Convergence in Markovian models with implications for efficiency of inference

• Published in: International journal of approximate reasoning Vol. 46; no. 2; pp. 300 - 319
• Main Authors: Charitos, Theodore, de Waal, Peter R., van der Gaag, Linda C.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier Inc 01-10-2007; Elsevier
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Consecutive similar observations; Convergence; Efficiency; Exact sciences and technology; Inference; Learning and adaptive systems; Markovian models; Software; Inference; Consecutive similar observations; Markovian models; Efficiency; Convergence; Statistical analysis; Probabilistic approach; Probability distribution; Markov model; Distributed system; Stochastic process; Modeling; Limit distribution; Posterior probability; Hidden Markov model; Bayes network; Convergence rate; Dynamic model; Artificial intelligence; Medical application; Posterior distribution
• ISSN: 0888-613X; 1873-4731
• DOI: 10.1016/j.ijar.2006.09.011

Sequential statistical models such as dynamic Bayesian networks and hidden Markov models more specifically, model stochastic processes over time. In this paper, we study for these models the effect of consecutive similar observations on the posterior probability distribution of the represented process. We show that, given such observations, the posterior distribution converges to a limit distribution. Building upon the rate of the convergence, we further show that, given some wished-for level of accuracy, part of the inference can be forestalled. To evaluate our theoretical results, we study their implications for a real-life model from the medical domain and for a benchmark model for agricultural purposes. Our results indicate that whenever consecutive similar observations arise, the computational requirements of inference in Markovian models can be drastically reduced.