M. Palma

Modeling and prediction of multivariate space-time random fields

Abstract In various environmental studies multivariate spatial–temporal correlated data are involved, hence appropriate techniques to enhance space–time prediction are in great demand. An extension of multivariate spatial geostatistics to a spatio-temporal domain might be a straightforward task; nevertheless, up to now, little has been done in a multivariate spatial–temporal context. Modeling and prediction techniques are described for a multivariate space–time random field, moreover some theoretical and practical aspects are investigated for a bivariate space–time random field through a case study.

Using Simultaneous Diagonalization to Identify a Space–Time Linear Coregionalization Model

Although there are multiple methods for modeling matrix covariance functions and matrix variograms in the geostatistical literature, the linear coregionalization model is still widely used. In particular it is easy to check to ensure whether the matrix covariance function is positive definite or that the matrix variogram is conditionally negative definite. One of the difficulties in using a linear coregionalization model is in determining the number of basic structures and the corresponding covariance functions or variograms. In this paper, a new procedure is given for identifying the basic structures of the space–time linear coregionalization model and modeling the matrix variogram. This procedure is based on the near simultaneous diagonalization of the sample matrix variograms computed for a set of spatiotemporal lags. A case study using a multivariate spatiotemporal data set provided by the Environmental Protection Agency of Lombardy, Italy, illustrates how nearly simultaneous diagonalization of the empirical matrix variograms simplifies modeling of the matrix variograms. The new methodology is compared with a previous one by analyzing various indices and statistics.

Geostatistics and the Role of Variogram in Time Series Analysis: A Critical Review

Exploratory data analysis and prediction in time series modeling are not typically based on geostatistical techniques, although in several cases applying these techniques might be convenient.

Continuing evolution of statistical tests in medical research

The role of statistics in medical research starts at the planning stage of a clinical trial or laboratory experiment to establish the design and size of an experiment that will ensure a good prospect of detecting effects of clinical or scientific interest. Statistics is again used during data analysis (sample data) to make inferences valid in a wider population. In simple situations, computation of simple quantities such as P-values, confidence intervals, standard deviations, standard errors or application of some standard parametric or nonparametric tests may suffice. Moreover, despite the wide use of statistics in medical research, simple notions are sometimes misunderstood or misinterpreted by medical research workers, who have only a limited knowledge of statistics. This article, written for non-statisticians, is to explain what are the most common statistical tests used today in the field of medical research, tracing the evolution of statistical tests over time, in particular the introduction of nonparametric methods and, more recently, the NonParametric Combination (NPC) methodology. At the same time, this work seeks to identify some of the errors associated with their use, that often lead to an incorrect assessment and interpretation of results of medical research.