Related papers: Improper vs finitely additive distributions as lim…
This paper examines the joint problem of detection and identification of a sudden and unobservable change in the probability distribution function (pdf) of a sequence of independent and identically distributed (i.i.d.) random variables to…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one…
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…
We investigate the occurrence of additive and multiplicative structures in random subsets of the natural numbers. Specifically, for a Bernoulli random subset of $\mathbb{N}$ where each integer is included independently with probability…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
We present theoretical analysis and a suite of tests and procedures for addressing a broad class of redundant and misleading association rules we call \emph{specious rules}. Specious dependencies, also known as \emph{spurious},…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
Computing the similarity between two probability distributions is a recurring theme across control. We introduce a unified family of distances between the probability distributions of two random variables that is based on the discrepancy…
We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution $Q$ to be approximated and its proxy $P$. This non-symmetric…
We study the problem of bounding the posterior distribution of discrete probabilistic programs with unbounded support, loops, and conditioning. Loops pose the main difficulty in this setting: even if exact Bayesian inference is possible,…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
For a fixed positive integer d, we show the existence of the limiting gap distribution measure for the sets of Farey fractions a/q of order Q with a not divisible by d, and respectively with q relatively prime with d, as Q tends to…
Real-time probability forecasts for binary outcomes are routine in sports, online experimentation, medicine, and finance. Retrospective narratives, however, often hinge on pathwise extremes: for example, a forecast that becomes "90%…
In many covering settings, it is natural to consider the presence both of elements that we seek to include and of elements that we seek to avoid. This paper introduces a novel combinatorial problem formalizing this tradeoff: from a…
Approximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy…
Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well-suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing…
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…
Probabilistic Answer Set Programming under the credal semantics (PASP) extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However,…