
Abstract: Empirical and Bayesian reasoning complement each other. Rather than opposing schools of statistics here we illustrate how Bayesian Statistics can improve Empirical Frequentist-Scientific Measures. Illustrative Examples:
• Why does the ”impossible” happen all the time? Accurate Bayesian Prediction of Catastrophes and Extreme Values.
• Turning Type-I errors-α into False Discovery Rates, through Bayesian Expected Trees.
• Why ”most statistical findings turn out to be false”? Replacement of p-values by Bayes Factors.
• Is the Extra-Sensory Perception Real? ”Do you want to reject a Hypothesis? Take a Large Enough Sample, and Do Not Use BayesFactors”.
• If you have a data set with outliers, like in the famous Darwin’s data. Can you make predictions weighting a Normal and an Outlier prone Distribution, by their posterior model probabilities?
• Applications to Health Studies by Bayesian Model Averaging and Inclusion Probabilities.
• Some of the most important questions of the world are Demographic and Modern Demography is Probabilistic and Bayesian with Hierarchical Models across countries (United Nations Models).