Related papers: De Finetti + Sanov = Bayes
We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically…
This paper studies a class of exponential family models whose canonical parameters are specified as linear functionals of an unknown infinite-dimensional slope function. The optimal minimax rates of convergence for slope function estimation…
In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…
Chernoff information upper bounds the probability of error of the optimal Bayesian decision rule for $2$-class classification problems. However, it turns out that in practice the Chernoff bound is hard to calculate or even approximate. In…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions…
The prior distribution on parameters of a sampling distribution is the usual starting point for Bayesian uncertainty quantification. In this paper, we present a different perspective which focuses on missing observations as the source of…
We point out that the quantum de Finetti representation, unique for infinitely extendable exchangeable systems, assigns a non-zero Quantum Discord to uncorrelated systems and thus cannot serve as an universal prior distribution in the…
We study stochastic team (known also as decentralized stochastic control or identical interest stochastic dynamic game) problems with large or countably infinite number of decision makers, and characterize existence and structural…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various…
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…
Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…
This paper reformulates a classical result in probability theory from the 1930s in modern categorical terms: de Finetti's representation theorem is redescribed as limit statement for a chain of finite spaces in the Kleisli category of the…
In statistical practice, a realistic Bayesian model for a given data set can be defined by a likelihood function that is analytically or computationally intractable, due to large data sample size, high parameter dimensionality, or complex…
In order to improve forecasts, a decisionmaker often combines probabilities given by various sources, such as human experts and machine learning classifiers. When few training data are available, aggregation can be improved by incorporating…
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via the Bayes theorem. In usual fluctuation theorems, a forward path and its…
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…
In causal inference, and specifically in the \textit{Causes of Effects} problem, one is interested in how to use statistical evidence to understand causation in an individual case, and so how to assess the so-called {\em probability of…