Related papers: Evidential Decision Theory via Partial Markov Cate…
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
In this paper we extend the predicate logic introduced in [Beauquier et al. 2002] in order to deal with Semi-Markov Processes. We prove that with respect to qualitative probabilistic properties, model checking is decidable for this logic…
The synthesis problem for partially observable Markov decision processes (POMDPs) is to compute a policy that satisfies a given specification. Such policies have to take the full execution history of a POMDP into account, rendering the…
We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases…
In this paper, we develop category theory of Markov kernels to study categorical aspects of Bayesian inversions. As a result, we present a unified model for Bayesian supervised learning, encompassing Bayesian density estimation. We…
We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To…
We study sequential Bayesian inference in stochastic kinetic models with latent factors. Assuming continuous observation of all the reactions, our focus is on joint inference of the unknown reaction rates and the dynamic latent states,…
Markov categories are the central framework for categorical probability theory. Many important concepts from probability theory can be formalized in terms of Markov categories. In particular, conditional probability distributions and Bayes'…
We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…
We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…
Recently, a class of stochastic processes known as piecewise deterministic Markov processes has been used to define continuous-time Markov chain Monte Carlo algorithms with a number of attractive properties, including compatibility with…
The present work develops a construction of a CD category of partial kernels from a particular type of Markov category called a partializable Markov category. These are a generalization of earlier models of categories of partial morphisms…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…
Markov categories have recently turned out to be a powerful high-level framework for probability and statistics. They accommodate purely categorical definitions of notions like conditional probability and almost sure equality, as well as…
The roles played by decision factors in making complex subject are decisions are characterized by how these factors affect the overall decision. Evidence that partially matches a factor is evaluated, and then effective computational rules…
We study a category of probability spaces and measure-preserving Markov kernels up to almost sure equality. This category contains, among its isomorphisms, mod-zero isomorphisms of probability spaces. It also gives an isomorphism between…
In this paper we will give a categorical proof of the Radon-Nikodym theorem. We will do this by describing the trivial version of the result on finite probability spaces as a natural isomorphism. We then proceed to Kan extend this…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…