The format is very similar to a BIG cheat sheet. This cookbook integrates a variety of topics in probability theory and statistics. It is based on literature and in-class material from courses of the statistics department at the University of California in Berkeley but also influenced by other sources .
Author: Matthias Vallentin
Contents
1 Distribution Overview 3
- 1.1 Discrete Distributions . . . . . . . . . . 3
- 1.2 Continuous Distributions . . . . . . . . 4
2 Probability Theory 6
3 Random Variables 6
- 3.1 Transformations . . . . . . . . . . . . . 7
4 Expectation 7
5 Variance 7
6 Inequalities 8
7 Distribution Relationships 8
8 Probability and Moment Generating Functions 9
9 Multivariate Distributions 9
- 9.1 Standard Bivariate Normal . . . . . . . 9
- 9.2 Bivariate Normal . . . . . . . . . . . . . 9
- 9.3 Multivariate Normal . . . . . . . . . . . 9
10 Convergence 9
- 10.1 Law of Large Numbers (LLN) . . . . . . 10
- 10.2 Central Limit Theorem (CLT) . . . . . 10
11 Statistical Inference 10
- 11.1 Point Estimation . . . . . . . . . . . . . 10
- 11.2 Normal-Based Confidence Interval . . . 11
- 11.3 Empirical distribution . . . . . . . . . . 11
- 11.4 Statistical Functionals . . . . . . . . . . 11
12 Parametric Inference 11
- 12.1 Method of Moments . . . . . . . . . . . 11
- 12.2 Maximum Likelihood . . . . . . . . . . . 12
- 12.2.1 Delta Method . . . . . . . . . . . 12
- 12.3 Multiparameter Models . . . . . . . . . 12
- 12.3.1 Multiparameter delta method . . 13
- 12.4 Parametric Bootstrap . . . . . . . . . . 13
13 Hypothesis Testing 13
14 Bayesian Inference 14
- 14.1 Credible Intervals . . . . . . . . . . . . . 14
- 14.2 Function of parameters . . . . . . . . . . 14
- 14.3 Priors . . . . . . . . . . . . . . . . . . . 15
- 14.3.1 Conjugate Priors . . . . . . . . . 15
- 14.4 Bayesian Testing . . . . . . . . . . . . . 15
15 Exponential Family 16
16 Sampling Methods 16
- 16.1 The Bootstrap . . . . . . . . . . . . . . 16
- 16.1.1 Bootstrap Confidence Intervals . 16
- 16.2 Rejection Sampling . . . . . . . . . . . . 17
- 16.3 Importance Sampling . . . . . . . . . . . 17
17 Decision Theory 17
- 17.1 Risk . . . . . . . . . . . . . . . . . . . . 17
- 17.2 Admissibility . . . . . . . . . . . . . . . 17
- 17.3 Bayes Rule . . . . . . . . . . . . . . . . 18
- 17.4 Minimax Rules . . . . . . . . . . . . . . 18
18 Linear Regression 18
- 18.1 Simple Linear Regression . . . . . . . . 18
- 18.2 Prediction . . . . . . . . . . . . . . . . . 19
- 18.3 Multiple Regression . . . . . . . . . . . 19
- 18.4 Model Selection . . . . . . . . . . . . . . 19
19 Non-parametric Function Estimation 20
- 19.1 Density Estimation . . . . . . . . . . . . 20
- 19.1.1 Histograms . . . . . . . . . . . . 20
- 19.1.2 Kernel Density Estimator (KDE) 21
- 19.2 Non-parametric Regression . . . . . . . 21
- 19.3 Smoothing Using Orthogonal Functions 21
20 Stochastic Processes 22
- 20.1 Markov Chains . . . . . . . . . . . . . . 22
- 20.2 Poisson Processes . . . . . . . . . . . . . 22
21 Time Series 23
- 21.1 Stationary Time Series . . . . . . . . . . 23
- 21.2 Estimation of Correlation . . . . . . . . 24
- 21.3 Non-Stationary Time Series . . . . . . . 24
- 21.3.1 Detrending . . . . . . . . . . . . 24
- 21.4 ARIMA models . . . . . . . . . . . . . . 24
- 21.4.1 Causality and Invertibility . . . . 25
- 21.5 Spectral Analysis . . . . . . . . . . . . . 25
22 Math 26
- 22.1 Gamma Function . . . . . . . . . . . . . 26
- 22.2 Beta Function . . . . . . . . . . . . . . . 26
- 22.3 Series . . . . . . . . . . . . . . . . . . . 27
- 22.4 Combinatorics . . . . . . . . . . . . . . 27
To read the PDF version, click here.
Related articles
- Reading List for Data Scientists
- 9 Off-the-beaten-path Statistical Science Topics with Interesting A…
DSC Resources
- Services: Hire a Data Scientist | Search DSC | Classifieds | Find a Job
- Contributors: Post a Blog | Ask a Question
- Follow us: @DataScienceCtrl | @AnalyticBridge
Popular Articles
