Search results for "Bayesian inference"
showing 10 items of 120 documents
The Recycling Gibbs sampler for efficient learning
2018
Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from complicated high-dimensional posterior distributions. The key point for the successful application of the Gibbs sampler is the ability to draw efficiently samples from the full-conditional probability density functions. Since in the general case this is not possible, in order to speed up the convergence of the chain, it is required to generate auxiliary samples whose information is eventually disregarded. In this work, we show that these auxiliary sample…
Conditional particle filters with diffuse initial distributions
2020
Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in statistical applications. We propose a simple but generally applicable auxiliary variable method, which can be used together with the CPF in order to perform efficient inference with diffuse initial distributions. The method only requires simulatable Markov transitions that are reversible with respect to the initial distribution, which can be improper. We focus in particular on random-walk type transitions which are reversible with respect to a uniform init…
Unbiased Inference for Discretely Observed Hidden Markov Model Diffusions
2021
We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead, our method uses standard time-discretised approximations of diffusions, such as the Euler--Maruyama scheme. Our approach is based on particle marginal Metropolis--Hastings, a particle filter, randomised multilevel Monte Carlo, and importance sampling type correction of approximate Markov chain Monte Carlo. The resulting estimator leads to inference without a bias from the time-discretisation as the number of Markov chain iterations increases. We give conver…
Bayesian inference for the extremal dependence
2016
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The…
Efficient Bayesian generalized linear models with time-varying coefficients : The walker package in R
2020
The R package walker extends standard Bayesian general linear models to the case where the effects of the explanatory variables can vary in time. This allows, for example, to model the effects of interventions such as changes in tax policy which gradually increases their effect over time. The Markov chain Monte Carlo algorithms powering the Bayesian inference are based on Hamiltonian Monte Carlo provided by Stan software, using a state space representation of the model to marginalise over the regression coefficients for efficient low-dimensional sampling.
Bayesian Analysis of Population Health Data
2021
The analysis of population-wide datasets can provide insight on the health status of large populations so that public health officials can make data-driven decisions. The analysis of such datasets often requires highly parameterized models with different types of fixed and random effects to account for risk factors, spatial and temporal variations, multilevel effects and other sources on uncertainty. To illustrate the potential of Bayesian hierarchical models, a dataset of about 500,000 inhabitants released by the Polish National Health Fund containing information about ischemic stroke incidence for a 2-year period is analyzed using different types of models. Spatial logistic regression and…
Can visualization alleviate dichotomous thinking? Effects of visual representations on the cliff effect
2021
Common reporting styles for statistical results in scientific articles, such as $p$ p -values and confidence intervals (CI), have been reported to be prone to dichotomous interpretations, especially with respect to the null hypothesis significance testing framework. For example when the $p$ p -value is small enough or the CIs of the mean effects of a studied drug and a placebo are not overlapping, scientists tend to claim significant differences while often disregarding the magnitudes and absolute differences in the effect sizes. This type of reasoning has been shown to be potentially harmful to science. Techniques relying on the visual estimation of the strength of evidence have been recom…
A Phylogenetic Analysis of Human Syntenies Revealed by Chromosome Painting in Euarchontoglires Orders
2010
To search for cytogenetic signatures that can help to clarify evolutionary affinities among the five orders within the Euarchontoglires clade, we focused on associations of conserved syntenic blocks that have been accumulated in the karyotypes of Primates (Strepsirhini and Haplorhini), five families of Rodentia, Scandentia (Tupaia belangeri), Dermoptera (Galeopterus variegatus) and Lagomorpha (Oryctolagus cuniculus). We examined available chromosome painting data to identify conserved chromosomes and chromosomal segments, and syntenic associations likely to have characterized the ancestral eutherian karyotype. The data set includes 161 characters that have been subjected to a concatenated a…
Selective phenotyping, entropy reduction, and the mastermind game.
2011
Abstract Background With the advance of genome sequencing technologies, phenotyping, rather than genotyping, is becoming the most expensive task when mapping genetic traits. The need for efficient selective phenotyping strategies, i.e. methods to select a subset of genotyped individuals for phenotyping, therefore increases. Current methods have focused either on improving the detection of causative genetic variants or their precise genomic location separately. Results Here we recognize selective phenotyping as a Bayesian model discrimination problem and introduce SPARE (Selective Phenotyping Approach by Reduction of Entropy). Unlike previous methods, SPARE can integrate the information of p…
Modelling the presence of disease under spatial misalignment using Bayesian latent Gaussian models.
2015
Modelling patterns of the spatial incidence of diseases using local environmental factors has been a growing problem in the last few years. Geostatistical models have become popular lately because they allow estimating and predicting the underlying disease risk and relating it with possible risk factors. Our approach to these models is based on the fact that the presence/absence of a disease can be expressed with a hierarchical Bayesian spatial model that incorporates the information provided by the geographical and environmental characteristics of the region of interest. Nevertheless, our main interest here is to tackle the misalignment problem arising when information about possible covar…