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Generative models based on diffusion have become the state of the art in the last few years, notably for image generation. Here, we analyse them in the high-dimensional limit, where data are formed by a very large number of variables. We…
In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability…
Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…
Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…
We present an error-diagnostic validation method for posterior distributions in Bayesian signal inference, an advancement of a previous work. It transfers deviations from the correct posterior into characteristic deviations from a uniform…
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…
Bayesian optimal design is a well-established approach to planning experiments. A distribution for the responses, i.e. a statistical model, is assumed which is dependent on unknown parameters. A utility function is then specified giving…
In segmentation problems, inference on change-point position and model selection are two difficult issues due to the discrete nature of change-points. In a Bayesian context, we derive exact, non-asymptotic, explicit and tractable formulae…
The methodology developed in this article is motivated by a wide range of prediction and uncertainty quantification problems that arise in Statistics, Machine Learning and Applied Mathematics, such as non-parametric regression, multi-class…
Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…
Spike-and-slab priors are popular Bayesian solutions for high-dimensional linear regression problems. Previous theoretical studies on spike-and-slab methods focus on specific prior formulations and use prior-dependent conditions and…
Many modern experiments, such as microarray gene expression and genome-wide association studies, present the problem of estimating a large number of parallel effects. Bayesian inference is a popular approach for analyzing such data by…
We present Wideband Back-Projection Diffusion, an end-to-end probabilistic framework for approximating the posterior distribution induced by the inverse scattering map from wideband scattering data. This framework produces highly accurate…
Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…
We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…
In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…
In this paper we adopt the familiar sparse, high-dimensional linear regression model and focus on the important but often overlooked task of prediction. In particular, we consider a new empirical Bayes framework that incorporates data in…
For a classification problem described by the joint density $P(\omega,x)$, models of $P(\omega\eq\omega'|x,x')$ (the ``Bayesian similarity measure'') have been shown to be an optimal similarity measure for nearest neighbor classification.…
Probabilistic models analyze data by relying on a set of assumptions. Data that exhibit deviations from these assumptions can undermine inference and prediction quality. Robust models offer protection against mismatch between a model's…