pitfalls of ABC based posterior probabilities, the review emphasizes mostly the solution proposed by Pudlo et al. (2016) on the use of random forests for aggregating summary statistics and and for estimating the posterior probability of the most likely model via a secondary random fores.

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arXiv2016

Hidden Gibbs random fields model selection using Block Likelihood Information Criterion

Performing model selection between Gibbs random fields is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical or numerical methods. Furthermore, such unobserved fields cannot be integrated out and the likelihood evaluztion is a doubly intractable problem. This forms a central issue to pick the model that best fits an observed data. We introduce a new approximate version of the Bayesian Information Criterion. We partition the lattice into continuous rectangular blocks and we approximate the probability measure of the hidden Gibbs field by the product of some Gibbs distributions over the blocks. On that basis, we estimate the likelihood and derive the Block Likelihood Information Criterion (BLIC) that answers model choice questions such as the selection of the dependency structure or the number of latent states. We study the performances of BLIC for those questions. In addition, we present a comparison with ABC algorithms to point out that the novel criterion offers a better trade-off between time efficiency and reliable results.

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arXiv2015

Reliable ABC model choice via random forests

Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior probabilities may be poorly evaluated by standard ABC techniques. We propose a novel approach based on a machine learning tool named random forests to conduct selection among the highly complex models covered by ABC algorithms. We thus modify the way Bayesian model selection is both understood and operated, in that we rephrase the inferential goal as a classification problem, first predicting the model that best fits the data with random forests and postponing the approximation of the posterior probability of the predicted MAP for a second stage also relying on random forests. Compared with earlier implementations of ABC model choice, the ABC random forest approach offers several potential improvements: (i) it often has a larger discriminative power among the competing models, (ii) it is more robust against the number and choice of statistics summarizing the data, (iii) the computing effort is drastically reduced (with a gain in computation efficiency of at least fifty), and (iv) it includes an approximation of the posterior probability of the selected model. The call to random forests will undoubtedly extend the range of size of datasets and complexity of models that ABC can handle. We illustrate the power of this novel methodology by analyzing controlled experiments as well as genuine population genetics datasets. The proposed methodologies are implemented in the R package abcrf available on the CRAN.

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arXiv2014

Consistency of the Adaptive Multiple Importance Sampling

Among Monte Carlo techniques, the importance sampling requires fine tuning of a proposal distribution, which is now fluently resolved through iterative schemes. The Adaptive Multiple Importance Sampling (AMIS) of Cornuet et al. (2012) provides a significant improvement in stability and effective sample size due to the introduction of a recycling procedure. However, the consistency of the AMIS estimator remains largely open. In this work we prove the convergence of the AMIS, at a cost of a slight modification in the learning process. Contrary to Douc et al. (2007a), results are obtained here in the asymptotic regime where the number of iterations is going to infinity while the number of drawings per iteration is a fixed, but growing sequence of integers. Hence some of the results shed new light on adaptive population Monte Carlo algorithms in that last regime.

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arXiv2013

Efficient learning in ABC algorithms

Approximate Bayesian Computation has been successfully used in population genetics to bypass the calculation of the likelihood. These methods provide accurate estimates of the posterior distribution by comparing the observed dataset to a sample of datasets simulated from the model. Although parallelization is easily achieved, computation times for ensuring a suitable approximation quality of the posterior distribution are still high. To alleviate the computational burden, we propose an adaptive, sequential algorithm that runs faster than other ABC algorithms but maintains accuracy of the approximation. This proposal relies on the sequential Monte Carlo sampler of Del Moral et al. (2012) but is calibrated to reduce the number of simulations from the model. The paper concludes with numerical experiments on a toy example and on a population genetic study of Apis mellifera, where our algorithm was shown to be faster than traditional ABC schemes.

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arXiv2012

Bounding rare event probabilities in computer experiments

We are interested in bounding probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo methods designed for rare events cannot be used. We then propose a strategy to deal with this difficulty based on importance sampling methods. This proposal relies on Kriging metamodeling and is able to achieve sharp upper confidence bounds on the rare event probabilities. The variability due to the Kriging metamodeling step is properly taken into account. The proposed methodology is applied to a toy example and compared to more standard Bayesian bounds. Finally, a challenging real case study is analyzed. It consists of finding an upper bound of the probability that the trajectory of an airborne load will collide with the aircraft that has released it.

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arXiv2011

Regularization in regression: comparing Bayesian and frequentist methods in a poorly informative situation

Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and real datasets. This comparison includes new global noninformative approaches for Bayesian variable selection built on Zellner's g-priors that are similar to Liang et al. (2008). The interest of those calibration-free proposals is discussed. The numerical experiments we present highlight the appeal of Bayesian regularization methods, when compared with non-Bayesian alternatives. They dominate frequentist methods in the sense that they provide smaller prediction errors while selecting the most relevant variables in a parsimonious way.

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arXiv2011

Adaptive Multiple Importance Sampling

The Adaptive Multiple Importance Sampling (AMIS) algorithm is aimed at an optimal recycling of past simulations in an iterated importance sampling scheme. The difference with earlier adaptive importance sampling implementations like Population Monte Carlo is that the importance weights of all simulated values, past as well as present, are recomputed at each iteration, following the technique of the deterministic multiple mixture estimator of Owen and Zhou (2000). Although the convergence properties of the algorithm cannot be fully investigated, we demonstrate through a challenging banana shape target distribution and a population genetics example that the improvement brought by this technique is substantial.

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arXiv2011

A new semi-parametric family of probability distributions for survival analysis

In the context of survival analysis, Marshall and Olkin (1997) introduced families of distributions by adding a scalar parameter to a given survival function, parameterized or not. In that paper, we generalize their approach. We show how it is possible to add more than a single parameter to a given distribution. We then introduce very flexible families of distributions for which we calculate some moments. Notably, we give some tractable expressions of these moments when the given baseline distribution is Log-logistic. Finally, we demonstrate how to generate sample from these new families.

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arXiv2011

Lack of confidence in ABC model choice

Approximate Bayesian computation (ABC) have become a essential tool for the analysis of complex stochastic models. Earlier, Grelaud et al. (2009) advocated the use of ABC for Bayesian model choice in the specific case of Gibbs random fields, relying on a inter-model sufficiency property to show that the approximation was legitimate. Having implemented ABC-based model choice in a wide range of phylogenetic models in the DIY-ABC software (Cornuet et al., 2008), we now present theoretical background as to why a generic use of ABC for model choice is ungrounded, since it depends on an unknown amount of information loss induced by the use of insufficient summary statistics. The approximation error of the posterior probabilities of the models under comparison may thus be unrelated with the computational effort spent in running an ABC algorithm. We then conclude that additional empirical verifications of the performances of the ABC procedure as those available in DIYABC are necessary to conduct model choice.

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