COVID-19 Shiny App

I have put together a COVID-19 Shiny App. It can be found at It’s a handful of graphs that, in particular, shows cases per population. I keep on seeing the number of raw COVID19 cases in the media. But I wanted to put that more into context with the state itself and account for… Read More »

R Code for Election Posterior Distribution From a Random Sample

I wrote a summary article a couple of years ago discussing some probability aspects of the 2012 Presidential general election with a particular focus on exit polling. I’ve had a few people email me asking for the code I used in some if the examples. I have used this code since before the 2008 elections so… Read More »

Recent Articles

  I have uploaded a few papers I have written and presented at some national conferences over the past several years.  Currently, all the articles relate to election research.

The Birthday Simulation

Nothing novel or unique about this problem.  This just extends the problem to measure the probability to three or more people sharing the same birthday using simulation approaches. Though there are other ways to approach this problem with built-in functions the example below shows some of the individual steps. For two people it’s fairly straight forward… Read More »

Probabilities and P-Values

P-values have been an issue for statistician for an extremely long time.  I’ve seen situations where entire narratives are written without p-values and only provide the effects. It can also be used as a data reduction tool but ultimately it reduces the world into a binary system: yes/no, accept/reject. Not only that but the binary… Read More »

Some Options for Testing Tables

Contingency tables are a very good way to summarize discrete data.  They are quite easy to construct and reasonably easy to understand. However, there are many nuances with tables and care should be taken when making conclusions related to the data. Here are just a few thoughts on the topic. Dealing with sparse data On… Read More »

Spatial Clustering With Equal Sizes

This is a problem I have encountered many times where the goal is to take a sample of spatial locations and apply constraints to the algorithm.  In addition to providing a pre-determined number of K clusters a fixed size of elements needs to be held constant within each cluster. An application of this algorithm is… Read More »

Tracking the 2013 Hurricane Season

With it nearing the end of hurricane season it’s only appropriate to do a brief summary of the activity this year.   It’s been a surprisingly low-key season as far as hurricanes are concerned.  There have been only a few hurricanes and the barometric pressure of any hurricane this season has not even come close… Read More »

Beta Distribution and the NJ U.S. Senate Election

The beta distribution is highly flexible distribution and applies to many situations and environments. The beta distribution applies well when there are percentages. The upcoming New Jersey U.S. Senate election on Wednesday fits that criterion quite well. So here I applied the beta distribution to some pre-election polls where the numbers were obtained through the… Read More »