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The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test…
This is a review of asymptotic and non-asymptotic behaviour of Bayesian methods under model specification. In particular we focus on consistency, i.e. convergence of the posterior distribution to the point mass at the best parametric…
An informative sampling design leads to the selection of units whose inclusion probabilities are correlated with the response variable of interest. Model inference performed on the resulting observed sample will be biased for the population…
We consider the problem of distributed estimation, where local processors observe independent samples conditioned on a common random parameter of interest, map the observations to a finite number of bits, and send these bits to a remote…
The Tweedie Compound Poisson-Gamma model is routinely used for modeling non-negative continuous data with a discrete probability mass at zero. Mixed models with random effects account for the covariance structure related to the grouping…
This research deals with the estimation and imputation of missing data in longitudinal models with a Poisson response variable inflated with zeros. A methodology is proposed that is based on the use of maximum likelihood, assuming that data…
The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted…
Suppose data are fitted to some parametric model but that the true model happens to be one with an additional parameter. When a parameter is to be estimated one can use likelihood estimation in the wider model or in the narrow model.…
Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
We develop a semiparametric Bayesian approach for estimating the mean response in a missing data model with binary outcomes and a nonparametrically modelled propensity score. Equivalently we estimate the causal effect of a treatment,…
We consider the Bayesian analysis of a few complex, high-dimensional models and show that intuitive priors, which are not tailored to the fine details of the model and the estimated parameters, produce estimators which perform poorly in…
Bayesian optimal experimental design provides a principled framework for selecting experimental settings that maximize obtained information. In this work, we focus on estimating the expected information gain in the setting where the…
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…
Image noise can often be accurately fitted to a Poisson-Gaussian distribution. However, estimating the distribution parameters from a noisy image only is a challenging task. Here, we study the case when paired noisy and noise-free samples…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
The Poisson distribution is often used as a standard model for count data. Quite often, however, such data sets are not well fit by a Poisson model because they have more zeros than are compatible with this model. For these situations, a…
Suppose that $X_1,X_2,\ldots$ are a stream of independent, identically distributed Poisson random variables with mean $\mu$. This work presents a new estimate $\mu_k$ for $\mu$ with the property that the distribution of the relative error…
This paper develops a Bayesian framework for robust causal inference from longitudinal observational data. Many contemporary methods rely on structural assumptions, such as factor models, to adjust for unobserved confounding, but they can…
The binary information collects all those events that may or may not occur. With this kind of variables, a large amount of information can be captured, in particular, about financial assets and their future trends. In our paper, we assume…