Statistics want to understand the world. The world is made of probabilities, we model probabilities with functions, and we model functions with parameters.

“Observe data and construct models, infer and refine hypotheses ”

Portal for all statistics notes:

Statistical theorems:

  • Asymptotic Theorem: Law of large numbers: Sample mean approaches the population mean.
    • finite mean assumption

Statistical Assumptions

Type 1 error and Power

Distributions

Statistical Tests

Monte Carlo Simulation

Logistic Regression: model how change and covariance influence the odds of an event

Proportional Hazard Model: time to an event

Hypothesis testing p values Confidence Interval

Central Limit Theorem

Correlation vs Causation

Markov chain

parametric vs non-parametric tests

Multicollinearity

univariate vs multivariate

R tidyverse: visualisation in R

Over parameterised models

Casual Inference

Bootstrap

Adaptive decision analysis: interrupting the experiment in the middle

Estimation Problems: using data to estimate model parameters

Likelihood ratio: Type 1 error and Power UMP test. used to maximise power. T-test is a consequence of this.

Dashboards/Animations: Shiny, gganimate

Estimator