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Bayesian Methods in Statistics: From Concepts to Practice [Pehme köide]

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  • Formaat: Paperback / softback, 272 pages, kõrgus x laius: 232x186 mm, kaal: 540 g
  • Ilmumisaeg: 02-Dec-2021
  • Kirjastus: Sage Publications Ltd
  • ISBN-10: 1529768608
  • ISBN-13: 9781529768602
Teised raamatud teemal:
Bayesian Methods in Statistics: From Concepts to PracticeSuurem pilt
  • Formaat: Paperback / softback, 272 pages, kõrgus x laius: 232x186 mm, kaal: 540 g
  • Ilmumisaeg: 02-Dec-2021
  • Kirjastus: Sage Publications Ltd
  • ISBN-10: 1529768608
  • ISBN-13: 9781529768602
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781529768602.html
Märksõnad:

This book walks you through learning probability and statistics from a Bayesian point of view.

From an introduction to probability theory through to frameworks for doing rigorous calculations of probability, it discusses Bayes’ Theorem before illustrating how to use it in a variety of different situations with data addressing social and psychological issues.

The book also:

  • Equips you with coding skills in the statistical modelling language Stan and programming language R.
  • Discusses how Bayesian approaches to statistics compare to classical approaches.
  • Introduces Markov Chain Monte Carlo methods for doing Bayesian statistics through computer simulations, so you understand how Bayesian solutions are implemented.

Features include an introduction to each chapter and a chapter summary to help you check your learning. All the examples and data used in the book are also available in the online resources so you can practice at your own pace.

For readers with some understanding of basic mathematical functions and notation, this book will get you up and running so you can do Bayesian statistics with confidence.



This book gets you up and running with doing complex Bayesian statistics, focussing on applied analysis rather than maths.

Arvustused

A concise and engaging introduction to Bayesian statistics for newcomers in the social sciences, using real world data to highlight these powerful methods of statistical inference. -- Alex Jones

List of Figures xi
List of Tables xv
Discover the Online Resources xvii
About the Author xix
Acknowledgements xxi
Preface xxiii
1 Probability 1(16)
Introduction
2(2)
Events
4(2)
Axioms of Probability
6(3)
Conditional Probabilities and Independence
9(2)
Assigning Probabilities
11(4)
Equal Probabilities
11(2)
Betting Odds
13(1)
Frequency
14(1)
Summary
15(1)
Online Resources
16(1)
2 Probability Distributions 17(36)
Introduction
18(4)
Summary Measures of Probability Distributions
22(2)
Some Common Distributions
24(22)
The Discrete Uniform Distribution
26(2)
The Continuous Uniform Distribution
28(1)
The Binomial Distribution
29(2)
The Beta Distribution
31(2)
The Negative Binomial Distribution
33(3)
The Poisson Distribution
36(2)
The Exponential Distribution
38(2)
The Gamma Distribution
40(1)
The Normal Distribution
41(2)
Lognormal Distribution
43(1)
The 'Student' t Distribution
44(1)
Inverse Gamma Distribution
45(1)
The Logistic Distribution
45(1)
Multivariate Distributions
46(6)
Distribution and Density Functions
46(2)
Summary Measures and Relationships
48(1)
A Probability Distribution Over Correlation Matrices
49(1)
The Multivariate Normal Distribution
50(1)
The Dirichlet Distribution
50(1)
The Multinomial Distribution
51(1)
Summary
52(1)
Online Resources
52(1)
3 Models and Inference 53(32)
Introduction
54(3)
Inferences About Parameters
57(26)
Inference About a Proportion
58(5)
Conjugate Priors
63(1)
Inference About the Mean and Standard Deviation of the Normal Distribution
64(4)
Inference About the Mean and Standard Deviation of the Normal Distribution With Improper Priors
68(3)
Inference on the Lognormal Distribution Using R and Stan
71(7)
Prior Distributions for the Parameters
78(2)
Using Stan for Inference About a Proportion
80(2)
de Finetti's Exchangeability Theorem
82(1)
Summary
83(1)
Online Resources
83(2)
4 Relationship 85(28)
Introduction
86(1)
Example of Derivation of Posterior Distributions
87(1)
Estimating the Linear Relationship for Males Only
88(4)
Using More Informed Priors
92(3)
Introducing a Factor
95(3)
Adding an Interaction Term
98(3)
Bayes Factors
101(3)
Bayes Factor for an Interval Hypothesis
102(1)
Bayes Factor for a Specific Value
103(1)
The Bayes Factor Is Highly Influenced by the Prior
104(1)
Comparing Models
104(6)
Watanabe-Akaike or Widely Applicable Information Criterion
107(1)
Leave-One-Out
107(3)
Vectorization
110(1)
Summary
111(1)
Online Resources
112(1)
5 General Models 113(40)
Introduction
114(1)
Examples of the General Linear Model
114(11)
The Typical Model
114(2)
Meaning of the Parameters
116(1)
Matrix Formulation
116(1)
A Bayesian Model
117(1)
A Normal Distribution Example
118(3)
Getting Away From the Normal
121(4)
Generalized Linear Models
125(26)
The Formulation
125(2)
The Normal Distribution
127(1)
The Poisson Distribution
128(1)
The Binomial Distribution
129(1)
A Poisson Model for Bystander Responses to Soccer Violence
130(6)
Multiple Response Variables
136(3)
An Alternative Parameterization
139(7)
Missing Data
146(5)
Summary
151(1)
Online Resources
151(2)
6 Questionnaires and Non-quantitative Responses 153(28)
Introduction
154(1)
Ordered Regression Models
155(6)
Concepts
155(2)
The Bystander Example Continued
157(4)
Categorical Logistic Regression
161(12)
Concepts
161(3)
Categorical Logistic Regression Example
164(6)
Criticizing the Model
170(3)
Binomial Logistic Model
173(6)
Concepts
173(1)
Bernoulli Logit Example: Bystander Intervention
174(1)
Criticizing the Model
175(4)
Summary
179(1)
Online Resources
180(1)
7 Multiple Issues 181(50)
Introduction
182(1)
Multivariate Responses Based on the Normal Distribution
182(8)
Concepts
182(2)
Application
184(6)
A Mixed Model Example
190(11)
Concepts
190(4)
Application to the Mimicry Data
194(4)
Partial Pooling
198(3)
Multivariate Responses Based on the Multinomial Distribution
201(10)
Concepts
201(2)
Application
203(3)
The Multinomial Logit Model
206(5)
Markov Chain Monte Carlo
211(11)
Monte Carlo Concepts
211(4)
Markov Chain Concepts
215(3)
Metropolis Examples
218(4)
Random Comments
222(6)
A Random Walk
222(3)
Observables and Unobservables
225(1)
Confidence Intervals
225(1)
Significance Tests
226(1)
Principles
227(1)
Summary
228(1)
A Complement to Stan: rstanarm
228(1)
Liberating
229(1)
The Rhat Value
229(1)
Online Resources
230(1)
References 231(4)
Index 235
Mel Slater is a Distinguished Investigator at the University of Barcelona, and co-Director of the Event Lab (Experimental Virtual Environments for Neuroscience and Technology). He was previously Professor of Virtual Environments at University College London (UCL) in the Department of Computer Science. He was awarded the 2005 IEEE Virtual Reality Career Award: In Recognition of Pioneering Achievements in Theory and Applications of Virtual Reality.

He is Field Editor of Frontiers in Virtual Reality, and Chief Editor of the Human Behaviour in VR section. He was awarded the Humboldt Research Prize from Germany in 2020. He is a Fellow of the Royal Statistical Society.