Related papers: Predictive Characterization of Mixtures of Markov …
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…
We present a new kind of structural Markov property for probabilistic laws on decomposable graphs, which allows the explicit control of interactions between cliques, so is capable of encoding some interesting structure. We prove the…
We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
Finite mixture and Markov-switching models generalize and, therefore, nest specifications featuring only one component. While specifying priors in the two: the general (mixture) model and its special (single-component) case, it may be…
We study the stochastic dynamics of a system of interacting species in a stochastic environment by means of a continuous-time Markov chain with transition rates depending on the state of the environment. Models of gene regulation in systems…
It is shown that the combinatorics of commutation relations is well suited for analyzing the convergence rate of certain Markov chains. Examples studied include random walk on irreducible representations, a local random walk on partitions…
We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from…
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] 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…
Markov processes are popular mathematical models, studied by theoreticians for their intriguing properties, and applied by practitioners for their flexible structure. With this book we teach how to model and analyze Markov processes. We…
We define the concept of an `open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of…
Substitution Markov chains have been introduced [7] as a new model to describe molecular evolution. In this note, we study the associated Martin boundaries from a probabilistic and topological viewpoint. An example is given that, although…
The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…
A sequence of real numbers (x_n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x_n) are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov…
Though the notion of exchangeability has been discussed in the causal inference literature under various guises, it has rarely taken its original meaning as a symmetry property of probability distributions. As this property is a standard…
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…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This can be done by considering as basic uncertainty models the so-called credal sets that…
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully…
We consider hundreds of thousands of individual economic transactions to ask: how predictable are consumers in their merchant visitation patterns? Our results suggest that, in the long-run, much of our seemingly elective activity is…