Probability Theory: The Logic of Science
| Date: 27 April 2011, 08:48
|
PART A -- PRINCIPLES and ELEMENTARY APPLICATIONS
Chapter 1 PLAUSIBLE REASONING
Deductive and Plausible Reasoning 101
Analogies with Physical Theories 103
The Thinking Computer 104
Introducing the Robot 105
Boolean Algebra 106
Adequate Sets of Operations 108
The Basic Desiderata 111
COMMENTS 113
Common Language vs. Formal Logic 114
Nitpicking 116
Chapter 2 THE QUANTITATIVE RULES
The Product Rule 201
The Sum Rule 206
Qualitative Properties 210
Numerical Values 212
Notation and Finite Sets Policy 217
COMMENTS 218
``Subjective'' vs. ``Objective'' 218
G Theorem 218
Venn Diagrams 220
The ``Kolmogorov Axioms'' 222
Chapter 3 ELEMENTARY SAMPLING THEORY
Sampling Without Replacement 301
Logic Versus Propensity 308
Reasoning from Less Precise Information 311
Expectations 313
Other Forms and Extensions 314
Probability as a Mathematical Tool 315
The Binomial Distribution 315
Sampling With Replacement 318
Digression: A Sermon on Reality vs. Models 318
Correction for Correlations 320
Simplification 325
COMMENTS 326
A Look Ahead 328
Chapter 4 ELEMENTARY HYPOTHESIS TESTING
Prior Probabilities 401
Testing Binary Hypotheses with Binary Data 404
Non-Extensibility Beyond the Binary Case 409
Multiple Hypothesis Testing 411
Continuous Probability Distributions (pdf's) 418
Testing an Infinite Number of Hypotheses 419
Simple and Compound (or Composite) Hypotheses 424
COMMENTS 425
Etymology 425
What Have We Accomplished? 426
Chapter 5 QUEER USES FOR PROBABILITY THEORY
Extrasensory Perception 501
Mrs. Stewart's Telepathic Powers 502
Converging and Diverging Views 507
Visual Perception 511
The Discovery of Neptune 512
Digression on Alternative Hypotheses 514
Horseracing and Weather Forecasting 517
Paradoxes of Intuition 520
Bayesian Jurisprudence 521
COMMENTS 522
CONTENTS CONTENTS
Chapter 6 ELEMENTARY PARAMETER ESTIMATION
Inversion of the Urn Distributions 601
Both N and R Unknown 601
Uniform Prior 604
Truncated Uniform Priors 608
A Concave Prior 609
The Binomial Monkey Prior 611
Metamorphosis into Continuous Parameter Estimation 613
Estimation with a Binomial Sampling Distribution 614
Digression on Optional Stopping 616
The Likelihood Principle 617
Compound Estimation Problems 617
A Simple Bayesian Estimate: Quantitative Prior Information 618
From Posterior Distribution to Estimate 621
Back to the Problem 624
Effects of Qualitative Prior Information 626
The Jeffreys Prior 629
The Point of it All 630
Interval Estimation 632
Calculation of Variance 632
Generalization and Asymptotic Forms 634
A More Careful Asymptotic Derivation 635
COMMENTS 636
Chapter 7 THE CENTRAL GAUSSIAN, OR NORMAL DISTRIBUTION
The Gravitating Phenomenon 701
The Herschel--Maxwell Derivation 702
The Gauss Derivation 703
Historical Importance of Gauss' Result 704
The Landon Derivation 705
Why the Ubiquitous Use of Gaussian Distributions? 707
Why the Ubiquitous Success? 709
The Near--Irrelevance of Sampling Distributions 711
The Remarkable Efficiency of Information Transfer 712
Nuisance Parameters as Safety Devices 713
More General Properties 714
Convolution of Gaussians 715
Galton's Discovery 715
Population Dynamics and Darwinian Evolution 717
Resolution of Distributions into Gaussians 719
The Central Limit Theorem 722
Accuracy of Computations 723
COMMENTS 724
Terminology Again 724
The Great Inequality of Jupiter and Saturn 726
Chapter 8 SUFFICIENCY, ANCILLARITY, AND ALL THAT
Sufficiency 801
Fisher Sufficiency 803
Generalized Sufficiency 804
Examples
Sufficiency Plus Nuisance Parameters
The Pitman--Koopman Theorem
The Likelihood Principle
Effect of Nuisance Parameters
Use of Ancillary Information
Relation to the Likelihood Principle
Asymptotic Likelihood: Fisher Information
Combining Evidence from Different Sources: Meta--Analysis
Pooling the Data
Fine--Grained Propositions: Sam's Broken Thermometer
COMMENTS
The Fallacy of Sample Re--use
A Folk--Theorem
Effect of Prior Information
Clever Tricks and Gamesmanship
Chapter 9 REPETITIVE EXPERIMENTS -- PROBABILITY AND FREQUENCY
Physical Experiments 901
The Poorly Informed Robot 902
Induction 905
Partition Function Algorithms 907
Relation to Generating Functions 911
Another Way of Looking At It 912
Probability and Frequency 913
Halley's Mortality Table 915
COMMENTS: The Irrationalists 918
Chapter
|
DISCLAIMER:
This site does not store Probability Theory: The Logic of Science on its server. We only index and link to Probability Theory: The Logic of Science provided by other sites. Please contact the content providers to delete Probability Theory: The Logic of Science if any and email us, we'll remove relevant links or contents immediately.
Comments (0)
All
