Mathematics – Statistics Theory
Scientific paper
2007-03-24
Mathematics
Statistics Theory
14 pages, 12 figures; http://cse.ucdavis.edu/~cmg/compmech/pubs/imc.html
Scientific paper
10.1103/PhysRevE.76.011106
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a novel method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.
Crutchfield James P.
Hubler Alfred W.
Strelioff Christopher C.
No associations
LandOfFree
Inferring Markov Chains: Bayesian Estimation, Model Comparison, Entropy Rate, and Out-of-class Modeling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Inferring Markov Chains: Bayesian Estimation, Model Comparison, Entropy Rate, and Out-of-class Modeling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inferring Markov Chains: Bayesian Estimation, Model Comparison, Entropy Rate, and Out-of-class Modeling will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-360969