In many experiments investigating possible mind-matter interrelations it is attempted to correlate mental (intentional) states of subjects with external material systems. A contribution to this area of research is a reanalysis of the data used in the metaanalysis by Radin and Nelson (1989). In our approach the focus was shifted from the establishment of effects to the explicit modeling of mechanisms capable of producing the observed data. The reanalysis indicated both random effects in the variability of parameters and selection effects. The significance of the experimental effect reported by Radin and Nelson is reduced or vanishes if selection effects are included in the model. A large part of the analyzed data, collected by PEAR (Princeton), shows no significant selection, however. Nevertheless, a correction for possible selection reduces the significance of the experimental effect considerably even in this case.

A number of incompletely documented studies in the analysis of Radin and Nelson was not included in our analysis. Therefore it was possible that the detected selection effects simply reflect the missing incomplete data sets. In order to check this possibility, the incomplete data sets were randomly complemented (multiple random imputation) such that they reflected the statistical structure of the complete data sets, including the assumed selection mechanism. Repeating the original analysis with the completed data sets yielded essentially unaltered results.

The processes underlying the perception of ambiguous stimuli (e.g., Necker cube) have so far been investigated with the usual averaging methods of standard EEG analysis. Further insight may be expected from higher-frequency EEG oscillations, in particular concerning the role of phase synchronization in the gamma band (between 30 and 80 Hz) for object representation and neuronal integration (binding problem). However, extracting frequency-specific phase information from noisy, non-stationary EEG data is not straightforward. We developed a corresponding strategy which will be applied to experimental data as soon as its tests are completed.

Methodologically less involved are power analyses based on time-frequency decompositions. In a corresponding analysis we found significant discrepancies concerning level and structure of gamma activity between subjects. Intra-individually the activity was similar across various experimental conditions, with little temporal variability. These (preliminary) results do not fit well into the current literature and require further examination.

The temporal durations estimated by subjects who are asked to reproduce a presented time interval have been modeled as first passage times of a stochastic process ("stochastic dual klepsydra model"). Applying the model to experimental data requires knowledge of the distribution of reproduced durations and methods for estimating the model parameters. The latter task is severely nontrivial due to the insufficient determination of the estimation problem. We developed an iterative procedure which first estimates the primarily important parameters only (leakage rate and inflow rates) using weighted least squares. In a second step the method of quasi-likelihoods provides at least some rough (order-of-magnitude) estimate of the signal-to-noise ratio. Questions as to the experimental design (e.g., choice of presentation and waiting times) have been settled using suitable variance approximations.

Positron emission tomography (PET) is a powerful imaging technique that can be used to visualize metabolic processes in the brain such as increased glucose intake during the execution of some task or by a tumor. Mathematically, the method depends on inversion algorithms for reconstructing the concentration of the substance of interest from the measured data. Criteria for the reliability and accuracy of such algorithms are of great interest but could only be evaluated quite crudely for PET studies so far. For an important class of algorithms (filtered back-projection) the exact form of such a quality criterion, the mean integrated square error, could be derived in the limit of high intensity. This result provides a basis for comparisons of efficiency and for the identification of optimal filters.

Physiological time series are generally non-stationary over long periods, although they cannot be distinguished from stationary processes on short time scales. An important technical tool to test the assumption of stationarity is the factorization of positive definite functions. A complete classification of factorizable positive functions has been completed. Interesting remaining questions are related, e.g., to the factorization of the "spherical model" for planar random processes or the representation of self-reciprocal densities. However, progress in these directions requires new ideas and cannot be anticipated currently.