arXiv subjects

Guillaume Kon Kam King

Publications and source records attributed to Guillaume Kon Kam King.

13 recordsLinked to original sources

arXiv2026

Bayesian Analysis of Covariate-Driven Hawkes Processes with Application in Plant Epidemiology

Hawkes processes are widely used to model temporal point patterns exhibiting self-exciting behavior. In this work, we consider a Hawkes model with a baseline intensity depending on a set of dynamic covariates and an exponential triggering function. A Bayesian approach is applied to variable selection in this context. Spike-and-slab priors are proposed to enable a parsimonious choice of relevant variables. We also provide practical simulation procedures for the fitted covariate-driven Hawkes model, which support posterior predictive checks and probabilistic forecasting. This approach is illustrated by the example of spore release of Venturia inaequalis, the fungus responsible for apple scab disease. We study the dependence of primary spore releases on environmental covariates and highlight the self-exciting behavior of subsequent releases. The Bayesian framework also provides a natural basis to forecast future spore releases. By delivering interpretable posterior inclusion probabilities alongside uncertainty-aware predictive risk bands, this new methodology provides a rigorous foundation for managing temporal event risks driven by both external environmental forcing and internal contagion.

stat.ME↗

arXiv2026

Credible rectangles for high-dimensional posterior comparison

We propose a Bayesian framework for uncertainty quantification and comparison in brain connectivity graph analysis. Standard graph-based approaches typically rely on point estimates of correlation matrices, overlooking the uncertainty induced by high-dimensional estimation from limited data. Our methodology constructs and compares credible hyperrectangles derived from posterior distributions, providing interpretable tools for subject-level inference and longitudinal monitoring. We develop scalable algorithms for estimating these regions in high dimensions and establish theoretical guarantees in the inverse-Wishart model for resting-state fMRI data, including a Bernstein--von Mises theorem for correlation matrices and control of a Bayesian family-wise error rate. The proposed framework enables principled detection of significant connectivity differences both globally and locally while preserving joint dependency structures. While demonstrating competitive performance against multiple-testing procedures on synthetic datasets, our approach also facilitates the direct comparison of two distinct scans from a single patient, a capability currently absent from the literature. We leverage this novelty on real datasets to improve interpretability. Beyond fMRI data, the approach provides a general framework for comparison problems in high-dimensional dependent settings.

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arXiv2026

Prior elicitation for Bayesian estimation of single-subject connectivity networks

Inference of brain functional connectivity networks from resting-state fMRI data is a key focus in neuroimaging. This paper introduces new Bayesian approaches for inferring a functional connectivity graph from multivariate resting-state fMRI time series of a single subject. Our methods rely on novel Bayesian priors on correlation matrices and a dedicated prior elicitation framework, which translates prior beliefs about the expected level and variability of correlations into interpretable hyperparameter choices, enabling the construction of expert-informed priors. When combined with a Gaussian likelihood, these priors also exhibit computational advantages. Compared to most existing methods for this problem that estimate constant weights, our model provides distributional weights defined by the posterior distributions for the connectivity graph, yielding more robust point estimates through the regularizing effect of expert-informed priors, evaluating uncertainty, and enabling a range of post-inference analyses. In particular, we derive a procedure for identifying significant connectivities based on posterior distributions of weights and credible sets. To the best of our knowledge, only one existing Bayesian functional connectivity model is applicable to single-subject resting-state fMRI data, making our approach a valuable addition to the field and demonstrating superior performance in our experiments.

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arXiv2026

Species Sensitivity Distribution revisited: a Bayesian nonparametric approach

We present a novel approach to ecological risk assessment by recasting the Species Sensitivity Distribution (SSD) method within a Bayesian nonparametric (BNP) framework. Widely mandated by environmental regulatory bodies globally, SSD has faced criticism due to its historical reliance on parametric assumptions when modeling species variability. By adopting nonparametric mixture models, we address this limitation, establishing a statistically robust foundation for SSD. Our BNP approach offers several advantages, including its efficacy in handling small datasets or censored data, which are common in ecological risk assessment, and its ability to provide principled uncertainty quantification alongside simultaneous density estimation and clustering. We utilize a specific nonparametric prior as the mixing measure, chosen for its robust clustering properties, a crucial consideration given the lack of strong prior beliefs about the number of components. Through simulation studies and analysis of real datasets, we demonstrate the superiority of our BNP-SSD over classical SSD methods. We also provide a BNP-SSD Shiny application, making our methodology available to the Ecotoxicology community. Moreover, we exploit the inherent clustering structure of the mixture model to explore patterns in species sensitivity. Our findings underscore the effectiveness of the proposed approach in improving ecological risk assessment methodologies.

