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E-raamat: Think Bayes

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  • Formaat: 338 pages
  • Ilmumisaeg: 18-May-2021
  • Kirjastus: O'Reilly Media
  • Keel: eng
  • ISBN-13: 9781492089414
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Think BayesSuurem pilt
  • Formaat: 338 pages
  • Ilmumisaeg: 18-May-2021
  • Kirjastus: O'Reilly Media
  • Keel: eng
  • ISBN-13: 9781492089414
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If you know how to program with Python, you're ready to tackle Bayesian statistics. With this book, you'll learn how to solve statistical problems with Python code instead of mathematical formulas, using discrete probability distributions instead of continuous mathematics. Once you get the math out of the way, the Bayesian fundamentals will become clearer, and you'll begin to apply these techniques to real-world problems.

Bayesian statistical methods are becoming more common and more important, but not many resources are available to help beginners. Based on undergraduate classes taught by author Allen Downey, this book's computational approach helps you get a solid start.

  • Use your existing programming skills to learn and understand Bayesian statistics
  • Work with problems involving estimation, prediction, decision analysis, evidence, and hypothesis testing
  • Get started with simple examples, using coins, dice, and a bowl of cookies
  • Learn computational methods for solving real-world problems
Preface ix
1 Probability
1(16)
Linda the Banker
1(1)
Probability
2(1)
Fraction of Bankers
3(1)
The Probability Function
4(1)
Political Views and Parties
4(1)
Conjunction
5(1)
Conditional Probability
6(1)
Conditional Probability Is Not Commutative
7(1)
Condition and Conjunction
8(1)
Laws of Probability
8(5)
Theorem 1
9(1)
Theorem 2
10(1)
Theorem 3
10(1)
The Law of Total Probability
11(2)
Summary
13(1)
Exercises
14(3)
2 Bayes's Theorem
17(12)
The Cookie Problem
17(2)
Diachronic Bayes
19(1)
Bayes Tables
20(2)
The Dice Problem
22(1)
The Monty Hall Problem
23(2)
Summary
25(1)
Exercises
26(3)
3 Distributions
29(14)
Distributions
29(1)
Probability Mass Functions
29(3)
The Cookie Problem Revisited
32(2)
101 Bowls
34(4)
The Dice Problem
38(1)
Updating Dice
39(1)
Summary
40(1)
Exercises
41(2)
4 Estimating Proportions
43(14)
The Euro Problem
43(1)
The Binomial Distribution
44(3)
Bayesian Estimation
47(2)
Triangle Prior
49(2)
The Binomial Likelihood Function
51(1)
Bayesian Statistics
52(1)
Summary
53(1)
Exercises
54(3)
5 Estimating Counts
57(12)
The Train Problem
57(3)
Sensitivity to the Prior
60(1)
Power Law Prior
61(2)
Credible Intervals
63(1)
The German Tank Problem
64(1)
Informative Priors
65(1)
Summary
66(1)
Exercises
66(3)
6 Odds and Addends
69(14)
Odds
69(1)
Bayes's Rule
70(1)
Oliver's Blood
71(2)
Addends
73(3)
Gluten Sensitivity
76(1)
The Forward Problem
77(1)
The Inverse Problem
78(2)
Summary
80(1)
More Exercises
81(2)
7 Minimum, Maximum, and Mixture
83(16)
Cumulative Distribution Functions
83(3)
Best Three of Four
86(2)
Maximum
88(1)
Minimum
89(1)
Mixture
90(3)
General Mixtures
93(3)
Summary
96(1)
Exercises
97(2)
8 Poisson Processes
99(14)
The World Cup Problem
99(1)
The Poisson Distribution
100(1)
The Gamma Distribution
101(2)
The Update
103(2)
Probability of Superiority
105(1)
Predicting the Rematch
106(2)
The Exponential Distribution
108(2)
Summary
110(1)
Exercises
110(3)
9 Decision Analysis
113(16)
The Price Is Right Problem
113(1)
The Prior
114(1)
Kernel Density Estimation
115(1)
Distribution of Error
116(2)
Update
118(2)
Probability of Winning
