Dear Reader!

Welcome to my website!

Here I am frequently tweeting and blogging on statistics, signal processing, inverse problems, probability theory, telecommunications, history, and software development in English and German. Now it is even optimized for mobile viewing. Since LaTeX, Maxima, and Python are powerful open-source tools for doing research, I give some words of advice and present some code snippets. The software section shows some of my old software projects (C/C++).

Enjoy reading my website and don't hesitate to give me feedback!

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Currently, I am with Frequentis AG. I have been a consultant and a service provider in information technology with focus on statistics, programming, communications, and streaming of live events, which reflect my interests and hobbies.

From mid-2008 to mid-2009, I did my master thesis on RFID with NXP Semiconductors Austria. Afterwards, I was researcher in statistics / signal processing and teaching assistant with Institute of Telecommunications of Vienna University of Technology.  From autumn of 2013 to spring of 2014, I did my research at Institute of Telecommunications of TU Darmstadt due to a fellowship of Federation of Austrian Industries. Afterward I was self-employed and became a certified project-management associate. See my LinkedIn profile or contact me for my detailed curriculum vitae.

My research's foci are statistics, signal processing, and probability theory in the area of (mobile) communications. I did my work in cooperation with Prof. Christoph Mecklenbräuker (PhD advisor), Prof. Peter Gerstoft, Prof. Gerald Matz, Prof. Marius Pesavento, and Prof. Norbert Goertz.

Favorite Quotation

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

John von Neumann (1903-1957)

Games with Two Dice and the Double Rule

Some days ago I played Monopoly, a board game that is played using two dice. Afterwards I was eager to calculate the probability that a player arrives at one of the streets. I started by computing the probabilities to roll numbers. This is not as trivial as you might guess, because there are rules for doubles, e.g. $(1,1), (2,2)...(6,6).$  Later I realized that there are very good internet resources on Monopoly by J. Bewersdorff including a graphical simulation. It shows that the probability of arriving a particular street is close to uniform after many rounds. Except fields after the jail and special non-street fields. If you want to know more about Monopoly look at [1,German], Bewersdorff's book "Glück, Logik und Bluff: Mathematik im Spiel - Methoden, Ergebnisse und Grenzen" [2, German], or the bachelor thesis "Monopoly und Markow-Ketten" by Julia Tenie [3, German]. There is also a "FAQ" about probabilities of throwing dice [4, English] and an article at Wolfram's Mathworld on computing the probability of the points using several dice [5, English].

In what follows, I will address dice games using two dice with a double rule. Particularly, I will answer following questions:

  • What is the probability of particular points (sum) of two dice using a double rule?
  • What is expected number of points (sum) of two dice using a double rule? What is different compared to without double rule?

I use Monopoly's double rule:

  1. If a player rolls a double, roll the dice again and add the new result to the previous result.
  2. If a player rolls a double three times in a row, your turn is over. 

If you are only interested in the probabilities, then jump to Tables I and II. If you are interested in the theory in addition to the probabilities, then you will also find the answer of following question:

  • How are the probability masses (probability mass function) defined? 

Classification of Bayesian Inverse Problems by their Continuous/Discrete Nature

Two traditional classes of inverse problems are the estimation of absolute-continuous random parameters and the detection/classification of discrete random parameters by continuous random measurements. But what about the inference of mixed discrete-continuous problems? In the following, I will summarize my proposal of six classes of inverse problems and, hence, six classes of inferrers. See [1] for a table and formulars.