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Raking is widely used in categorical data modeling and survey practice but faced with methodological and computational challenges. We develop a Bayesian paradigm for raking by incorporating the marginal constraints as a prior distribution…
Self-Exciting models are statistical models of count data where the probability of an event occurring is influenced by the history of the process. In particular, self-exciting spatio-temporal models allow for spatial dependence as well as…
Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge…
Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty…
The ranking of experiments by expected information gain (EIG) in Bayesian experimental design is sensitive to changes in the model's prior distribution, and the approximation of EIG yielded by sampling will have errors similar to the use of…
In recent years, Bayesian inference in large-scale inverse problems found in science, engineering and machine learning has gained significant attention. This paper examines the robustness of the Bayesian approach by analyzing the stability…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Microplastics contamination is one of the most rapidly growing research topics. However, monitoring microplastics contamination in the environment presents both logistical and statistical challenges, particularly when constrained resources…
We adapt the canonical Laplace mechanism, widely used in differentially private data analysis, to achieve near instance optimality with respect to the hardness of the underlying dataset. In particular, we construct a piecewise Laplace…
Traditionally Bayesian decision-theoretic design of experiments proceeds by choosing a design to minimise expectation of a given loss function over the space of all designs. The loss function encapsulates the aim of the experiment, and the…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
Bayesian optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
This paper addresses the integration of additional information sources into a Bayesian optimization framework while ensuring that safety constraints are satisfied. The interdependencies between these information sources are modeled using an…
Bayesian hierarchical models with latent Gaussian layers have proven very flexible in capturing complex stochastic behavior and hierarchical structures in high-dimensional spatial and spatio-temporal data. Whereas simulation-based Bayesian…
Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…
This paper introduces a Laplace approximation to Bayesian inference in Dirichlet regression models, which can be used to analyze a set of variables on a simplex exhibiting skewness and heteroscedasticity, without having to transform the…
We discuss Bayesian methods for learning Bayesian networks when data sets are incomplete. In particular, we examine asymptotic approximations for the marginal likelihood of incomplete data given a Bayesian network. We consider the Laplace…
Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…