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Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
Recent decades have seen an interest in prediction problems for which Bayesian methodology has been used ubiquitously. Sampling from or approximating the posterior predictive distribution in a Bayesian model allows one to make inferential…
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the…
As machine learning models are increasingly deployed in dynamic environments, it becomes paramount to assess and quantify uncertainties associated with distribution shifts. A distribution shift occurs when the underlying data-generating…
Given a sequence \xi_1, \xi_2,... of X-valued, exchangeable random elements, let q(\xi^(n)) and p_m(\xi^(n)) stand for posterior and predictive distribution, respectively, given \xi^(n) = (\xi_1,..., \xi_n). We provide an upper bound for…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…
Quantifying uncertainty in automatically generated text is important for letting humans check potential hallucinations and making systems more reliable. Conformal prediction is an attractive framework to provide predictions imbued with…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
We characterize the exponential distribution as the only one which satisfies a regression condition. This condition involves the regression function of a fixed record value given two other record values, one of them being previous and the…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…
The analysis of practical probabilistic models on the computer demands a convenient representation for the available knowledge and an efficient algorithm to perform inference. An appealing representation is the influence diagram, a network…
A characterization of the exponential distribution based on equidistribution conditions for maxima of random samples with consecutive sizes n-1 and n for an arbitrary and fixed n>2 is proved. This solves an open problem stated recently in…
We consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…
Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…
We introduce a general Bayesian framework for graph matching grounded in a new theory of exchangeable random permutations. Leveraging the cycle representation of permutations and the literature on exchangeable random partitions, we define,…