Related papers: Inference for SDE models via Approximate Bayesian …

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC…

For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set…

Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an…

Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the…

We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and…

State space models (SSMs) are widely used to describe dynamic systems. However, when the likelihood of the observations is intractable, parameter inference for SSMs cannot be easily carried out using standard Markov chain Monte Carlo or…

This paper presents a novel approach to level set estimation for any function/simulation with an arbitrary number of continuous inputs and arbitrary numbers of continuous responses. We present a method that uses existing data from computer…

Approximate Bayesian computation (ABC) methods are used to approximate posterior distributions using simulation rather than likelihood calculations. We introduce Gaussian process (GP) accelerated ABC, which we show can significantly reduce…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

We propose a novel approach to approximate Bayesian computation (ABC) that seeks to cater for possible misspecification of the assumed model. This new approach can be equally applied to rejection-based ABC and to popular regression…

Despite their widespread applications, Large Language Models (LLMs) often struggle to express uncertainty, posing a challenge for reliable deployment in high stakes and safety critical domains like clinical diagnostics. Existing standard…

Bayesian methods have shown success in deep learning applications. For example, in predictive tasks, Bayesian neural networks leverage Bayesian reasoning of model uncertainty to improve the reliability and uncertainty awareness of deep…

Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…

Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…

Scientists often express their understanding of the world through a computationally demanding simulation program. Analyzing the posterior distribution of the parameters given observations (the inverse problem) can be extremely challenging.…

Also known as likelihood-free methods, approximate Bayesian computational (ABC) methods have appeared in the past ten years as the most satisfactory approach to untractable likelihood problems, first in genetics then in a broader spectrum…

Minimax optimization problems have attracted a lot of attention over the past few years, with applications ranging from economics to machine learning. While advanced optimization methods exist for such problems, characterizing their…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process, computational cost can be prohibitive for networks of…