Mu Zhu: Essential Statistics for Data Science

Cover: 9780192867742 | Essential Statistics for Data Science | A Concise Crash Course | Zhu

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Beschreibung

Essential Statistics for Data Science: A Concise Crash Course is for students entering a serious graduate program in data science without knowing enough statistics.

Über den Autor

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.

Inhaltsverzeichnis

Prologue

I Talking Probability

1: 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

3.A. 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: 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: 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: 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

Details

Erscheinungsjahr:	2023
Genre:	Technik allg.
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	Kartoniert / Broschiert
ISBN-13:	9780192867742
ISBN-10:	0192867741
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Zhu, Mu
Hersteller:	Oxford University Press
Maße:	226 x 163 x 15 mm
Von/Mit:	Mu Zhu
Erscheinungsdatum:	04.07.2023
Gewicht:	0,295 kg

Artikel-ID: 125884165

Über den Autor

Inhaltsverzeichnis

Prologue

I Talking Probability

1: 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

3.A. 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: 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: 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: 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

Details

Erscheinungsjahr:	2023
Genre:	Technik allg.
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	Kartoniert / Broschiert
ISBN-13:	9780192867742
ISBN-10:	0192867741
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Zhu, Mu
Hersteller:	Oxford University Press
Maße:	226 x 163 x 15 mm
Von/Mit:	Mu Zhu
Erscheinungsdatum:	04.07.2023
Gewicht:	0,295 kg