Formal & Natural Sciences
Statistics & Data Science
Reasoning under uncertainty — the discipline most often invoked and least often applied correctly.
7 fields · 59 topics · 10 curated works
Fields within Statistics & Data Science
Statistical Inference
9Drawing conclusions from samples, and knowing how much to trust them.
Estimation Theory · Hypothesis Testing · Confidence Intervals · Likelihood Theory · Sufficiency & Information
Bayesian Statistics
8Probability as degree of belief, updated by evidence.
Prior Selection · Posterior Inference · Markov Chain Monte Carlo · Variational Inference · Hierarchical Models
Causal Inference
9The difference between correlation and cause, formalised.
Potential Outcomes Framework · Directed Acyclic Graphs · Confounding & Adjustment · Instrumental Variables · Regression Discontinuity
Experimental Design
8Structuring an experiment so the answer means something.
Randomised Controlled Trials · Factorial Designs · Blocking & Randomisation · A/B Testing · Sequential & Adaptive Designs
Regression & Modelling
9Fitting structure to data without fooling yourself.
Linear Models · Generalised Linear Models · Mixed Effects Models · Time Series Analysis · Survival Analysis
Statistical Computing
6Doing statistics at a scale where the arithmetic matters.
Monte Carlo Methods · Numerical Optimisation · Simulation Studies · Bootstrap Computation · Reproducible Research
Data Literacy & Statistical Misuse
10The failure modes — worth more practical attention than most of the theory.
p-Hacking & Garden of Forking Paths · The Replication Crisis · Base Rate Fallacy · Simpson's Paradox · Survivorship Bias
Reading in Statistics & Data Science
10Start here
No prior grounding assumed.
- BookThe Visual Display of Quantitative InformationEdward Tufte, 1983
Establishes data-ink ratio and graphical integrity as the standards by which any chart should be judged.
- BookHow to Lie with StatisticsDarrell Huff, 1954
A short catalogue of the standard statistical deceptions, still the fastest inoculation against most of them.
- BookR for Data ScienceHadley Wickham & Garrett Grolemund, 2017· Free
Teaches the whole analysis cycle — import, tidy, transform, visualise, model — as one workflow rather than as separate tools.
Then
Assumes you know the vocabulary.
- PaperWhy Most Published Research Findings Are FalseJohn P. A. Ioannidis, 2005· 6 pages· Free
Shows that under realistic assumptions about power, bias and prior probability, most published positive findings will not replicate.
- BookThe Book of WhyJudea Pearl & Dana Mackenzie, 2018
Causation cannot be extracted from correlation without a causal model, and now there is a formal language for writing one.
- BookAn Introduction to Statistical LearningGareth James, Daniela Witten, Trevor Hastie & Robert Tibshirani, 2013
The approachable companion to Elements: the same models with the proofs traded for intuition and worked examples.
Go deeper
Primary sources and full treatments.
- BookThe Design of ExperimentsRonald A. Fisher, 1935
Introduces randomisation, replication and the null hypothesis, and founds the idea that an experiment can be designed to answer a question.
- BookBayesian Data AnalysisGelman, Carlin, Stern, Dunson, Vehtari & Rubin, 1995
The reference for applied Bayesian work, and unusually candid about model checking and the ways a posterior can be confidently wrong.
- BookStatistical InferenceGeorge Casella & Roger L. Berger, 1990
The standard graduate text: estimation and hypothesis testing derived rather than recited, which is where the assumptions become visible.
- PaperStatistical Modeling: The Two CulturesLeo Breiman, 2001
Distinguishes data modelling from algorithmic modelling and argues statistics lost ground by ignoring the second.