Poisson-Driven Stationary Markov Models

Learning Markov Models for Stationary System Behaviors

Abstract. Establishing an accurate model for formal verification of an existing hardware or software system is often a manual process that is both time consuming and resource demanding. In order to ease the model construction phase, methods have recently been proposed for automatically learning accurate system models from data in the form of observations of the target system. Common for these a...

Observation Driven Models for Poisson Counts

This paper is concerned with a general class of observation driven models for time series of counts whose conditional distributions given past observations and explanatory variables follow a Poisson distribution. These models provide a flexible framework for modeling a wide range of dependence structures. Conditions for stationarity and ergodicity of these processes are established from which t...

A reservoir-driven non-stationary hidden Markov model

In this work, we propose a novel approach towards sequential data modeling that leverages the strengths of hidden Markov models and echo-state networks (ESNs) in the context of nonparametric Bayesian inference approaches. We introduce a non-stationary hidden Markov model, the time-dependent state transition probabilities of which are driven by a high-dimensional signal that encodes the whole hi...

Multivariate Poisson Hidden Markov Models for Analysis of Spatial Counts

Bayesian posterior mean estimates for Poisson hidden Markov models

This paper focuses on the Bayesian posterior mean estimates (or Bayes’ estimate) of the parameter set of Poisson hidden Markov models in which the observation sequence is generated by a Poisson distribution whose parameter depends on the underlining discrete-time time-homogeneous Markov chain. Although the most commonly used procedures for obtaining parameter estimates for hidden Markov models ...