Risk-sensitive filtering and smoothing for hidden Markov models

Asymptotic smoothing errors for hidden Markov models

In this paper, the asymptotic smoothing error for hidden Markov models (HMMs) is investigated using hypothesis testing ideas. A family of HMMs is studied parametrised by a positive constant , which is a measure of the frequency of change. Thus, when 0, the HMM becomes increasingly slower moving. We show that the smoothing error is ( ). These theoretical predictions are confirmed by a series of ...

Inverse Filtering for Hidden Markov Models

This paper considers a number of related inverse filtering problems for hidden Markov models (HMMs). In particular, given a sequence of state posteriors and the system dynamics; i) estimate the corresponding sequence of observations, ii) estimate the observation likelihoods, and iii) jointly estimate the observation likelihoods and the observation sequence. We show how to avoid a computationall...

Sequential Monte Carlo Methods for Filtering and Smoothing in Hidden Markov Models

Lapped Transforms and Hidden Markov Models for Seismic Data Filtering

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Risk - sens tive filtering and smoothing for h olden Markov models *

In this paper, we address the problem of risk-sensitive tiitering and smoothing for discrete-time Hidden Markov Models (HMM ) with finite-discrete states. The objective of risk-sensitive tiltering is to minimise the expectation of the exponential of the squared estimation error weighted by a risk-sensitive parameter. Wc use the so-called Reference Probability Method in solving this problem. We ...