Efficient Computation of Updated Lower Expectations for Imprecise ContinuousTime Hidden Markov Chains
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Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 62:193204, 2017.
Abstract
We consider the problem of performing inference with imprecise continuoustime hidden Markov chains, that is, imprecise continuoustime Markov chains that are augmented with random output variables whose distribution depends on the hidden state of the chain. The prefix ‘imprecise’ refers to the fact that we do not consider a classical continuoustime Markov chain, but replace it with a robust extension that allows us to represent various types of model uncertainty, using the theory of imprecise probabilities. The inference problem amounts to computing lower expectations of functions on the statespace of the chain, given observations of the output variables. We develop and investigate this problem with very few assumptions on the output variables in particular, they can be chosen to be either discrete or continuous random variables. Our main result is a polynomial runtime algorithm to compute the lower expectation of functions on the statespace at any given timepoint, given a collection of observations of the output variables.
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