MAST90100 - Inference Methods in Biostatistics Notes

Description

This is a comprehensive compilation of information from MAST90100 lectures, the textbook, tutorials, practicals, workshops, problem booklets and other useful sources I found online to aid my study. Includes all summarised formulae required to know for each topic. Topics included are: 1. Overview of statistical inference (data, outcomes, event, types of samples). 2. Estimation concepts (statistical model, parameter, statistic, estimators, bias, standard error, relative efficiency, precision, mean squared error, prevalence estimation) 3. Large sample theory (Central Limit Theorem, LLN, convergence in distribution/probability, consistency, asymptotic efficiency) 4. Interval estimation (point estimate, confidence intervals, coverage probability) 5. Likelihood (likelihood function, log-likelihood, sufficient statistics, profile likelihood, nuisance parameters, reparametrisation) 6. Maximum likelihood estimation (score equation, observed information, Fisher information, optimal estimator, Cramer-Rao lower bound, invariance, observed/expected information matrices) 7. Bayesian inference (Bayes' theorem, posterior/prior distributions, improper priors, conjugate priors, inference for normal mean, credible intervals) 8. Hypothesis testing (null/alternative hypothesis, critical regions, p-value, Type I/II errors, power, power function, two-sample t-test, Type S/M errors, p-hacking, Bonferroni correction). 9. Hypothesis testing methods (LRT, Score test, Wald test, exact methods, Fisher's exact test, non-parametric methods, bootstrapping).