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E-raamat: Bayesian Data Analysis for the Behavioral and Neural Sciences: Non-Calculus Fundamentals

(New York University)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 24-Jun-2021
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108880046
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Bayesian Data Analysis for the Behavioral and Neural Sciences: Non-Calculus FundamentalsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 24-Jun-2021
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108880046
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This textbook bypasses the need for advanced mathematics by providing in-text computer code, allowing students to explore Bayesian data analysis without the calculus background normally considered a prerequisite for this material. Now, students can use the best methods without needing advanced mathematical techniques. This approach goes beyond “frequentist” concepts of p-values and null hypothesis testing, using the full power of modern probability theory to solve real-world problems. The book offers a fully self-contained course, which demonstrates analysis techniques throughout with worked examples crafted specifically for students in the behavioral and neural sciences. The book presents two general algorithms that help students solve the measurement and model selection (also called “hypothesis testing”) problems most frequently encountered in real-world applications.

This textbook teaches undergraduates in psychology, neuroscience, and medicine modern data analysis techniques. It uses non-calculus-based mathematics with examples specific to behavioral and neural sciences. Perfect for statistics courses, it shows students how to write code for their own data analyses, even those involving individual differences.

Arvustused

'Todd E. Hudson's book is very readable and nicely put together. It should be a useful addition to the growing Bayesian literature aimed at university students.' D. S. Sivia, College Lecturer, St Catherine's College, Oxford, UK 'This accessible, comprehensive textbook is a self-contained introduction to data analysis in the behavioral, neural, and biomedical sciences. Starting from logical first principles and requiring only minimal mathematical background, Hudson builds and explains the formal edifice of modern probability theory and data analysis. It is an impressive work.' Joachim Vandekerckhove, Associate Professor of Cognitive Sciences, University of California, Irvine, USA

