Brief Professional Bio

I’m a retired mathematician. My area of specialty is Mathematical Statistics. I worked in industry for my entire career in the area of scientific computing, including:

• Spacecraft Navigation 1980-87
  • Space Shuttle Onboard & Ground Navigation
  • McDonnell Douglas Astronautics Co., Johnson Space Center, Houston, Texas
• Artificial Intelligence 1987-1995
  • Joint DARPA & US Army program in Artificial Intelligence
  • Automated Planning using Spatio-Temporal Reasoning
  • Lockheed Austin Division, Knowledge-Based Systems, Austin, Texas
• Semiconductor Manufacturing 1995-2007
  • Optical Proximity Correction (OPC) and Design for Manufacturing (DfM)
  • Motorola Semiconductor Products Sector and Freescale Semiconductor, Austin, Texas
• National Defense 2007-2017
  • Data Science, Data Fusion, and Cyber-Security using Machine Learning methods
  • Potomac Fusion, Inc. and Sotera Defense Solutions, Austin, Texas

Experience & Skills

Over the course of my career, my work involved many different technologies and application domains.

Here’s an abbreviated list: Anomaly Detection, Artificial Intelligence (AI), Astrodynamics, Automated Reasoning, Bayesian Data Analysis (BDA), Bayesian Networks, Classical Statistical Methods, Computational Geometry, Computer Programming, Cyber-Security, Data Fusion, Data Science, Expert Systems, Machine Learning, Mathematical Models, Network Analysis, Numerical Methods, Optical Proximity Correction (OPC), Orbit Determination, Phase Shift Masks (PSM), Physical Semiconductor Design Formats (GDSII, OASIS), Semantic Web Technologies (RDF, OWL), Software Engineering, Spacecraft Navigation, Spatio-Temporal Reasoning, Statistical Models, Technical Writing, and Uncertainty Reasoning.

More on my work and educational history can be found on my LinkedIn profile.

Publications & Patents

A list of my papers and patents can be found at Google Scholar. (Here’s a PDF version, in case the link doesn’t work.)

Mathematical & Statistical Topics

Here are a few presentations & tutorials that I’ve written:

• Sqrt(-1) Explained – A very, very brief (minimal) explanation of the “square root of -1”

  This is a very, very brief (minimal) explanation of the “square root of -1”, without mathematical jargon, so that it can be read and understood by a broad audience, and so that they can see that there is nothing “imaginary” going on here.

• Extreme Value Analysis (EVA) – A presentation on the statistical modeling of rare events

  This is the PDF file from a presentation on Extreme Value Analysis (EVA) that I gave to the central Texas IEEE Section on Oct 20, 2022.

  “EVA is widely used in many disciplines, such as structural engineering, finance, earth sciences, traffic prediction, and geological engineering. For example, EVA might be used in the field of hydrology to estimate the probability of an unusually large flooding event, such as the 100-year flood.” – Wikipedia

• Covid-19 and Blood Types (using a Bayesian approach) – An alternative approach to a 2020 paper in medRxiv

  In the recent paper by Jiao Zhao, et al. it was reported that blood group (e.g., A, B, AB, or O) appears to have an effect on the likelihood of becoming infected with the Covid-19 virus. Basically, people with blood type A appear to be more susceptible to the virus, while people with blood type O appear to be less susceptible.

  The authors of the paper performed several types of statistical analyses to arrive at their conclusion: one-way ANOVA, 2-tailed chi-square, and a meta-analysis using random effects models. In this Jupyter notebook, I’ve performed a different type of analysis, Bayesian Data Analysis (BDA), using the data reported in their paper.

  [CAVEAT: No one has checked my work, so there could be errors in it] This BDA appears to support their conclusion, but also provides posterior density estimates for the proportions of A, B, AB, and O blood groups among the infected, along with credible intervals for those proportions. See the four posterior density plots at the end of this notebook.

• Bayesian Beta-Binomial Example – An example of Bayesian parameter estimation

  This Jupyter notebook provides a very simple example of Bayesian parameter estimation using the Beta-Binomial model. Both analytical and simulation-based results are presented. Three different approaches are used to obtain a parameter estimate for this model:

  • Exact Analytical Solution
  • Simple Non-MCMC Solution
  • MCMC Solution

• Monoids 101 for Apache Spark – A tutorial on large scale, distributed computing

  This Jupyter notebook describes what monoids are and the role they play in reduction and aggregation in Spark, specifically PySpark. To illustrate the use of the monoid concept, the following examples are included:

  • Word count
  • Max/Min as monoids
  • Histogram calculation using vectors as monoids
  • Calculating sample means and standard deviations
  • Calculating covariances and correlations using vectors and matrices as monoids
  • Sets as monoids
  • A HyperLogLog monoid (a “sketch method” for approximating set cardinality). NOTE: Uses the implementation, hll.py at https://github.com/Parsely/probably, which has been modified here to remove the dependency on the “smhasher” module and so that it can be run using the Anaconda Python distribution.

Python APIs (on github & readthedocs):

• Gaussian Integers & Gaussian Rational Numbers: Number theory in the complex plane. source code
• Qualitative Reasoning: Spatio-Temporal Reasoning using Relation Algebras and Constraint Networks. source code
• Abstract Algebra - Finite Algebras in Python (Groups, Rings, Fields, Vector Spaces, Modules, Monoids, Semigroups, and Magmas) documentation and source code

Education

• Texas Tech University, Ph.D., Mathematics (Mathematical Statistics), 1980
  • Dissertation: “Robust and adaptive estimation of location and scale”
  • Citable Link: http://hdl.handle.net/2346/16490
• University of Utah, B.A. & M.A., Mathematics, 1973 & 1975

Hobbies

I’m an avid photographer. Many of my photos can be seen at Flickr: https://www.flickr.com/photos/alreich

I also enjoy drawing and painting. My art work can be found on Instagram: https://www.instagram.com/al.reich/

I also enjoy bicycling