ISBN : 9780198841296

Price(incl.tax):

¥13,695

- Pages
- 432 Pages

- Format
- Hardcover

- Size
- 189 x 246 mm

- Pub date
- May 2019

Bayesian statistics is currently undergoing something of a renaissance. At its heart is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. It is an approach that is ideally suited to making initial assessments based on incomplete or imperfect information; as that information is gathered and disseminated, the Bayesian approach corrects or replaces the assumptions and alters its decision-making accordingly to generate a new set of probabilities. As new data/evidence becomes available the probability for a particular hypothesis can therefore be steadily refined and revised. It is very well-suited to the scientific method in general and is widely used across the social, biological, medical, and physical sciences. Key to this book's novel and informal perspective is its unique pedagogy, a question and answer approach that utilizes accessible language, humor, plentiful illustrations, and frequent reference to on-line resources.

Index:

Section 1

Basics of Probability

1 Introduction to Probability

2 Joint, Marginal, and Conditional Probability

Section 2

Bayes' Theorem and Bayesian Inference

3 Bayes' Theorem

4 Bayesian Inference

5 The Author Problem - Bayesian Inference with Two Hypotheses

6 The Birthday Problem: Bayesian Inference with Multiple Discrete Hypotheses

7 The Portrait Problem - The Portrait Problem: Bayesian Inference with Joint Likelihood

Section 3

Probability Distributions

8 Probability Mass Functions

9 Probability Density Functions

Section 4

Bayesian Conjugates

10 The White House Problem: The Beta-Binomial Conjugate

11 The Shark Attack Problem: The Gamma-Poisson Conjugate

12 The Maple Syrup Problem: The Normal-Normal Conjugate

Section 5

Monte Carlo Markov Chains (MCMC)

13 The Shark Attack Problem Revisited: MCMC with the Metropolis Algorithm

14 MCMC Diagnostic Approaches

15 The White House Problem Revisited: MCMC with the Metropolis-Hastings Algorithm

16 The Maple Syrup Problem Revisited: MCMC with Gibbs Sampling

Section 6

Applications

17 The Survivor Problem: Simple Linear Regression with MCMC

18 The Survivor Problem Continued: Introduction to Bayesian Model Selection

19 The Lorax Problem: Introduction to Bayesian Networks

20 The Onceler Problem: Introduction to Decision Trees

Appendices

Appendix 1: Beta-Binomial Conjugate

Appendix 2: Gamma-Poisson Conjugate

Appendix 3: Normal-Normal Conjugate

Appendix 4: Simple Linear Regression Conjugates

Appendix 5: Regression Standardization in MCMC