arXiv subjects

Alice Corbella

Publications and source records attributed to Alice Corbella.

5 recordsLinked to original sources

arXiv2025

A discomfort-informed adaptive Gibbs sampler for finite mixture models

Finite mixture models are frequently used to uncover latent structures in high-dimensional datasets (e.g.\ identifying clusters of patients in electronic health records). The inference of such structures can be performed in a Bayesian framework, and involves the use of sampling algorithms such as Gibbs samplers aimed at deriving posterior distribution of the probabilities of observations to belong to specific clusters. Unfortunately, traditional implementations of Gibbs samplers in this context often face critical challenges, such as inefficient use of computational resources and unnecessary updates for observations that are highly likely to remain in their current cluster. This paper introduces a new adaptive Gibbs sampler that improves the convergence efficiency over existing methods. In particular, our sampler is guided by a function that, at each iteration, uses the past of the chain to focus the updating on observations potentially misclassified in the current clustering, i.e.\ those with a low probability of belonging to their current component. Through simulation studies and two real data analyses, we empirically demonstrate that, in terms of convergence time, our method tends to perform more efficiently compared to state-of-the-art approaches.

stat.ME↗

arXiv2022

The Lifebelt Particle Filter for robust estimation from low-valued count data

Particle filtering methods can be applied to estimation problems in discrete spaces on bounded domains, to sample from and marginalise over unknown hidden states. As in continuous settings, problems such as particle degradation can arise: proposed particles can be incompatible with the data, lying in low probability regions or outside the boundary constraints, and the discrete system could result in all particles having weights of zero. In this paper we introduce the Lifebelt Particle Filter (LBPF), a novel method for robust likelihood estimation in low-valued count problems. The LBPF combines a standard particle filter with one (or more) lifebelt particles which, by construction, lie within the boundaries of the discrete random variables, and therefore are compatible with the data. A mixture of resampled and non-resampled particles allows for the preservation of the lifebelt particle, which, together with the remaining particle swarm, provides samples from the filtering distribution, and can be used to generate unbiased estimates of the likelihood. The main benefit of the LBPF is that only one or few, wisely chosen, particles are sufficient to prevent particle collapse. Differently from other methods, there is no need to increase the number of particles, and therefore the computational effort, in regions of the parameter space that generate less likely hidden states. The LBPF can be used within a pseudo-marginal scheme to draw inferences on static parameters, $ \boldsymbol{\theta} $, governing the system. We address here the estimation of a parameter governing probabilities of deaths and recoveries of hospitalised patients during an epidemic.

stat.CO↗

arXiv2022

Automatic Zig-Zag sampling in practice

Novel Monte Carlo methods to generate samples from a target distribution, such as a posterior from a Bayesian analysis, have rapidly expanded in the past decade. Algorithms based on Piecewise Deterministic Markov Processes (PDMPs), non-reversible continuous-time processes, are developing into their own research branch, thanks their important properties (e.g., correct invariant distribution, ergodicity, and super-efficiency). Nevertheless, practice has not caught up with the theory in this field, and the use of PDMPs to solve applied problems is not widespread. This might be due, firstly, to several implementational challenges that PDMP-based samplers present with and, secondly, to the lack of papers that showcase the methods and implementations in applied settings. Here, we address both these issues using one of the most promising PDMPs, the Zig-Zag sampler, as an archetypal example. After an explanation of the key elements of the Zig-Zag sampler, its implementation challenges are exposed and addressed. Specifically, the formulation of an algorithm that draws samples from a target distribution of interest is provided. Notably, the only requirement of the algorithm is a closed-form function to evaluate the target density of interest, and, unlike previous implementations, no further information on the target is needed. The performance of the algorithm is evaluated against another gradient-based sampler, and it is proven to be competitive, in simulation and real-data settings. Lastly, we demonstrate that the super-efficiency property, i.e. the ability to draw one independent sample at a lesser cost than evaluating the likelihood of all the data, can be obtained in practice.

stat.CO↗

arXiv2022

Inferring Epidemics from Multiple Dependent Data via Pseudo-Marginal Methods

Health-policy planning requires evidence on the burden that epidemics place on healthcare systems. Multiple, often dependent, datasets provide a noisy and fragmented signal from the unobserved epidemic process including transmission and severity dynamics. This paper explores important challenges to the use of state-space models for epidemic inference when multiple dependent datasets are analysed. We propose a new semi-stochastic model that exploits deterministic approximations for large-scale transmission dynamics while retaining stochasticity in the occurrence and reporting of relatively rare severe events. This model is suitable for many real-time situations including large seasonal epidemics and pandemics. Within this context, we develop algorithms to provide exact parameter inference and test them via simulation. Finally, we apply our joint model and the proposed algorithm to several surveillance data on the 2017-18 influenza epidemic in England to reconstruct transmission dynamics and estimate the daily new influenza infections as well as severity indicators such as the case-hospitalisation risk and the hospital-intensive care risk.

stat.AP↗

arXiv2017

Exploiting routinely collected severe case data to monitor and predict influenza outbreaks

Influenza remains a significant burden on health systems. Effective responses rely on the timely understanding of the magnitude and the evolution of an outbreak. For monitoring purposes, data on severe cases of influenza in England are reported weekly to Public Health England. These data are both readily available and have the potential to provide valuable information to estimate and predict the key transmission features of seasonal and pandemic influenza. We propose an epidemic model that links the underlying unobserved influenza transmission process to data on severe influenza cases. Within a Bayesian framework, we infer retrospectively the parameters of the epidemic model for each seasonal outbreak from 2012 to 2015, including: the effective reproduction number; the initial susceptibility; the probability of admission to intensive care given infection; and the effect of school closure on transmission. The model is also implemented in real time to assess whether early forecasting of the number of admission to intensive care is possible. Our model of admissions data allows reconstruction of the underlying transmission dynamics revealing: increased transmission during the season 2013/14 and a noticeable effect of Christmas school holiday on disease spread during season 2012/13 and 2014/15. When information on the initial immunity of the population is available, forecasts of the number of admissions to intensive care can be substantially improved. Readily available severe case data can be effectively used to estimate epidemiological characteristics and to predict the evolution of an epidemic, crucially allowing real-time monitoring of the transmission and severity of the outbreak.

stat.AP↗