Probability and Random Samples Statistical inference Probability Random variables Probability distributions Independence Random samples Sampling bias Sampling variation Large samples Extended example Estimation Concepts Statistical models Parametric models Statistics and data reduction Estimators and estimates Properties of estimators Large sample properties Interval estimation Coverage probability Towards hypothesis testing Extended example Likelihood Statistical likelihood Likelihood function Log-likelihood function Sufficient statistics and data reduction Multiple parameters Nuisance parameters Extended example Estimation Methods Maximum likelihood estimation Computation of the MLE Information and standard errors Properties of the MLE Multiple parameters Further estimation methods Extended example Hypothesis Testing Concepts Hypotheses Statistical tests Acceptance versus non-rejection Statistical errors Power and sample size P-values Extended example Hypothesis Testing Methods Approaches to hypothesis testing Likelihood ratio test Score test Wald test Comparison of the three approaches Multiple parameters Hypotheses about all parameters Hypotheses about one parameter Hypotheses about some parameters Test-based confidence intervals Extended example Bayesian Inference Probability and uncertainty Bayes' rule Prior and posterior distributions Conjugate prior distributions Estimation of a normal mean Credible intervals Non-informative prior distributions Multiple parameters Connection to likelihood inference Extended example Further Inference Topics Exact methods Non-parametric methods Semi-parametric methods Bootstrapping Permutation methods Extended example Appendix A: Common probability distributions Appendix B: Simulation tools.