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Low-rank approximation is a popular strategy to tackle the "big n problem" associated with large-scale Gaussian process regressions. Basis functions for developing low-rank structures are crucial and should be carefully specified.…
Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This…
This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…
In this paper, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not…
We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
Questions about information encoded by the brain demand statistical frameworks for inferring relationships between neural firing and features of the world. The landmark discovery of grid cells demonstrates that neurons can represent spatial…
Database alignment is a variant of the graph alignment problem: Given a pair of anonymized databases containing separate yet correlated features for a set of users, the problem is to identify the correspondence between the features and…
The Cox model is an indispensable tool for time-to-event analysis, particularly in biomedical research. However, medicine is undergoing a profound transformation, generating data at an unprecedented scale, which opens new frontiers to study…
Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…
Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a…
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…
We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly…
Presence-only data, point locations where a species has been recorded as being present, are often used in modeling the distribution of a species as a function of a set of explanatory variables---whether to map species occurrence, to…
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that…
Global data association is an essential prerequisite for robot operation in environments seen at different times or by different robots. Repetitive or symmetric data creates significant challenges for existing methods, which typically rely…
Supervised topic models with a logistic likelihood have two issues that potentially limit their practical use: 1) response variables are usually over-weighted by document word counts; and 2) existing variational inference methods make…
We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex…