Related papers: Piecewise Deterministic Markov Processes for Bayes…
An important task of uncertainty quantification is to identify {the probability of} undesired events, in particular, system failures, caused by various sources of uncertainties. In this work we consider the construction of Gaussian…
Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…
The Bouncy Particle Sampler is a Markov chain Monte Carlo method based on a nonreversible piecewise deterministic Markov process. In this scheme, a particle explores the state space of interest by evolving according to a linear dynamics…
The computational efficiency of approximate Bayesian computation (ABC) has been improved by using surrogate models such as Gaussian processes (GP). In one such promising framework the discrepancy between the simulated and observed data is…
Digital twins are developed to model the behavior of a specific physical asset (or twin), and they can consist of high-fidelity physics-based models or surrogates. A highly accurate surrogate is often preferred over multi-physics models as…
We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts for uncertainty in…
Bayesian optimization is a highly efficient approach to optimizing objective functions which are expensive to query. These objectives are typically represented by Gaussian process (GP) surrogate models which are easy to optimize and support…
A piecewise-deterministic Markov process, specified by random jumps and switching semi-flows, as well as the associated Markov chain given by its post-jump locations, are investigated in this paper. The existence of an exponentially…
We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the…
Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. However, when employing GPs in practice, important considerations must be made, regarding the high computational burden,…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…
Stochastic Petri Nets (SPNs) are an increasingly popular tool of choice for modeling discrete-event dynamics in areas such as epidemiology and systems biology, yet their parameter estimation remains challenging in general and in particular…
General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate…
We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
The paper addresses Bayesian inferences in inverse problems with uncertainty quantification involving a computationally expensive forward map associated with solving a partial differential equations. To mitigate the computational cost, the…
A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For…
We present a numerical method to compute the survival function and the moments of the exit time for a piecewise-deterministic Markov process (PDMP). Our approach is based on the quantization of an underlying discrete-time Markov chain…
We propose a Bayesian nonparametric mixture model for the reconstruction and prediction from observed time series data, of discretized stochastic dynamical systems, based on Markov Chain Monte Carlo methods (MCMC). Our results can be used…
Modeled along the truncated approach in Panigrahi (2016), selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection…
Partially observed Markov process (POMP) models are powerful tools for time series modeling and analysis. Inherited the flexible framework of R package pomp, the is2 package extends some useful Monte Carlo statistical methodologies to…