Authors:
Robert J. Elliott,
William P. Malcolm,
Volume: 1, Page 4678 Paper number 1419
Abstract:
In this article we consider robust filtering and smoothing for Markov
Modulated Poisson Processes (MMPPs). Using the EM algorithm, these
filters and smoothers can be applied to estimate the parameters of
our model. Our dynamics do not involve stochastic integrals and our
new formulae, in terms of time integrals, are easily discretized.
Authors:
François LeGland,
Laurent Mével,
Volume: 1, Page 4686 Paper number 1829
Abstract:
In this paper, the problem of detecting a change in the transition
probability matrix of a hidden Markov chain is addressed, using the
local asymptotic approach. The score function, evaluated at the nominal
value, is used as the residual, and is expressed as an additive functional
of the extended Markov chain consisting of the hidden state, the observation,
the prediction filter and its gradient w.r.t. the parameter. The problem
of residual evaluation is solved using available limit theorems on
the extended Markov chain, which allow to replace the original detection
problem by the simpler problem of detecting a change in the mean of
a Gaussian r.v.
Authors:
Laurent Mével,
Lorenzo Finesso,
Volume: 1, Page 4691 Paper number 1664
Abstract:
In this paper we consider the problem of the identification of a partially
observed finite state Markov chain (or Hidden Markov Model, HMM), with
continuous observations. Maximum Likelihood (ML) is the most popular
approach to parameter estimation for this class of models. The asymptotic
properties of the ML estimator (MLE) have already been investigated
under a variety of conditions. Under the assumption of stationarity,
Leroux has proved the almost sure consistency of the MLE, and Bykel,
Ritov and Ryden have proved its asymptotic normality. More general
results, encompassing both previous ones, have been given by Mevel.
A new technique for the study of the convergence of HMM's has been
developed. This technique is based on geometric ergodicity properties
of the prediction filter and its derivatives, derived via results for
products of random matrices. The main advantage is that convergence
results for Hidden Markov Models can now be reduced to the analysis
of a Markov process, with a properly defined state space. In this paper
we apply the new technique to derive the almost sure rate of convergence
of the MLE and give an example of application in the context of the
model selection problem. As will be mentioned in the paper, these results
extend easily to conditional least squares estimators.
Authors:
Louis Shue,
Subhrakanti Dey,
Volume: 1, Page 4697 Paper number 1167
Abstract:
In this paper, we investigate approximate smoothing schemes for a class
of hidden Markov models (HMM), namely, HMMs with underlying Markov
chains that are nearly completely decomposable. The objective is to
obtain substantial computational savings. Our algorithm can not only
be used to obtain aggregate smoothed estimates, but can be used to
obtain systematically approximate full-order smoothed estimates with
computational savings, unlike many of the aggregation methods proposed
earlier.
Authors:
Jason J. Ford,
Volume: 1, Page 4703 Paper number 1032
Abstract:
This paper considers adaptive estimation of noisy finite impulse response
linear systems driven by stationary inputs from a discrete set. An
equivalent hidden Markov model representations is presented which allows
some powerful signal processing techniques to be applied to this estimation
problem. A new adaptive estimation algorithm is presented and simulation
studies illustrate the performance of the proposed algorithm.
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