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High-dimensional data are routinely collected in many areas. We are particularly interested in Bayesian classification models in which one or more variables are imbalanced. Current Markov chain Monte Carlo algorithms for posterior…
Bayesian optimisation is an adaptive sampling strategy for constructing a Gaussian process surrogate to efficiently search for the global minimum of a black-box computational model. Gaussian processes have limited applicability in…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
Bayesian experimental design (BED) has been used as a method for conducting efficient experiments based on Bayesian inference. The existing methods, however, mostly focus on maximizing the expected information gain (EIG); the cost of…
The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…
Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy…
A Monte Carlo algorithm is said to be adaptive if it automatically calibrates its current proposal distribution using past simulations. The choice of the parametric family that defines the set of proposal distributions is critical for good…
Nested nonparametric processes are vectors of random probability measures widely used in the Bayesian literature to model the dependence across distinct, though related, groups of observations. These processes allow a two-level clustering,…
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…
Understanding how stochastic gene expression is regulated in biological systems using snapshots of single-cell transcripts requires state-of-the-art methods of computational analysis and statistical inference. A Bayesian approach to…
Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood. In this paper we develop theoretical bounds for the distance between the statistics used…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…
Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood…
Ensembling can improve the performance of Neural Networks, but existing approaches struggle when the architecture likelihood surface has dispersed, narrow peaks. Furthermore, existing methods construct equally weighted ensembles, and this…
Consider a real-valued function that can only be observed with stochastic noise at a finite set of design points within a Euclidean space. We wish to determine whether there exists a convex function that goes through the true function…
The development of a new diagnostic test ideally follows a sequence of stages which, amongst other aims, evaluate technical performance. This includes an analytical validity study, a diagnostic accuracy study and an interventional clinical…
Optimization is becoming increasingly common in scientific and engineering domains. Oftentimes, these problems involve various levels of stochasticity or uncertainty in generating proposed solutions. Therefore, optimization in these…
We develop a scalable multi-step Monte Carlo algorithm for inference under a large class of nonparametric Bayesian models for clustering and classification. Each step is "embarrassingly parallel" and can be implemented using the same Markov…
Approximate Bayesian computation is an established and popular method for likelihood-free inference with applications in many disciplines. The effectiveness of the method depends critically on the availability of well performing summary…