Related papers: Model selection and parameter inference in phyloge…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

Gaussian Process (GPs) models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through the optimisation of kernel hyperparameters using the marginal likelihood as the objective.…

Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…

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…

We present dynesty, a public, open-source, Python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using Dynamic Nested Sampling. By adaptively allocating samples based on posterior structure, Dynamic Nested…

The posterior probability distribution for a set of model parameters encodes all that the data have to tell us in the context of a given model; it is the fundamental quantity for Bayesian parameter estimation. In order to infer the…

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

Stochastic reaction network models are often used to explain and predict the dynamics of gene regulation in single cells. These models usually involve several parameters, such as the kinetic rates of chemical reactions, that are not…

A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…

The abundance of new cosmological data becoming available means that a wider range of cosmological models are testable than ever before. However, an important distinction must be made between parameter fitting and model selection. While…

Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption,…

State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…

We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…

Rate variation among the sites of a molecular sequence is commonly found in applications of phylogenetic inference. Several approaches exist to account for this feature but they do not usually enable the investigator to pinpoint the sites…

Bayesian neural networks (BNNs) have been long considered an ideal, yet unscalable solution for improving the robustness and the predictive uncertainty of deep neural networks. While they could capture more accurately the posterior…

Bayesian inference provides a methodology for parameter estimation and uncertainty quantification in machine learning and deep learning methods. Variational inference and Markov Chain Monte-Carlo (MCMC) sampling methods are used to…

Bayesian inference allows us to define a posterior distribution over the weights of a generic neural network (NN). Exact posteriors are usually intractable, in which case approximations can be employed. One such approximation - variational…