Features

• Probability models are developed from the shape of the sample empirical cumulative distribution function, (cdf) or a transformation of it.
• Bounds for the value of the population cumulative distribution function are obtained from the Beta distribution at each point of the empirical cdf.
• Bayes's theorem is developed from the properties of the screening test for a rare condition.
• The multinomial distribution provides an always-true model for any randomly sampled data.
• The model-free bootstrap method for finding the precision of a sample estimate has a model-based parallel - the Bayesian bootstrap - based on the always-true multinomial distribution.
• The Bayesian posterior distributions of model parameters can be obtained from the maximum likelihood analysis of the model.