Surveillance of the interaction parameter of the ising model

Abstract

Surveillance to detect changes of spatial patterns is of interest in many areas such as environmental control and regional analysis. Here the interaction parameter of the Ising model, is considered. -4 minimal sufficient statistic and its asymptotic distribution are used. It is demonstrated that the convergence to normal distribution is rapid. The main result is that when the lattice is large, all approximations are better in several respects. It is shown that, for large lattice sizes, earlier results on surveillance of a normally distributed random variable can be used in cases of most interest. The expected delay of alarm at a fixed level of false alarm probability is examined for some examples.

A Review and Discussion of Prospective Statistical Surveillance in Public Health

“…In that way the dependence between the different observations is not taken into account, which leads to a loss of information. Instead, the surveillance situation should be handled as a multivariate problem (Wessman, 1998a, b;Järpe, 2000).…”

“…In this case no information about the spatial structure will be lost. This approach was used in Järpe (1999) in the surveillance of clustering in a spatial log-linear model with a fixed lattice: the Ising model. Here the sufficient reduction resulted in the surveillance of a univariate statistic involving the sufficient spatial components for each time point.…”

“…A complete separation of the spatial and the temporal components was possible. In Järpe (2000) a shift process spreading spatially as time increased was considered. Here a likelihood ratio statistic was suggested, including a sufficient reduction in the spatial structure.…”

A CUSUM framework for detection of space–time disease clusters using scan statistics

“…Multivariate surveillance methods have been developed mainly in the general statistical literature or in journals aimed at industrial applications. However, several spatial surveillance methods with public health applications have recently been proposed for space-time cluster detection, see [2][3][4][5][6][7][8]. The paper by Woodall [9] provides an excellent review of the connection between industrial and public health applications and points to the opportunity of knowledge transfer between these two application areas.…”

Properties and Use of the Shewhart Method and Its Followers

“…Järpe (1999) suggested an ED-optimal likelihood ratio surveillance method of clustering in a spatial log-linear model. If the alternatives are completely specified, general techniques to achieve minimax optimality can be found in Lai (1995).…”