ISSN:
1436-3259
Keywords:
Hidden markov models
;
maximum likelihood estimation
;
EM algorithm
;
martingale estimating function
;
forward-backward algorithm
;
Monte Carlo
;
filtering
;
Nash cascade model
;
rainfall runoff modeling
Source:
Springer Online Journal Archives 1860-2000
Topics:
Architecture, Civil Engineering, Surveying
,
Energy, Environment Protection, Nuclear Power Engineering
,
Geography
,
Geosciences
Notes:
Abstract Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (Xn, n ≥ 0) or (Xt, t ≥ 0) for which the parameters are of interest and physically meaningful, and an observable process (Yn, n ≥ 0) or (Yt, t ≥ 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01581757
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