Introduction to Statistical Modelling and Inference

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.