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Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…

The statistical evidence (or marginal likelihood) is a key quantity in Bayesian statistics, allowing one to assess the probability of the data given the model under investigation. This paper focuses on refining the power posterior approach…

In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid…

We investigate the theoretical foundations of the simulated tempering method and use our findings to design efficient algorithms. Employing a large deviation argument first used for replica exchange molecular dynamics [Plattner et al., J.…

In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…

Tempering is a popular tool in Bayesian computation, being used to transform a posterior distribution $p_1$ into a reference distribution $p_0$ that is more easily approximated. Several algorithms exist that start by approximating $p_0$ and…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

In this short note, we show how the parallel adaptive Wang-Landau (PAWL) algorithm of Bornn et al. (2013) can be used to automate and improve simulated tempering algorithms. While Wang-Landau and other stochastic approximation methods have…

Bayesian inference provides a principled probabilistic framework for quantifying uncertainty by updating beliefs based on prior knowledge and observed data through Bayes' theorem. In Bayesian deep learning, neural network weights are…

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…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

Bayesian inference is useful to obtain a predictive distribution with a small generalization error. However, since posterior distributions are rarely evaluated analytically, we employ the variational Bayesian inference or sampling method to…

Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior…

This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a…

Bayesian Optimization is methodology used in statistical modelling that utilizes a Gaussian process prior distribution to iteratively update a posterior distribution towards the true distribution of the data. Finding unbiased informative…

We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…

We conduct a detailed investigation of tempered posteriors and uncover a number of crucial and previously undiscussed points. Contrary to previous results, we first show that for realistic models and datasets and the tightly controlled case…