Muu info

Bayesian analyses go beyond frequentist techniques of p-values and null hypothesis tests, providing a modern understanding of data analysis.
Preface xi
Acknowledgments xv
1 Logic And Data Analysis
1(50)
1.1 The Logic of Inference
5(17)
1.1.1 Deductive Inference and Rational Belief Networks
5(2)
1.1.2 Plausible Inference
7(6)
1.1.3 Uncertainty
13(3)
1.1.4 The Logic of Data Analysis
16(6)
1.2 Data Visualization
22(25)
1.2.1 The Goal of Data Visualization
24(1)
1.2.2 Histograms
25(7)
1.2.3 Scatterplots
32(3)
1.2.4 Descriptive Statistics
35(7)
1.2.5 Data Checks: Expected versus Unexpected Data Values and Patterns
42(5)
1.3 Summary
47(4)
1.3.1 Emphasis on Worked Examples
47(2)
1.3.2 Comment on Reality
49(1)
1.3.3 Outline of the Text
49(2)
2 Mechanics Of Probability Calculations
51(68)
2.1 Symbolic Manipulations
51(38)
2.1.1 Formal Symbolic Operations for Logical Expressions
52(5)
2.1.2 Intuitive Rationale behind the Basic Rules of Probability Theory
57(4)
2.1.3 Extending the Question
61(1)
2.1.4 Marginalization
62(4)
2.1.5 The Five-Card Monty Hall Problem
66(4)
2.1.6 Inverse Probability
70(19)
2.2 Probabilities and Probability Distributions
89(8)
2.2.1 Multiplicity Factors
89(3)
2.2.2 Bernoulli Trials: The Binomial Distribution
92(2)
2.2.3 Bernoulli Trials: The Negative Binomial Distribution
94(3)
2.3 Sampling Distributions and Likelihood Functions
97(12)
2.3.1 Constructing Likelihood Functions from Sampling Distributions
98(5)
2.3.2 The Optional Stopping Problem
103(6)
2.4 Distributions Derived from Bernoulli Trials
109(7)
2.4.1 Multinomial Distribution
109(4)
2.4.2 Poisson Distribution
113(3)
2.5 Summary
116(3)
2.5.1 Marginalization: The Core of Advanced Techniques
116(1)
2.5.2 Single Probabilities
117(1)
2.5.3 Probability Distributions
117(1)
2.5.4 More to Come
117(2)
3 Probability And Information: From Priors To Posteriors
119(63)
3.1 Probability Distributions: Definition and Characteristics
120(4)
3.1.1 Probability and Information
120(4)
3.2 Discrete Distributions
124(7)
3.2.1 Uniform Distribution
124(3)
3.2.2 Binomial Distribution"
127(2)
3.2.3 Poisson Distribution
129(2)
3.3 Continuous Distributions
131(10)
3.3.1 Uniform Distribution
131(3)
3.3.2 Exponential Distribution
134(3)
3.3.3 Gaussian Distribution
137(4)
3.4 Assigning Prior Probabilities over Parameters
141(22)
3.4.1 Three Types of Prior over Parameter Values
142(1)
3.4.2 Uniform Priors
143(7)
3.4.3 Conjugate Priors
150(6)
3.4.4 Jeffreys Priors
156(2)
3.4.5 Inference under Reparameterization
158(5)
3.5 Updating Information Based on Data: The Effect of Prior Information
163(16)
3.6 Summary
179(3)
3.6.1 Prior Paralysis: Don't Be a Victim
179(1)
3.6.2 Comparison to the Frequentist Algorithm
179(1)
3.6.3 What's Next?
180(2)
4 Prediction And Decision
182(75)
4.1 Predictive Sampling Distributions
184(18)
4.1.1 Prior Predictive
186(9)
4.1.2 Posterior Predictive
195(7)
4.2 Prediction in Time-Varying Systems
202(18)
4.2.1 Optimal State Estimation
205(5)
4.2.2 Range Effects
210(10)
4.3 Decision
220(33)
4.3.1 The Mathematics of Decision Theory
221(10)
4.3.2 Decision and Measurement
231(15)
4.3.3 Clinically Relevant Differences
246(7)
4.4 Summary
253(4)
4.4.1 Integrating Basic Measurement and Predictive Distributions
253(1)
4.4.2 Decision theory Is everywhere
254(3)
5 Models And Measurements
257(102)
5.1 Observables, Models, and Measurements
259(18)
5.1.1 Measurement and Uncertainty
259(5)
5.1.2 Data versus Parameter Coordinates
264(5)
5.1.3 Graphical Models
269(8)
5.2 The Measurement Algorithm
277(6)
5.2.1 Logic
277(1)
5.2.2 The Algorithm
278(5)
5.3 Single-Source Measurements
283(55)
5.3.1 Transparent Measurement
283(8)
5.3.2 Rate Measurement
291(5)
5.3.3 Duration
296(8)
5.3.4 Straight-Line Models
304(6)
5.3.5 Binary Classification
310(7)
5.3.6 Two-Alternative Forced-Choice
317(8)
5.3.7 Exponential Decay
325(13)
5.4 Multiple-Source Measurements
338(16)
5.4.1 Central Problem of Multiple-Source Measurement
339(1)
5.4.2 Multiple Sources: Transparent I
340(3)
5.4.3 Multiple Sources: Transparent II
343(4)
5.4.4 Multiple Sources: Straight-Line Model
347(6)
5.4.5 Multiple Sources: Summary
353(1)
5.5 Summary
354(5)
5.5.1 Common Mistakes
355(3)
5.5.2 Measurement: Summary
358(1)
6 Model Comparison
359(148)
6.1 Model Comparison Algorithm
362(20)
6.1.1 Models and Measurement
362(2)
6.1.2 Hypotheses and Models
364(2)
6.1.3 Logic: General
366(7)
6.1.4 The Algorithm
373(9)
6.2 Occam Factor
382(17)
6.2.1 Occam's Razor: History and Implementation
382(3)
6.2.2 Occam Factor: Examples
385(14)
6.3 Model Comparison
399(37)
6.3.1 Binomial Rates
399(6)
6.3.2 Rate Differences
405(5)
6.3.3 Model Comparison for the Gaussian Likelihood
410(15)
6.3.4 Straight-Line Models
425(11)
6.4 Multiple Sources
436(41)
6.4.1 Logic of Model Comparison with S Sources
437(16)
6.4.2 Interrelationships among Variables: Multisource Method of Testing
453(24)
6.5 Multiple Models
477(9)
6.5.1 Logic of in Competing Models Revisited
477(9)
6.6 Summary
486(21)
6.6.1 Other Approaches to Hypothesis Testing
486(13)
6.6.2 Pitfalls of the Frequentist Algorithm as Used in Practice
499(5)
6.6.3 The Full Monty
504(1)
6.6.4 Where Do We Go from Here?
505(2)
Appendices
A Coding Basics
507(12)
A.1 Add, Subtract, Multiply, Divide, Evaluate: How to Ask Arithmetic Questions
507(1)
A.2 Assignment, Indexing, and Variable Types
508(3)
A.3 Logical Expressions, Indexing, and Flow Control
511(2)
A.4 Plotting
513(1)
A.5 Functions
514(3)
A.6 Give It a Try and See What Happens
517(2)
B Mathematics Review: Logarithmic And Exponential Functions
519(9)
B.1 Overview
519(1)
B.2 Exponential Functions
519(2)
B.3 Logarithmic Functions
521(1)
B.3.1 Computing Logarithmic Functions
521(3)
B.3.2 Uses of Logarithmic Functions
524(1)
B.3.3 Marginalization and the Logsum Problem
525(3)
C The Bayesian Toolbox: Marginalization And Coordinate Transformation
528(15)
C.1 Probability Mass Functions versus Probability Density Functions
528(1)
C.1.1 Unity Probability Mass
529(1)
C.1.2 Limitless Possibilities
530(2)
C.1.3 Area under the Curve
532(3)
C.1.4 Sequences of Areas: Discretization
535(6)
C.1.5 Approximate Marginalization of Probability Densities
541(2)
C.2 Coordinate Transforms
543(36)
C.2.1 Linking Functions for Coordinate Transformation
544(2)
C.2.2 Transforming Probability Mass Functions
546(11)
C.2.3 Approximate Transformation of Probability Densities
557(18)
C.2.4 Calculus-Based Methods for Coordinate Transformation
575(4)
C.2.5 Summary
579(1)
References 580(9)
Index 589
Todd E. Hudson is a professor of rehabilitation medicine at New York University's Grossman School of Medicine, holding cross-appointments in neurology, and also in the Department of Biomedical Engineering at the New York University Tandon School of Engineering. Dr Hudson has taught statistics, perception and sensory processes, experimental design, and/or advanced topics in neurobiology and behavior at several major universities, including Brandeis University and Columbia University. He co-founded, and serves as Chief Scientific Advisor to, Tactile Navigation Tools, LLC, which develops navigation aids for the visually impaired.
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