This module introduces the maximum likelihood estimator. We show how the MLE implements the likelihood principle. Methods for computing th MLE are covered. Properties of the MLE are discussed including asymptotic e ciency and invariance under reparameterization. The maximum likelihood estimator (MLE) is an alternative to the minimum variance unbiased estimator (MVUE). For many estimation proble...

We present a stochastic model of suprathreshold perceptual differences based on difference measurement. We develop a maximum likelihood difference scaling (MLDS) method for estimating its parameters and evaluate the reliability and distributional robustness of the fitting method. We also describe a method for testing whether the difference measurement model is appropriate as a description of hu...

Abstract An inhomogeneous gamma process is a compromise between renewal and nonhomogeneous Poisson process, since its failure probability at given time depends both on the age of system distance from last time. The with log-linear rate function often used in modelling recurrent event data. In this paper, it proved that suitably non-uniform scaled maximum likelihood estimator three-dimensional p...

The method of maximum likelihood (ML), introduced by Fisher (1921), is widely used in human and quantitative genetics and we draw upon this approach throughout the book, especially in Chapters 13–16 (mixture distributions) and 26–27 (variance component estimation). Weir (1996) gives a useful introduction with genetic applications, while Kendall and Stuart (1979) and Edwards (1992) provide more ...

This paper presents a novel framework, based on maximum likelihood, for training models to recognise simple spatial-motion events, such as those described by the verbs pick up, put down, push, pull, drop, and throw, and classifying novel observations into previously trained classes. The model that we employ does not presuppose prior recognition or tracking of 3D object pose, shape, or identity....

The problem of estimating the parameters for continuous-time partially observed systems is discussed. New exact lters for obtaining Maximum Likelihood (ML) parameter estimates via the Expectation Maximization algorithm are derived. The methodology exploits relations between incomplete and complete data likelihood and gradient of likelihood functions, which are derived using Girsanov's measure t...