REMARKS ON OPTIMAL INFERENCE FOR MARKOV BRANCHING PROCESSES: A SEQUENTIAL APPROACH

Use of a suitable stopping rule yields exact uniformly most powerful tests and minimum variance unbiased estimators of various parameters of a Markov branching model with or without immigration. The population model discussed includes the pure birth, simple epidemic, immigration-death, M/M/ 1 queue, linear birth-death and a branching diffusion process, among others, as special cases.     

Statistical morphology

This paper first introduces a parametric model for the generation of stationary random correlated binary sequences. The parameters of the model include the probability that a pixel is a binary one pixel and the length of the structuring element which dilates the initially spatially uncorrelated sequence. The spatial statistics of such eroded, dilated, opened and closed correlated binary sequences are derived in terms of the spatial statistics of the input binary sequence. Understanding of such one-dimensional processing is a precondition for understanding what happens in the more interesting two- dimensional case.     

Models of gambling and gambling addictions as perceptual filters

Models, in the sense of loosely entertained clusters of beliefs, attitudes, assumptions and expectations which direct the work of researchers and clinicians, also act as perceptual filters, tending to focus the attention of those who use them on certain aspects of reality and relegating to the background or ignoring altogether other aspects of the field of study and action. The central characteristics of social learning and of medical models are briefly reviewed and they are compared as perceptual filters for their distorting effects on research in gambling and in gambling addictions and on intervention strategies for problem gamblers. It is concluded that the exclusive predominance of any one model leads to the impoverishment of both research and intervention.     

AN ALGORITHM FOR THE DESIGN OF 2? FACTORIAL EXPERIMENTS ON CONTINUOUS PROCESSES

Saunders & Eccleston (1992) presented an approach to the design of 2-level factorial experiments for continuous processes. It determined sets of contrasts between the observations that could be well estimated, and then selected a design so that those contrasts estimated the parameters of interest. This paper shows that a well-estimated contrast must have a large number of changes of sign or level, and also be ‘paired’ in a particular sense. It develops an algorithm which constructs designs that must have a large number of changes of sign, evenly spread among the contrasts and optimal or near optimal. When such designs exist they are often preferable to those produced by the reverse foldover algorithm of Cheng & Steinberg (1991).