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A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…

Bayes linear kinematics and Bayes linear Bayes graphical models provide an extension of Bayes linear methods so that full conditional updates may be combined with Bayes linear belief adjustment. In this paper we investigate the application…

This paper introduces a sequential multiple importance sampling (SeMIS) algorithm for high-dimensional Bayesian inference. The method estimates Bayesian evidence using all generated samples from each proposal distribution while obtaining…

In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…

Recent likelihood theory produces $p$-values that have remarkable accuracy and wide applicability. The calculations use familiar tools such as maximum likelihood values (MLEs), observed information and parameter rescaling. The usual…

In decision modelling with time to event data, parametric models are often used to extrapolate the survivor function. One such model is the piecewise exponential model whereby the hazard function is partitioned into segments, with the…

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…

This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…

An exploit of the Sequential Importance Sampling (SIS) algorithm using Differential Algebra (DA) techniques is derived to develop an efficient particle filter. The filter creates an original kind of particles, called scout particles, that…

Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…

Bayesian inference is an effective approach for solving statistical learning problems especially with uncertainty and incompleteness. However, inference efficiencies are physically limited by the bottlenecks of conventional computing…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

Estimating the parameters of general state-space models is a topic of importance for many scientific and engineering disciplines. In this paper we present an online parameter estimation algorithm obtained by casting our recently proposed…

Precision achieved by stochastic sampling algorithms for Bayesian networks typically deteriorates in face of extremely unlikely evidence. To address this problem, we propose the Evidence Pre-propagation Importance Sampling algorithm…

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple…

Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…