Research Interests Prof. W. Schwarz

In many of these topics I am mainly interested in the context of the modeling efforts described above. At times, related research questions simply arose as a consequence of problems I faced in the analysis of statistical data.

My paper [Schwarz (1992b)] finds the solutions of a class of parabolic partial differential equations that arise as boundary condition problems associated with stochastic diffusion processes. A somewhat related subject is my interest in the Inverse Gaussian distribution, eg the formal structure of its convolution with exponential random variables which relies essentially on properties of the complex error function [Schwarz (2002)]. My work [Schwarz & Miller, (2010)] with Jeff Miller looks at the spatial distribution of diffusion processes backwards in time from the moment of the first passage through a given level. I am also interested in the application of functional equations, for example, to models of binocular signal detection [Schwarz (1992a), Schwarz & Miller (2014)].

In the area of mathematical statistics I have, for example, studied the degree of dependence of successive F-tests that are all based on the same common denominator [Schwarz (1993a)], as is typical of standard ANOVA applications.I also studied [Schwarz (1992c)] certain functional transformations that are useful in analyzing so-called random utility models. Somewhat related work I did looks at the distribution large and small temporal gaps in stochastic renewal processes [Schwarz (1995)], at Poisson models of football results [Schwarz (2000), see also Schwarz (2011, 2013)], at the Ehrenfest model of particle physics [Schwarz (1993b)], or at extensions and variations of the birthday coincidence problem [Schwarz (1988c), Schwarz (2010)]. Together with Jeff Miller we formulated a general stochastic random-effects model of the research process to investigate so-called replication probabilities (Miller & Schwarz, 2011), and derived basic results related to so-called Delta plots (Schwarz & Miller, 2012). Part of these efforts related to probability and mathematical statistics is contained in my book (Schwarz, 2008) on puzzles and problems in probability and mathematical statistics.