stat.ME↗

arXiv2026

A forward-only scheme for online learning of proposal distributions in particle filters

We introduce a new online approach for constructing proposal distributions in particle filters using a forward scheme. Our method progressively incorporates future observations to refine proposals. This is in contrast to backward-scheme algorithms that require access to the entire dataset, such as the iterated auxiliary particle filters (Guarniero et al., 2017, arXiv:1511.06286) and controlled sequential Monte Carlo (Heng et al., 2020, arXiv:1708.08396) which leverage all future observations through backward recursion. In comparison, our forward scheme achieves a gradual improvement of proposals that converges toward the proposal targeted by these backward methods. We show that backward approaches can be numerically unstable even in simple settings. Our forward method, however, offers significantly greater robustness with only a minor trade-off in performance, measured by the variance of the marginal likelihood estimator. Numerical experiments on both simulated and real data illustrate the enhanced stability of our forward approach.

stat.CO↗

arXiv2024

Bayesian mixture models (in)consistency for the number of clusters

Bayesian nonparametric mixture models are common for modeling complex data. While these models are well-suited for density estimation, recent results proved posterior inconsistency of the number of clusters when the true number of components is finite, for the Dirichlet process and Pitman--Yor process mixture models. We extend these results to additional Bayesian nonparametric priors such as Gibbs-type processes and finite-dimensional representations thereof. The latter include the Dirichlet multinomial process, the recently proposed Pitman-Yor, and normalized generalized gamma multinomial processes. We show that mixture models based on these processes are also inconsistent in the number of clusters and discuss possible solutions. Notably, we show that a post-processing algorithm introduced for the Dirichlet process can be extended to more general models and provides a consistent method to estimate the number of components.

math.ST↗

arXiv2024

Bayesian high-dimensional covariate selection in non-linear mixed-effects models using the SAEM algorithm

High-dimensional variable selection, with many more covariates than observations, is widely documented in standard regression models, but there are still few tools to address it in non-linear mixed-effects models where data are collected repeatedly on several individuals. In this work, variable selection is approached from a Bayesian perspective and a selection procedure is proposed, combining the use of a spike-and-slab prior and the Stochastic Approximation version of the Expectation Maximisation (SAEM) algorithm. Similarly to Lasso regression, the set of relevant covariates is selected by exploring a grid of values for the penalisation parameter. The SAEM approach is much faster than a classical MCMC (Markov chain Monte Carlo) algorithm and our method shows very good selection performances on simulated data. Its flexibility is demonstrated by implementing it for a variety of nonlinear mixed effects models. The usefulness of the proposed method is illustrated on a problem of genetic markers identification, relevant for genomic-assisted selection in plant breeding.

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arXiv2023

Approximate filtering via discrete dual processes

We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a discrete state space is available. Recently, it was shown that duality with respect to a death-like process implies that the filtering distributions are finite mixtures, making exact filtering and smoothing feasible through recursive algorithms with polynomial complexity in the number of observations. Here we provide general results for the case of duality between the diffusion and a regular jump continuous-time Markov chain on a discrete state space, which typically leads to filtering distribution given by countable mixtures indexed by the dual process state space. We investigate the performance of several approximation strategies on two hidden Markov models driven by Cox-Ingersoll-Ross and Wright-Fisher diffusions, which admit duals of birth-and-death type, and compare them with the available exact strategies based on death-type duals and with bootstrap particle filtering on the diffusion state space as a general benchmark.

math.PR↗

arXiv2021

BNPdensity: Bayesian nonparametric mixture modeling in R

Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models seem often out of reach to practitioners, as inference algorithms need careful design to deal with the infinite number of parameters. The aim of this work is to facilitate the journey by providing computational tools for Bayesian nonparametric inference. The article describes a set of functions available in the \R package BNPdensity in order to carry out density estimation with an infinite mixture model, including all types of censored data. The package provides access to a large class of such models based on normalized random measures, which represent a generalization of the popular Dirichlet process mixture. One striking advantage of this generalization is that it offers much more robust priors on the number of clusters than the Dirichlet. Another crucial advantage is the complete flexibility in specifying the prior for the scale and location parameters of the clusters, because conjugacy is not required. Inference is performed using a theoretically grounded approximate sampling methodology known as the Ferguson & Klass algorithm. The package also offers several goodness of fit diagnostics such as QQ-plots, including a cross-validation criterion, the conditional predictive ordinate. The proposed methodology is illustrated on a classical ecological risk assessment method called the Species Sensitivity Distribution (SSD) problem, showcasing the benefits of the Bayesian nonparametric framework.

