Statistical Inference
A detailed course for University students into Statistical Inference.
This is really the crux of what statistics is all about: how do we
get from a small sample to a constructive inference about the whole population?
Likelihood
Likelihood | Log-likelihood | Sufficiency | Multiple Parameters
Maximum Likelihood Estimation (MLE)
MLE | Score equation | Information | Invariance
Hypothesis Testing (Comprehensive)
Hypothesis testing Intuition | Null hypotheses | Test Statistic | p-value | Confidence Intervals | Significant treatment difference | Power and Sample Size
Score test | Wald test | Likelihood Ratio (LR) test
Visualisation and intuition of each test
Introduction to Bayesian Statistics
Bayesian vs Frequentist statistics | Bayes Theory | Bayesian inference for a normal mean | Conjugate priors | Credible Intervals
Other inference methods
Exact Test | Empirical Distribution | Bootstrapping
Non-parametric tests
Sign Test | Wilcoxon Signed Rank test | Mann-Whitney U test