Related papers: In-Context Parametric Inference: Point or Distribu…

We present a multi-fidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional…

Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…

Statistics comes in two main flavors: frequentist and Bayesian. For historical and technical reasons, frequentist statistics has dominated data analysis in the past; but Bayesian statistics is making a comeback at the forefront of science.…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…

We compare the accuracy, precision and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modelling and…

Especially when facing reliability data with limited information (e.g., a small number of failures), there are strong motivations for using Bayesian inference methods. These include the option to use information from physics-of-failure or…

We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…

This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derived based on the limited information…

Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…

Consider a linear regression model with regression parameter beta and normally distributed errors. Suppose that the parameter of interest is theta = a^T beta where a is a specified vector. Define the parameter tau = c^T beta - t where c and…

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…

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…

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…

We consider amortized Bayesian inference for nonlinear inverse problems in settings where only samples from the joint distribution of parameters and observations are available. Classical methods such as Markov chain Monte Carlo require…

Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…

We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…