Essential Statistics for Data Science A Concise Crash Course

Essential Statistics for Data Science: A Concise Crash Course is for students entering a serious graduate program or advanced undergraduate teaching in data science without knowing enough statistics. The three-part text starts from the basics of probability and random variables and guides readers towards relatively advanced topics in both frequentist and Bayesian approaches in a matter of weeks.

Part I, Talking Probability explains that the statistical approach to analysing data starts with a probability model to describe the data generating process. Part II, Doing Statistics explains that much of statistical inference is about learning unknown quantities in the model (e.g. its parameters) from the data it is presumed to have generated. Part III, Facing Uncertainty explains the importance of explicitly describing how much uncertainty we have about the model parameters, especially those with intrinsic scientific meaning, and of taking that into account when making decisions.

Essential Statistics for Data Science: A Concise Crash Course provides an in-depth introduction for beginners, while being more serious than a typical undergraduate text, but still lighter and more accessible than an average graduate text.

Mu Zhu, Professor, University of Waterloo,

Mu Zhu is Professor in the Department of Statistics & Actuarial Science at the University of Waterloo, and Fellow of the American Statistical Association. He received his AB magna cum laude in applied mathematics from Harvard University, and his PhD in statistics from Stanford University. He is currently Director of the Graduate Data Science Program at Waterloo.

Prologue
I Talking Probability
1. 1 The Eminence of Models
1.A For brave eyes only
2. Building Vocabulary
2.1. Probability
2.1.1 Basic rules
2.2. Conditional probability
2.2.1 Independence
2.2.2 Law of total probability
2.2.3 Bayes law
2.3. Random variables
2.3.1 Summation and integration
2.3.2 Expectations and variances
2.3.3 Two simple distributions
2.4. The bell curve
3. Gaining Fluency
3.1. Multiple random quantities
3.1.1 Higher-dimensional problems
3.2. Two “hard” problems
3.2.1 Functions of random variables
3.2.2 Compound distributions
3A. Sums of independent random variables
3.A.1 Convolutions
3.A.2 Moment generating functions
3.A.3 Formulae for expectations and variances
II Doing Statistics
4. An Overview of Statistics
4.1. Frequentist approach
4.1.1 Functions of random variables
4.2. Bayesian approach
4.2.1 Compound distributions
4.3. Two more distributions
4.3.1 Poisson distribution
4.3.2 Gamma distribution
4.A. Expectation and variance of the Poisson
4.B. Waiting time in Poisson process
5. The Frequentist Approach
5.1. Maximum likelihood estimation
5.1.1 Random variables that are i.i.d.
5.1.2 Problems with covariates
5.2 Statistical properties of estimators
5.3 Some advanced techniques
5.3.1 EM algorithm
5.3.2 Latent variables
5.A. Finite mixture models
6. The Bayesian Approach
6.1. Basics
6.2. Empirical Bayes
6.3. Hierarchical Bayes
6.A. General sampling algorithms
6.A.1 Metropolis algorithm
6.A.2 Some theory
6.A.3 Metropolis-Hastings algorithm
III Facing Uncertainty
7. Interval Estimation
7.1. Uncertainty quantification
7.1.1 Bayesian version
7.1.2 Frequentist version
7.2. Main difficulty
7.3. Two useful methods
7.3.1 Likelihood ratio
7.3.2 Bootstrap
8. Tests of Significance
8.1. Basics
8.1.1 Relation to interval estimation
8.1.2 The p-value
8.2. Some challenges
8.2.1 Multiple testing
8.2.2 Six degrees of separation
8.A. Intuition of Benjamini-Hockberg
IV Appendices
A. Some Further Topics
A.1 Graphical models
A.2 Regression models
A.3 Data collection
Epilogue
Bibliography
Index