120(2)
Decision Analysis
122(2)
Maximizing Expected Gain
124(2)
Summary
126(1)
Discussion
126(1)
More Exercises
127(2)
10 Testing
129(16)
Estimation
129(2)
Evidence
131(1)
Uniformly Distributed Bias
132(2)
Bayesian Hypothesis Testing
134(1)
Bayesian Bandits
134(1)
Prior Beliefs
135(1)
The Update
136(1)
Multiple Bandits
137(1)
Explore and Exploit
138(2)
The Strategy
140(2)
Summary
142(1)
More Exercises
142(3)
11 Comparison
145(16)
Outer Operations
145(2)
How Tall Is A?
147(1)
Joint Distribution
148(1)
Visualizing the Joint Distribution
149(2)
Likelihood
151(1)
The Update
152(1)
Marginal Distributions
153(3)
Conditional Posteriors
156(1)
Dependence and Independence
157(1)
Summary
158(1)
Exercises
158(3)
12 Classification
161(14)
Penguin Data
161(2)
Normal Models
163(1)
The Update
164(2)
Naive Bayesian Classification
166(2)
Joint Distributions
168(2)
Multivariate Normal Distribution
170(2)
A Less Naive Classifier
172(1)
Summary
173(1)
Exercises
173(2)
13 Inference
175(16)
Improving Reading Ability
175(2)
Estimating Parameters
177(1)
Likelihood
178(2)
Posterior Marginal Distributions
180(1)
Distribution of Differences
181(3)
Using Summary Statistics
184(2)
Update with Summary Statistics
186(1)
Comparing Marginals
187(1)
Summary
188(1)
Exercises
189(2)
14 Survival Analysis
191(16)
The Weibull Distribution
191(3)
Incomplete Data
194(2)
Using Incomplete Data
196(3)
Light Bulbs
199(2)
Posterior Means
201(1)
Posterior Predictive Distribution
202(2)
Summary
204(1)
Exercises
204(3)
15 Mark and Recapture
207(16)
The Grizzly Bear Problem
207(2)
The Update
209(2)
Two-Parameter Model
211(1)
The Prior
212(1)
The Update
213(2)
The Lincoln Index Problem
215(2)
Three-Parameter Model
217(3)
Summary
220(1)
Exercises
221(2)
16 Logistic Regression
223(18)
Log Odds
223(3)
The Space Shuttle Problem
226(3)
Prior Distribution
229(1)
Likelihood
230(1)
The Update
231(1)
Marginal Distributions
232(1)
Transforming Distributions
233(2)
Predictive Distributions
235(2)
Empirical Bayes
237(1)
Summary
238(1)
More Exercises
238(3)
17 Regression
241(16)
More Snow?
241(2)
Regression Model
243(1)
Least Squares Regression
244(1)
Priors
245(1)
Likelihood
246(1)
The Update
247(3)
Marathon World Record
250(2)
The Priors
252(2)
Prediction
254(1)
Summary
255(1)
Exercises
255(2)
18 Conjugate Priors
257(12)
The World Cup Problem Revisited
257(1)
The Conjugate Prior
258(2)
What the Actual?
260(1)
Binomial Likelihood
261(2)
Lions and Tigers and Bears
263(1)
The Dirichlet Distribution
264(2)
Summary
266(1)
Exercises
267(2)
19 MCMC
269(18)
The World Cup Problem
269(1)
Grid Approximation
270(1)
Prior Predictive Distribution
270(1)
Introducing PyMC3
271(1)
Sampling the Prior
272(2)
When Do We Get to Inference?
274(1)
Posterior Predictive Distribution
275(1)
Happiness
276(1)
Simple Regression
277(3)
Multiple Regression
280(2)
Summary
282(1)
Exercises
283(4)
20 Approximate Bayesian Computation
287(18)
The Kidney Tumor Problem
287(1)
A Simple Growth Model
288(1)
A More General Model
289(2)
Simulation
291(3)
Approximate Bayesian Computation
294(1)
Counting Cells
295(3)
Cell Counting with ABC
298(1)
When Do We Get to the Approximate Part?
299(3)
Summary
302(1)
Exercises
303(2)
Index 305
Allen Downey is a Professor of Computer Science at the Olin College of Engineering. He has taught computer science at Wellesley College, Colby College and U.C. Berkeley. He has a Ph.D. in Computer Science from U.C. Berkeley and Master's and Bachelor's degrees from MIT. He is author of Think Python, Think Bayes, Think DSP, and a blog, Probably Overthinking It.
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