Dietrich von Rosen

Advanced multivariate statistics with matrices

Basic Matrix Theory and Linear Algebra.- Multivariate Distributions.- Distribution Expansions.- Multivariate Linear Models.

ECT of major depressed patients in relation to biological and clinical variables: A brief overview

The knowledge that spontaneous or induced convulsions can improve mental disorders has been present for several centuries. electroconvulsive therapy (ECT) has undergone fundamental changes since its introduction, and in the last 15–20 years there has been a legitimate renewal of interest for this therapy. Today the indications for use of ECT seem well codified, and its technique and practices have evolved considerably. It is now firmly established as an important and effective method of treating certain severe forms of depression. However, still very little is known about the mechanism of ECT. In this paper, first, we will give a short overview as to how far we have got concerning ECT in relation to various clinical and biological variables. Second, we will describe ECT in relation to electroencephalographic (EEG) technique and clinical outcome as well as give some proposals as to how to go on with the data analysis of EEG. In conclusion, the superior effect of ECT compared to other antidepressives in severe depression may depend on neurochemical and neurobiological cascade effects initiated by repeated treatments. Above all, ECT offers a unique experimental opportunity to study how neuromodulation of the major transmitter systems may be involved in brain dynamics and alteration of connectivity.

Inferring the location of catchment characteristic soil moisture monitoring sites. Covariance structures in the temporal domain

Information shortage is a fundamental constraint in catchment hydrology that severely affects the possibilities for secure inference of the generic hydrologic landscape, as well as for secure validation of physically deduced distributed models. The introduction of databases with high enough spatiotemporal resolution to properly reflect generic hydrological catchment characteristics may therefore be considered as an inferential breakthrough. The work presented here is part of a project where observations from such an Australian catchment (the Tarrawarra) are utilised to estimate the discrepancy for individual soil moisture monitoring sites in reflecting generic catchment characteristics. With low enough discrepancy, observation sites may be considered as catchment characteristic soil moisture monitoring (CASMM) sites, thus capturing unbiased catchment characteristics and being well suited to represent the catchment in a monitoring effort. In this particular study, covariance structures in the temporal domain are inferred in order to enable subsequent enquiries regarding CASMM discrepancies. This is accomplished with ARMAX filters applied to the conditional auto- and cross-covariance structures that connect observations of soil moisture to the temporal variation of meteorology. The results suggest that weekly observations of Tarrawarra soil moisture are quite consistent realisations of first order auto-regressive processes, which means that the present state of soil moisture is generally acquired through the past week. With auto-correlative effects filtered out, cross-correlative meteorological effects on Tarrawarra soil moisture are identified and generally represented by the present weeks accumulation of rainfall, the present weeks accumulation of global radiation, and the previous weeks maximum wind speed. After successive filtering of conditional cross-correlative effects, residual time-series observations may be considered as temporally independent, and therefore are well suited for subsequent inferences regarding covariance structures in the spatial domain. Since the exclusion of auto-correlative effects is necessary for unambiguous model interpretation, the estimated cross-correlative parameters should reflect the true nature of underlying physical processes.

The multilinear normal distribution: Introduction and some basic properties

In this paper, the multilinear normal distribution is introduced as an extension of the matrix-variate normal distribution. Basic properties such as marginal and conditional distributions, moments, and the characteristic function, are also presented. A trilinear example is used to explain the general contents at a simpler level. The estimation of parameters using a flip-flop algorithm is also briefly discussed.

Moments for matrix normal variables

In order to obtain moments for matrix normally distributed variables the moment generating function is differentiated by aid of matrix derivatives. Moments of arbitrary order as well as a recursive relation are obtained. Further, some more details are given for the first four moments

Benchmark Calculations in Risk Assessment Using Continuous Dose‐Response Information: The Influence of Variance and the Determination of a Cut‐Off Value

A benchmark dose (BMD) is the dose of a chemical that corresponds to a predetermined increase in the response (the benchmark response, BMR) of a health effect. In this article, a method (the hybrid approach) for benchmark calculations from continuous dose-response information is investigated. In the formulation of the methodology, a cut-off value for an adverse health effect has to be determined. It is shown that the influence of variance on the hybrid model depends on the choice of determination of the cut-off point. If the cut-off value is determined as corresponding to a specified tail proportion of the control distribution, P(0), the BMD becomes biased upward when the variance is biased upward. On the contrary, if the cut-off value is directly determined to some level of the continuous response variable, the BMD becomes biased upward when the variance is biased downward. A simulation study was also performed in which the accuracy and precision of the BMD was compared for the two ways of determining the cut-off value. In general, considering BMRs of 1, 5, and 10% (additional risk) the precision of the BMD became higher when the cut-off value was estimated by specifying P(0), relative to the case with a direct determination. Use of the square-root of the maximum-likelihood estimator of the variance in BMD estimation may provide a bias that is reflected by the cut-off formulation (downward bias if specifying P(0), and upward bias if specifying the cut-off, c, directly). This feature may be reduced if an unbiased estimator of the standard deviation is used in the calculations.

Regression models with unknown singular covariance matrix

In the analysis of the classical multivariate linear regression model, it is assumed that the covariance matrix is nonsingular. This assumption of nonsingularity limits the number of characteristics that may be included in the model. In this paper, we relax the condition of nonsingularity and consider the case when the covariance matrix may be singular. Maximum likelihood estimators and likelihood ratio tests for the general linear hypothesis are derived for the singular covariance matrix case. These results are extended to the growth curve model with a singular covariance matrix. We also indicate how to analyze data where several new aspects appear.

Effect of dimensionality on discrimination

Discrimination problems in a high-dimensional setting is considered. New results are concerned with the role of the dimensionality in the performance of the discrimination procedure. Assuming that data consist of a block structure two different asymptotic approaches are presented. These approaches are characterized by different types of relations between the dimensionality and the size of the training samples. Asymptotic expressions for the error probabilities are obtained and a consistent approximation of the discriminant function is proposed. Throughout the paper the importance of the dimensionality in the asymptotic analysis is stressed.

Explicit estimators of parameters in the Growth Curve model with linearly structured covariance matrices

Estimation of parameters in the classical Growth Curve model, when the covariance matrix has some specific linear structure, is considered. In our examples maximum likelihood estimators cannot be obtained explicitly and must rely on optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple non-iterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linear structured covariance matrix.

More on the Kronecker Structured Covariance Matrix

In this article, the multivariate normal distribution with a Kronecker product structured covariance matrix is studied. Particularly focused is the estimation of a Kronecker structured covariance matrix of order three, the so called double separable covariance matrix. The suggested estimation generalizes the procedure proposed by Srivastava et al. (2008) for a separable covariance matrix. The restrictions imposed by separability and double separability are also discussed.