This is based upon my solution of Exercise 2.3, page 18, R. Christensen, W. Johnson, A. Branscum, T. E. Hanson, Bayesian Ideas and Data Analysis, Chapman & Hall, 2011. The purpose is to show how information latent in a set of data can be revealed by Bayesian inference or, as it is sometimes called in this case, Bayesian inversion.
There’s data about numbers of cars manufactured on different days, and data regarding numbers of those cars which are defective.
Applying Bayes Rule, this can be calculated as
My point? This needed be limited to problems regarding defective cars. Rather than calculating p-values from mysteriously posed t-tests applied to statistical populations for which the assumptions regarding t-tests are questionable, such as might arise in determining whether a temperature trend is statistically important, with a bit more sophistication, the odds of there being a trend versus their not being a trend can be calculated. Moreover, different models can be compared in similar ways.