Related papers: Predictive Characterization of Mixtures of Markov …
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
Predictive equivalence in discrete stochastic processes have been applied with great success to identify randomness and structure in statistical physics and chaotic dynamical systems and to inferring hidden Markov models. We examine the…
Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…
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,…
Markov Chains with variable length are useful stochastic models for data compression that avoid the curse of dimensionality faced by that full Markov Chains. In this paper we introduce a Variable Length Markov Chain whose transition…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
Markov chains with variable length are useful parsimonious stochastic models able to generate most stationary sequence of discrete symbols. The idea is to identify the suffixes of the past, called contexts, that are relevant to predict the…
In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,. . .) and they are…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as…
In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…
Rule-based modelling allows to represent molecular interactions in a compact and natural way. The underlying molecular dynamics, by the laws of stochastic chemical kinetics, behaves as a continuous-time Markov chain. However, this Markov…
We analyse the structure of imprecise Markov chains and study their convergence by means of accessibility relations. We first identify the sets of states, so-called minimal permanent classes, that are the minimal sets capable of containing…
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
We give a probabilistic characterization of the set of measures that can be represented by the matrix product ansatz. By suitably enlarging the state space, we show that a probability measure can be described in terms of non negative…
We extend de Finetti's (1937) notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than (linear) previsions. We prove…
Probabilistic model checking for systems with large or unbounded state space is a challenging computational problem in formal modelling and its applications. Numerical algorithms require an explicit representation of the state space, while…
A Profile Mixture Model is a model of protein evolution, describing sequence data in which sites are assumed to follow many related substitution processes on a single evolutionary tree. The processes depend in part on different amino acid…
Markov chains provide a foundational framework for modeling sequential stochastic processes, with the transition probability matrix characterizing the dynamics of state evolution. While classical estimation methods such as maximum…