Statistics
Uncertainty, inference, and decision-making
A structured system for probability → models → inference → asymptotics → computation → learning → causality.
Probability Foundations
The Mathematics of Uncertainty
Building rigorous foundations for probability theory and random variables.
Statistical Models
Parametric Families and Distributions
Understanding statistical models, parametric families, and their properties.
Point Estimation
Estimating Parameters from Data
Methods for estimating parameters: maximum likelihood, method of moments, and Bayesian estimation.
Interval Estimation
Confidence and Credible Intervals
Constructing and interpreting confidence intervals and credible regions.
Hypothesis Testing
Statistical Inference and Decision Theory
Frameworks for hypothesis testing, p-values, power, and multiple testing.
Bayesian Inference
Posterior Distributions and Belief Updates
Bayesian methods, prior elicitation, posterior computation, and decision-making.
Asymptotic Theory
Large-Sample Behavior
Consistency, asymptotic normality, and the delta method.
Multivariate Linear Models
Regression and ANOVA
Linear regression, generalized linear models, and analysis of variance.
Computational Statistics
Monte Carlo and Resampling Methods
Bootstrap, permutation tests, MCMC, and computational inference.
Model Selection & Learning
Bias-Variance Tradeoff and Regularization
Cross-validation, information criteria, regularization, and statistical learning theory.
Causality
Causal Inference and Graphical Models
Causal graphs, do-calculus, potential outcomes, and experimental design.
Guided instruction and research mentorship are offered separately → hbar.work