Related papers: Some developments of exchangeable measure-valued P…
Matrix Dirichlet processes, in reference to their reversible measure, appear in a natural way in many different models in probability. Applying the language of diffusion operators and the method of boundary equations, we describe Dirichlet…
Importance sampling is a Monte Carlo technique for efficiently estimating the likelihood of rare events by biasing the sampling distribution towards the rare event of interest. By drawing weighted samples from a learned proposal…
Some characterizations of mixed renewal processes in terms of exchangeability and of different types of disintegrations are given. As a consequence, an existence result for mixed renewal processes, providing also a new construction for…
Markov chain Monte Carlo (MCMC) methods are simulated by local exploration of complex statistical distributions, and while bypassing the cumbersome requirement of a specific analytical expression for the target, this stochastic exploration…
Based on previous work of Paul Ressel and myself, I show that the space of all "continuous" exchangeable probability measures on a certain set of order processes is a Bauer simplex.
We define and prove limit results for a class of dominant P\'olya sequences, which are randomly reinforced urn processes with color-specific random weights and unbounded number of possible colors. Under fairly mild assumptions on the…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call…
We consider a piecewise-deterministic Markov process (PDMP) with general conditional distribution of inter-occurrence time, which is called a general PDMP here. Our purpose is to establish the theory of measure-valued generator for general…
Discrete random probability measures and the exchangeable random partitions they induce are key tools for addressing a variety of estimation and prediction problems in Bayesian inference. Indeed, many popular nonparametric priors, such as…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
We study the distribution of the unobserved states of two measure-valued diffusions of Fleming-Viot and Dawson-Watanabe type, conditional on observations from the underlying populations collected at past, present and future times. If seen…
This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous…
Let $(\mathbf{W,W'})$ be an exchangeable pair of vectors in $\mathbb{R}^k$. Suppose this pair satisfies \beas E(\mathbf{W}'|\mathbf{W})=(I_k-\Lambda)\mathbf{W}+\mathbf{R(W)}. \enas If $||\mathbf{W-W'}||_2\le K$ and $\mathbf{R(W)}=0$, then…
Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same…
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…
We construct the entropic measure $\mathbb{P}^\beta$ on compact manifolds of any dimension. It is defined as the push forward of the Dirichlet process (another random probability measure, well-known to exist on spaces of any dimension)…
We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive…
Stochastic linear combinations of some random vectors are studied where the distribution of the random vectors and the joint distribution of their coefficients are Dirichlet. A method is provided for calculating the distribution of these…
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 presents a Distributed Stochastic Model Predictive Control algorithm for networks of linear systems with multiplicative uncertainties and local chance constraints on the states and control inputs. The chance constraints are…