Statistical inference and data mining

es of probability distributions, estimation, hypothesis testing, model scoring, Gibbs sampling, rational decision making, causal inference, prediction, and model averaging. For a rigorous survey of statistics, the mathematically inclined reader should see 7. Due to space limitations, we must also ignore a number of interesting topics, including time series analysis and meta-analysis. Probability Distributions The statistical literature contains mathematical characterizations of a wealth of probability distributions, as well as properties of random variables---functions defined on the events to which a probability measure assigns values. Important relations among probability distributions include marginalization (summing over a subset of values) and conditionalization (forming a conditional probability measure from a probability measure on a sample space and some event of positive probability. Essential relations among random variable