## Wednesday, April 19, 2017

### Philosophy in Statistics and Statistics in Philosophy

Statistics is the development of specific methods for evaluating hypotheses by utilizing and assessing empirical facts. Statistics evaluates a data set and interprets probability distributions over the possible sets. The philosophy of statistics is the understanding and proper interpretation of statistical methods, their utility, abuse, and meaning. Uncovering the steps that were taken to interpret statistical results is quite important to maintain integrity and honesty. This means that the foundation for the motivation and justification of data analysis and experimental design are considered. David Cox, a prominent British statistician, claims that any kind of interpretation of evidence is in fact a statistical model and should be treated as such. Statistical philosophy also tries to make a clear distinction between induction and logical deduction, which is usually not valued. But one of the best aspect of this approach is the awareness of the abuse of statistics, such as selection of method or transformations of the data. The philosophy of statistics is a great progressive movement which can help improve the quality of science being reported.

Statistics can be used to address questions in philosophy. It is not uncommon for there to be more than one way to solve a statistics problem; but there are times when more than one or no solution is correct. I would say that these kinds of problems intrigue people the most. One unanswered statistic problem of a philosophical nature is the “Sunrise Problem.” The question is “What is the probability that the sun will rise tomorrow?” There two ways to solve this problem is by using the “one sun, many days” or the “one day, many suns” approach. As long as you establish the proper axioms, both approaches come to a solution that is considered statistically correct, yet completely different. Another philosophically relevant statistic problem is the two envelopes problem, also known as the exchange paradox. In this brainteaser, the setup is as follows: you are given two identical envelopes, one envelope has \$100, the other has \$50; you pick one but are given the option to change your decision. There are many proposed solutions to this problem and none is widely accepted as definitive. It would seem obvious that switching the envelopes is pointless, but one can argue that it is better to switch envelopes. The following equations can be used to argue both sides of the argument. The amount in the envelope is denoted by “A”. The first equation states that by switching, the expected value is greater by 25% (1/4). Whereas the bottom equation (3x=total money so one envelope is 2x, and the other 1x) shows that there is no difference in amount expected if you swap.

Unanswerable questions (especially ones regarding philosophical statistics) challenge people to develop new theories. But most importantly, these questions bring about new ways to approaching problems.