Related papers: A synthetic approach to Markov kernels, conditiona…
Real-world complex systems are often modelled by sets of equations with endogenous and exogenous variables. What can we say about the causal and probabilistic aspects of variables that appear in these equations without explicitly solving…
We study product regular conditional probabilities under measures of two coordinates with respect to the second coordinate that are weakly continuous on the support of the marginal of the second coordinate. Assuming that there exists a…
Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov…
The present contribution derives an explicit expression for (a version of) every uni- and multi-variate conditional distribution (i.e., Markov kernel) of Archimedean copulas and uses this representation to generalize a recently established…
Necessary and sufficient conditions are given for a substochastic semigroup on $L^1$ obtained through the Kato--Voigt perturbation theorem to be either stochastic or strongly stable. We show how such semigroups are related to piecewise…
Markov random fields provide a compact representation of joint probability distributions by representing its independence properties in an undirected graph. The well-known Hammersley-Clifford theorem uses these conditional independences to…
Inference in current domains of application are often complex and require us to integrate the expertise of a variety of disparate panels of experts and models coherently. In this paper we develop a formal statistical methodology to guide…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
We introduce a general framework for measuring risk in the context of Markov control processes with risk maps on general Borel spaces that generalize known concepts of risk measures in mathematical finance, operations research and…
Inference metaprogramming enables effective probabilistic programming by supporting the decomposition of executions of probabilistic programs into subproblems and the deployment of hybrid probabilistic inference algorithms that apply…
We analyze multidimensional Markovian integral equations that are formulated with a time-inhomogeneous progressive Markov process that has Borel measurable transition probabilities. In the case of a path-dependent diffusion process, the…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
The ability to synthesize realistic data in a parametrizable way is valuable for a number of reasons, including privacy, missing data imputation, and evaluating the performance of statistical and computational methods. When the underlying…
We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e.g. these observations are collected…
Introduced in the 1990s in the context of the algebraic approach to graph rewriting, gs-monoidal categories are symmetric monoidal categories where each object is equipped with the structure of a commutative comonoid. They arise for example…
We propose a method for learning Markov network structures for continuous data without invoking any assumptions about the distribution of the variables. The method makes use of previous work on a non-parametric estimator for mutual…
We propose two new measures for extracting the unique information in $X$ and not $Y$ about a message $M$, when $X, Y$ and $M$ are joint random variables with a given joint distribution. We take a Markov based approach, motivated by…