Related papers: Poisson representations for tree-indexed Markov ch…
We define representations of continuous functions on infinite streams of discrete values, both in the case of discrete-valued functions, and in the case of stream-valued functions. We define also an operation on the representations of two…
Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
We investigate the mixed spin-$(s,\tfrac12)$ Ising model on a Cayley tree of order three ($k=3$), extending the approach of \cite{Akin2024}. For the representative case $s=5$, the associated recursion leads to an 11-dimensional dynamical…
We prove several results concerning classifications, based on successive observations $(X_1,..., X_n)$ of an unknown stationary and ergodic process, for membership in a given class of processes, such as the class of all finite order Markov…
We study Markov processes where the "time" parameter is replaced by paths in a directed graph from an initial vertex to a terminal one. Along each directed path the process is Markov and has the same distribution as the one along any other…
In this paper, we introduce Max Markov Chain (MMC), a novel representation for a useful subset of High-order Markov Chains (HMCs) with sparse correlations among the states. MMC is parsimony while retaining the expressiveness of HMCs. Even…
A new branch based on Markov processes is developing in the recent literature of financial time series modeling. In this paper, an Indexed Markov Chain has been used to model high frequency price returns of quoted firms. The peculiarity of…
Autoregressive models enable tractable sampling from learned probability distributions, but their performance critically depends on the variable ordering used in the factorization via complexities of the resulting conditional distributions.…
Suppose $ E$ is a space with a null-recurrent Markov kernel $ P$. Furthermore, suppose there are infinite particles with variable weights on $ E$ performing a random walk following $ P$. Let $ X_{t}$ be a weighted functional of the position…
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…
Max-linear Bayesian networks have emerged as highly applicable models for causal inference via extreme value data. However, conditional independence (CI) for max-linear Bayesian networks behaves differently than for classical Gaussian…
We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric…
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…
We investigate a spatial random graph model whose vertices are given as a marked Poisson process on $\mathbb{R}^d$. Edges are inserted between any pair of points independently with probability depending on the spatial displacement of the…
Conditionally Markov (CM) sequences are powerful mathematical tools for modeling problems. One class of CM sequences is the reciprocal sequence. In application, we need not only CM dynamic models, but also know how to design model…
Continuous-time Markov chains describing interacting processes exhibit a state space that grows exponentially in the number of processes. This state-space explosion renders the computation or storage of the time-marginal distribution, which…
In the present paper, we construct quantum Markov chains (QMC) over the Comb graphs. As an application of this construction, it is proved the existence of the disordered phase for the Ising type models (within QMC scheme) over the Comb…
Poisson representation techniques provide a powerful method for mapping master equations for birth/death processes -- found in many fields of physics, chemistry and biology -- into more tractable stochastic differential equations. However,…
We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with…