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Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…

We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…

Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…

This research proposes a flexible Bayesian extension of the composite Gaussian process (CGP) model of Ba and Joseph (2012) for predicting (stationary or) non-stationary $y(\mathbf{x})$. The CGP generalizes the regression plus stationary…

We develop a Bayesian model-based approach to finite population estimation accounting for spatial dependence. Our innovation here is a framework that achieves inference for finite population quantities in spatial process settings. A key…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

Modelling in biology must adapt to increasingly complex and massive data. The efficiency of the inference algorithms used to estimate model parameters is therefore questioned. Many of these are based on stochastic optimization processes…

In past decades, Gaussian processes has been widely applied in studying trait evolution using phylogenetic comparative analysis. In particular, two members of Gaussian processes: Brownian motion and Ornstein-Uhlenbeck process, have been…

Mapping people dynamics is a crucial skill for robots, because it enables them to coexist in human-inhabited environments. However, learning a model of people dynamics is a time consuming process which requires observation of large amount…

Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these…

We propose a geometric framework to assess sensitivity of Bayesian procedures to modeling assumptions based on the nonparametric Fisher-Rao metric. While the framework is general in spirit, the focus of this article is restricted to…

We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…

Background: Continuous traits evolution of a group of taxa that are correlated through a phylogenetic tree is commonly modelled using parametric stochastic differential equations to represent deterministic change of trait through time,…

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In…

We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…

We present a robust Bayesian method to analyze forestry data when samples are selected with probability proportional to length from a finite population of unknown size. Specifically, we use Bayesian predictive inference to estimate the…

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…

Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the…

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…