Related papers: Tweedie's Formula and Score-Driven Updating
Recursive graphical models usually underlie the statistical modelling concerning probabilistic expert systems based on Bayesian networks. This paper defines a version of these models, denoted as recursive exponential models, which have…
This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…
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…
Early identification of at risk students in higher education depends on predictive models that maintain accuracy across successive cohorts -- a requirement that single-cohort modeling approaches fail to meet. This study evaluates Bayesian…
Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score…
Denoising and score estimation have long been known to be linked via the classical Tweedie's formula. In this work, we first extend the latter to a wider range of distributions often called "energy models" and denoted elliptical…
Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…
The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…
Methods for automated discovery of causal relationships from non-interventional data have received much attention recently. A widely used and well understood model family is given by linear acyclic causal models (recursive structural…
We study the conjugacy approximation method in the context of Bayesian ranking and selection with unknown correlations. Under the assumption of normal-inverse-Wishart prior distribution, the posterior distribution remains a…
We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional…
In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case, where the prior distribution belongs to the…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
Statistical inference may follow a frequentist approach or it may follow a Bayesian approach or it may use the minimum description length principle (MDL). Our goal is to identify situations in which these different approaches to statistical…
This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning…
The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…
In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…
Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is…
A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…