Regularising properties of the truncated estimation maximisation algorithm

摘要

In many applications [1, 7, 8, 11, 12, 14], physical phenomena of interest are modelled by probability distributions f (x; #theta# ) for the data x which depend on unknown parameters #theta# . Bsed upon statistical principles and observed data from these phenomena, the aim of estimation theory is to obtain estimates of the parameters which characterise the model. Two approaches to modelling are to assume either that the parameters are deterministic (fixed) or stochastic (random variable with some probability distribution of their own [12]. For determinstic models, maximum likelihood (ML) is a common approach wherein for a given set of observations x, the estimate of #theta# is #theta# chemical bounds arg max log [f(x; #theta# ). In the stochastic case, Bayesian principles require that a prior proabability density h( #theta#) is assigned to the parameters and the maximum penalised likelihood estimate (MPLE) is obtained via #theta# chemical bounds arg max log [f(x; #theta# )h( #theta# )]. The idea nere is that the prior knwledge about the parameters is specified through h (#theta#). The determinisitc case is the reduction of the stochastic one when h( # theta# ) chemical bounds 1.