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Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient…
Density deconvolution is the task of estimating a probability density function given only noise-corrupted samples. We can fit a Gaussian mixture model to the underlying density by maximum likelihood if the noise is normally distributed, but…
In this paper some initial work towards a new approach to qualitative reasoning under uncertainty is presented. This method is not only applicable to qualitative probabilistic reasoning, as is the case with other methods, but also allows…
This paper offers a qualitative insight into the convergence of Bayesian parameter inference in a setup which mimics the modeling of the spread of a disease with associated disease measurements. Specifically, we are interested in the…
The Hastings algorithm is a key tool in computational science. While mathematically justified by detailed balance, it can be conceptually difficult to grasp. Here, we present two complementary and intuitive ways to derive and understand the…
Combining measurements which have "theoretical uncertainties" is a delicate matter, due to an unclear statistical basis. We present an algorithm based on the notion that a theoretical uncertainty represents an estimate of bias.
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
We develop a general theory to address a consensus-based combination of estimations in a parallelized or distributed estimation setting. Taking into account the possibility of very discrepant estimations, instead of a full consensus we…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
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…
This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…