Related papers: Exact Bayesian inference in spatio-temporal Cox pr…

In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…

Increasingly complex applications involve large datasets in combination with non-linear and high dimensional mathematical models. In this context, statistical inference is a challenging issue that calls for pragmatic approaches that take…

A central task in many applications is reasoning about processes that change over continuous time. Continuous-Time Bayesian Networks is a general compact representation language for multi-component continuous-time processes. However, exact…

Physical systems can often be described via a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors,…

We introduce a class of spatial stochastic processes in the max-domain of attraction of familiar max-stable processes. The new class is based on Cox processes and comprises models with short range dependence. We show that statistical…

We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…

High-precision measurements require optimal setups and analysis tools to achieve continuous improvements. Systematic corrections need to be modeled with high accuracy and known uncertainty to reconstruct underlying physical phenomena. To…

Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…

A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian…

Mechanistic models of single-neuron dynamics have been extensively studied in computational neuroscience. However, identifying which models can quantitatively reproduce empirically measured data has been challenging. We propose to overcome…

We introduce a Bayesian approach for multivariate spatio-temporal prediction for high-dimensional count-valued data. Our primary interest is when there are possibly millions of data points referenced over different variables, geographic…

Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…

We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…

We propose a flexible Bayesian approach for estimating the joint density of a multivariate outcome of interest in the presence of categorical covariates. Leveraging a Gaussian copula framework, our method effectively captures the dependence…

Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…

In this article, an overview of Bayesian methods for sequential simulation from posterior distributions of nonlinear and non-Gaussian dynamic systems is presented. The focus is mainly laid on sequential Monte Carlo methods, which are based…

This paper presents a new accelerated proximal Markov chain Monte Carlo methodology to perform Bayesian inference in imaging inverse problems with an underlying convex geometry. The proposed strategy takes the form of a stochastic relaxed…

We propose a class of dynamic vine copula models. This is an extension of static vine copulas and a generalization of dynamic C-vine and D-vine copulas studied by Almeida et al (2016) and Goel and Mehra (2019). Within this class, we allow…

Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…

Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…