Lecture 1

Lecture 2

Lecture 7

Lecture 5

Lecture 6

Lecture 3

Lecture 4

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Lecture 13

Lecture 14

Lecture 15

Probability & Distributions: Probability traps; Binomial & Poisson Distributons; Expectation and Variance; Estimators; Gaussian Distribution

Trials & Errors: Properties of Normal Distributions; Trials and Tribulations!; Regression to the Mean; Correlations Uncertainties & Error Propagation; Error bars

Testing Models: chi-squared; “Scientific Method”; Student’s t; Correlation test; Non-parametric tests

Distribution Tails & Likelihood: What is ‘Normal?’; Robust parameter estimation; p-values; Combined p-values; Maximum Likelihood; Neyman-Pearson Lemma; Fisher Information, Wilks' Theorem

Likelihood (continued) & Bayes' Theorem: Joint analysis; Constraints; Extended Likelihood; Asimov Data Sets; Binned Histogram PDFs &  Error Propagation; Bayes' Theorem

Priors, Unfolding  and Weighting: Mandatory Nature of Priors; Examples; Bernstein-von Mises; Deconvolution ("Unfolding"), Weighting

Confidence vs Credibility: More Condifence Issues; Bayesian Credibility Intervals;  CLs Method; Integration vs Maximisation; Dealing with Priors; Display of Frequentist and Bayesian Information

Hypothesis Testing & Data Presentation:  Selection & Rejection; Bayesian Information Criterion;

‘Binsmanship’ and Dodgy Deviations; Meaning of Error Bars (and what to use); More Things to Avoid; Displaying Uncertainties & Multi-Dimensional Data; Boxes, Whiskers and Violins

Useful Tools for Experimental Design: Effective Contributions to Uncertainties and “Pulls” Analysis; Blind Analysis; Bifurcated Side-Band Analysis; Statistical Optimisation; A Note on Redundancy & Calibration

Monte Carlo methods: Distribution sampling; Markov chains; MC Integration; Smart sampling, Weighted sampling

Optimisaton Methods: Grid Search; Golden Ratio; Powell's Method, Gradient Descent;  Markov Chain Monte Carlo techniques (with a simple example)

Machine Learning & Decision Trees: Supervised vs Unsupervised Learning; Decision Trees; Random Forests; Boosted Decision Trees (AdaBoost), with example & performance analysis

Data-Driven Approaches: Fisher Discriminant; Kernel Density Estimation (with a simple example); Gaussian Processes, Bayesian Optimisation (with example)

ANNs: Fisher Discriminant & Perceptrons; Neural Nets & Universal Approximation; Feed Forward, Propagate Backwards!; 3 Useful Tools; Playtime with PyTorch; Stability & Quantifying Uncertainties

Deep Learning & Transformers: Deep Learning Principles; Transformer Overview; Embedding and Encoding; Attention!; Encoders and Decoders; More Playtime with PyTorch

Problem Set

Likelihood Exercise

Kernel Density Estimation

Gaussian Processes

Artificial Neural Net

Transformer Encoder

Deconvolution

Boosted Decision Tree

Lecture 16

Confidence Intervals:  Wilks' and Neyman; Meaning and Misinterpretation; Issues with Confidence Intervals

MCMC Optimisation

Weighting