Modelling disease clustering over space and time can be helpful in providing indications of possible exposures and planning corresponding public health practices. Though a considerable number of studies focus on modelling spatio-temporal patterns of disease, most of them do not directly model a spatio-temporal clustering structure and could be ineffective for detecting clusters. In this paper, we extend a purely spatial cluster model to accommodate space-time clustering. Inference is performed in a Bayesian framework using reversible jump Markov chain Monte Carlo. This idea is illustrated using data on female breast cancer mortality from Japan. A hierarchical parametric space-time model for mapping disease is used for comparison.

Observations of multiple-response variables across space and over time occur often in environmental and ecological studies. Compared to purely spatial models for a single response variable in the exponential family of distributions, fewer statistical tools are available for multiple-response variables that are not necessarily Gaussian. An exception is a common-factor model developed for multivariate spatial data by Wang and Wall (2003, Biostatistics 4, 569-582). The purpose of this article is to extend this multivariate space-only model and develop a flexible class of generalized linear latent variable models for multivariate spatial-temporal data. For statistical inference, maximum likelihood estimates and their standard deviations are obtained using a Monte Carlo EM algorithm. We also use a novel way to automatically adjust the Monte Carlo sample size, which facilitates the convergence of the Monte Carlo EM algorithm. The methodology is illustrated by an ecological study of red pine trees in response to bark beetle challenges in a forest stand of Wisconsin.

The existing angular displacement measurement methods rely on the manufacturing precision of the fixedplate and moving-plate with high manufacturing cost, and it is difficult to overcome a static error and drift for the static measurement method. A kind of angular displacement measuring method based on correlation algorithm is presented with the characteristics of a low manufacturing cost, high precision, anti-noise and anti-partially damaged properties and so on. The method is that firstly full circle broadband or white noise, random data is a pre-prepared coaxially in a rotating body, then the periodic random signal is continuously formed using pickup head reads this data in the basic uniform rotation process of the rotating body. The instantaneous angular displacement of the pickup head relative to the rotating body is obtained by means of the correlation operations between the periodic random signal and the signal sequence of pre-stored data. The angular displacement among the different pickup heads is gained by subtraction for the instantaneous angular displacement of different pickup heads relative to the rotating body at the same instant. The functional relationship between the relative angular displacement of the different pickup heads and the measured angular displacement is determined by linkage equations, which is used to calculate the measured angular displacement. Furthermore, the schematics of detective devices and the principle of the signal processing are developed to implement the method.