Expectation–maximization algorithm

About: Expectation–maximization algorithm is a research topic. Over the lifetime, 11823 publications have been published within this topic receiving 528693 citations. The topic is also known as: EM algorithm & Expectation Maximization.

Aids for Fitting the Gamma Distribution by Maximum Likelihood

Abstract: This paper presents a new table and some approximating polynomials especially designed to facilitate maximum likelihood estimation of the parameters of the gamma distribution, and also applicable to the a-parameter Type V; it discusses methods of computing the sampling variances of the likelihood estimators; it illustrates the use of the tables in a numerical example; it mentions applications to the Erlang distribution and difficulties of application to the general Type III. Finally it inquires when the numbers extracted from the tables are maximum likelihood estimates, and what they are estimates of.

Maximum-Penalized-Likelihood Estimation for Independent and Markov-Dependent Mixture Models

Abstract: SUMMARY This paper concerns the use and implementation of maximum-penalized-likelihood procedures for choosing the number of mixing components and estimating the parameters in independent and Markov-dependent mixture models. Computation of the estimates is achieved via algorithms for the automatic generation of starting values for the EM algorithm. Computation of the information matrix is also discussed. Poisson mixture models are applied to a sequence of counts of movements by a fetal lamb in utero obtained by ultrasound. The resulting estimates are seen to provide plausible mechanisms for the physiological process. The analysis of count data that are overdispersed relative to the Poisson distribution (i.e., variance > mean) has received considerable recent attention. Such data might arise in a clinical study in which overdispersion is caused by unexplained or random subject effects. Alternatively, we might observe a time series of counts in which temporal patterns in the data suggest that a Poisson model and its implied randomness are inappropriate. This paper is motivated by analysis of a time series of overdispersed count data generated in a study of central nervous system development in fetal lambs. Our data set consists of observed movement counts in 240 consecutive 5-second intervals obtained from a single animal. In analysing these data, we focus on the use of Poisson mixture models assuming independent observations and also Markov-dependent mixture models (or hidden Markov models). These models assume that the counts follow independent Poisson distributions conditional on the rates, which are generated from a mixing distribution either independently or with Markov dependence. We believe finite mixture models are particularly attractive because they provide plausible explanations for variation in the data. This paper will emphasize the following issues concerning estimation, inference, and application of mixture models: (i) choosing the number of model components; (ii) applying the EM algorithm to obtain parameter estimates; (iii) generating sufficiently many starting values to identify a global maximum of the likelihood; (iv) avoiding numerical instability

The Geometry of Mixture Likelihoods, Part II: The Exponential Family

Abstract: Geometric analysis of the mixture likelihood set for univariate exponential family densities yields results which tie the number and location of support points for the nonparametric maximum likelihood estimator of the mixing distribution to sign changes in certain integrated polynomials. One corollary is a very general uniqueness theorem for the estimator.

A new statistical wideband spatio-temporal channel model for 5-GHz band WLAN systems

Abstract: In this paper, a new statistical wideband indoor channel model which incorporates both the clustering of multipath components (MPCs) and the correlation between the spatial and temporal domains is proposed. The model is derived based on measurement data collected at a carrier frequency of 5.2 GHz in three different indoor scenarios and is suitable for performance analysis of HIPERLAN/2 and IEEE 802.11a systems that employ smart antenna architectures. MPC parameters are estimated using the super-resolution frequency domain space-alternating generalized expectation maximization (FD-SAGE) algorithm and clusters are identified in the spatio-temporal domain by a nonparametric density estimation procedure. The description of the clustering observed within the channel relies on two classes of parameters, namely, intercluster and intracluster parameters which characterize the cluster and MPC, respectively. All parameters are described by a set of empirical probability density functions (pdfs) derived from the measured data. The correlation properties are incorporated in two joint pdfs for cluster and MPC positions, respectively. The clustering effect also gives rise to two classes of channel power density spectra (PDS)-intercluster and intracluster PDS-which are shown to exhibit exponential and Laplacian functions in the delay and angular domains, respectively. Finally, the model validity is confirmed by comparison with two existing models reported in the literature.

Disturbance smoother for state space models

Abstract: SUMMARY This paper develops a method to evaluate the smoothed estimator of the disturbance vector in a state space model together with its mean squared error matrix. This disturbance smoother also leads to an efficient smoother for the state vector. Applications include a method to calculate auxiliary residuals for unobserved components time series models and an EM algorithm for estimating covariance parameters in a state space model.