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Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of p-splines, we propose a Bayesian framework for choosing the smoothing parameter which…
In the following article we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which…
We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in Machine Learning, with Formal Methods rooted in the computer science community. Bayesian predictive inference allows for…
Simulation models for pedestrian crowds are a ubiquitous tool in research and industry. It is crucial that the parameters of these models are calibrated carefully and ultimately it will be of interest to compare competing models to decide…
Spatio-temporal models are widely used in many research areas including ecology. The recent proliferation of the use of in-situ sensors in streams and rivers supports space-time water quality modelling and monitoring in near real-time. A…
Approximate Bayesian Computation (ABC) methods have gained in their popularity over the last decade because they expand the horizon of Bayesian parameter inference methods to the range of models for which only forward simulation is…
Determining the best model or models for a particular data set, a process known as Bayesian model comparison, is a critical part of probabilistic inference. Typically, this process assumes a fixed model-space (that is, a fixed set of…
Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome…
We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…
Bayesian inference methods are useful in infectious diseases modeling due to their capability to propagate uncertainty, manage sparse data, incorporate latent structures, and address high-dimensional parameter spaces. However, parameter…
By the nature of their construction, many statistical models for extremes result in likelihood functions that are computationally prohibitive to evaluate. This is consequently problematic for the purposes of likelihood-based inference. With…
Recently, there has been a resurgence of interest in rigorous algorithms for the inference of cancer progression from genomic data. The motivations are manifold: (i) growing NGS and single cell data from cancer patients, (ii) need for novel…
The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs…
Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
A common approach in computational science is to use a set of of highly precise but expensive calculations to parameterize a model that allows less precise, but more rapid calculations on larger scale systems. Least-squares fitting on a…
Cancer pathology is unique to a given individual, and developing personalized diagnostic and treatment protocols are a primary concern. Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the…
Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…
Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…
Computer models are widely used to study complex real world physical systems. However, there are major limitations to their direct use including: their complex structure; large numbers of inputs and outputs; and long evaluation times.…