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Assessing the Goodness‐of‐Fit of Hidden Markov Models
Author(s) -
MacKay Altman Rachel
Publication year - 2004
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2004.00189.x
Subject(s) - goodness of fit , univariate , hidden markov model , mathematics , statistics , markov chain , marginal distribution , empirical distribution function , markov model , computer science , econometrics , multivariate statistics , artificial intelligence , random variable
Summary . In this article, we propose a graphical technique for assessing the goodness‐of‐fit of a stationary hidden Markov model (HMM). We show that plots of the estimated distribution against the empirical distribution detect lack of fit with high probability for large sample sizes. By considering plots of the univariate and multidimensional distributions, we are able to examine the fit of both the assumed marginal distribution and the correlation structure of the observed data. We provide general conditions for the convergence of the empirical distribution to the true distribution, and demonstrate that these conditions hold for a wide variety of time‐series models. Thus, our method allows us to compare not only the fit of different HMMs, but also that of other models as well. We illustrate our technique using a multiple sclerosis data set.