Related papers: De Finetti + Sanov = Bayes

The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach…

Multi-class systems having possibly both finite and infinite classes are investigated under a natural partial exchangeability assumption. It is proved that the conditional law of such a system, given the vector of the empirical measures of…

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…

Causal discovery methods have traditionally been developed under two different modeling assumptions: independent and identically distributed (i.i.d.) data and time series data. In this paper, we focus on the i.i.d. setting, arguing that it…

We introduce a framework uniting algorithmic randomness with exchangeable credences to address foundational questions in philosophy of probability and philosophy of science. To demonstrate its power, we show how one might use the framework…

We survey known solutions to the infinite extendibility problem for (necessarily exchangeable) probability laws on $\mathbb{R}^d$, which is: Can a given random vector $\vec{X} = (X_1,\ldots,X_d)$ be represented in distribution as the first…

Much is now known about the consistency of Bayesian updating on infinite-dimensional parameter spaces with independent or Markovian data. Necessary conditions for consistency include the prior putting enough weight on the correct…

The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…

This paper modifies Jaynes's axioms of plausible reasoning and derives the minimum relative entropy principle, Bayes's rule, as well as maximum likelihood from first principles. The new axioms, which I call the Optimum Information…

In solving Bayesian inverse problems, it is often desirable to use a common density parameterization to denote the prior and posterior. Typically we seek a density from the same family as the prior which closely approximates the true…

It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…

Although Bayes's theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes's theorem sometimes generates sensible procedures from improper priors, Pitman's estimator being a good…

We show how Bruno de Finetti's fundamental theorem of prevision has computable applications in statistical problems that involve only partial information. Specifically, we assess accuracy rates for median decision procedures used in the…

We propose a class of transformation hazard models for right-censored failure time data. It includes the proportional hazards model (Cox) and the additive hazards model (Lin and Ying) as special cases. Due to the requirement of a…

Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…

We develop the concept of exponential stochastic inequality (ESI), a novel notation that simultaneously captures high-probability and in-expectation statements. It is especially well suited to succinctly state, prove, and reason about…

Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…

A predictive distribution over a sequence of $N+1$ events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first $N$ events equals the relative frequency of successes among…

Bayesian persuasion is the study of information sharing policies among strategic agents. A prime example is signaling in online ad auctions: what information should a platform signal to an advertiser regarding a user when selling the…

Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn latent representations in modern multivariate data sets with complex dependency structures. Among…