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arXiv2020

Exact inference for a class of non-linear hidden Markov models on general state spaces

Exact inference for hidden Markov models requires the evaluation of all distributions of interest - filtering, prediction, smoothing and likelihood - with a finite computational effort. This article provides sufficient conditions for exact inference for a class of hidden Markov models on general state spaces given a set of discretely collected indirect observations linked non linearly to the signal, and a set of practical algorithms for inference. The conditions we obtain are concerned with the existence of a certain type of dual process, which is an auxiliary process embedded in the time reversal of the signal, that in turn allows to represent the distributions and functions of interest as finite mixtures of elementary densities or products thereof. We describe explicitly how to update recursively the parameters involved, yielding qualitatively similar results to those obtained with Baum--Welch filters on finite state spaces. We then provide practical algorithms for implementing the recursions, as well as approximations thereof via an informed pruning of the mixtures, and we show superior performance to particle filters both in accuracy and computational efficiency. The code for optimal filtering, smoothing and parameter inference is made available in the Julia package DualOptimalFiltering.

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arXiv2015

Hierarchical modelling of species sensitivity distribution: development and application to the case of diatoms exposed to several herbicides

The Species Sensitivity Distribution (SSD) is a key tool to assess the ecotoxicological threat of contaminant to biodiversity. It predicts safe concentrations for a contaminant in a community. Widely used, this approach suffers from several drawbacks: i)summarizing the sensitivity of each species by a single value entails a loss of valuable information about the other parameters characterizing the concentration-effect curves; ii)it does not propagate the uncertainty on the critical effect concentration into the SSD; iii)the hazardous concentration estimated with SSD only indicates the threat to biodiversity, without any insight about a global response of the community related to the measured endpoint. We revisited the current SSD approach to account for all the sources of variability and uncertainty into the prediction and to assess a global response for the community. For this purpose, we built a global hierarchical model including the concentration-response model together with the distribution law for the SSD. Working within a Bayesian framework, we were able to compute an SSD taking into account all the uncertainty from the original raw data. From model simulations, it is also possible to extract a quantitative indicator of a global response of the community to the contaminant. We applied this methodology to study the toxicity of 6 herbicides to benthic diatoms from Lake Geneva, measured from biomass reduction.

stat.AP↗

arXiv2014

On the use of human mobility proxy for the modeling of epidemics

Human mobility is a key component of large-scale spatial-transmission models of infectious diseases. Correctly modeling and quantifying human mobility is critical for improving epidemic control policies, but may be hindered by incomplete data in some regions of the world. Here we explore the opportunity of using proxy data or models for individual mobility to describe commuting movements and predict the diffusion of infectious disease. We consider three European countries and the corresponding commuting networks at different resolution scales obtained from official census surveys, from proxy data for human mobility extracted from mobile phone call records, and from the radiation model calibrated with census data. Metapopulation models defined on the three countries and integrating the different mobility layers are compared in terms of epidemic observables. We show that commuting networks from mobile phone data well capture the empirical commuting patterns, accounting for more than 87% of the total fluxes. The distributions of commuting fluxes per link from both sources of data - mobile phones and census - are similar and highly correlated, however a systematic overestimation of commuting traffic in the mobile phone data is observed. This leads to epidemics that spread faster than on census commuting networks, however preserving the order of infection of newly infected locations. Match in the epidemic invasion pattern is sensitive to initial conditions: the radiation model shows higher accuracy with respect to mobile phone data when the seed is central in the network, while the mobile phone proxy performs better for epidemics seeded in peripheral locations. Results suggest that different proxies can be used to approximate commuting patterns across different resolution scales in spatial epidemic simulations, in light of the desired accuracy in the epidemic outcome under study.

q-bio.PE↗

arXiv2014

MOSAIC_SSD: a new web-tool for the Species Sensitivity Distribution, allowing to include censored data by maximum likelihood

Censored data are seldom taken into account in Species Sensitivity Distribution (SSD) analysis. However, they are found in virtually every dataset and sometimes represent the better part of the data. Stringent recommendations on data quality often lead to discard a lot of this meaningful data, often resulting in datasets of reduced size, which lack representativeness of any realistic community. However, it is reasonably simple to include censored data into SSD by using an extension of the standard maximum likelihood method. In this paper, we detail this approach based on the use of the R-package \emph{fitdistrplus}, dedicated to the fit of parametric probability distributions. In particular, we introduce the new web-tool MOSAIC$\_$SSD to fit an SSD on datasets containing any kind of data, censored or not. MOSAIC$\_$SSD allows predicting any Hazardous Concentration (HC) and provides in addition bootstrap confidence intervals on the prediction. In the end, taking examples from published data, we illustrate the added value of including censored data in SSD.

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