The Equation of Knowledge From Bayes Rule to a Unified Philosophy of Science 1st edition by Lê Nguyên Hoang 1000063271 9781000063271

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ISBN-10 ‏ : ‎1000063271 

ISBN-13 ‏ : ‎ 9781000063271

Author: Lê Nguyên Hoang 

The Equation of Knowledge: From Bayes’ Rule to a Unified Philosophy of Science introduces readers to the Bayesian approach to science: teasing out the link between probability and knowledge. The author strives to make this book accessible to a very broad audience, suitable for professionals, students, and academics, as well as the enthusiastic amateur scientist/mathematician. This book also shows how Bayesianism sheds new light on nearly all areas of knowledge, from philosophy to mathematics, science and engineering, but also law, politics and everyday decision-making. Bayesian thinking is an important topic for research, which has seen dramatic progress in the recent years, and has a significant role to play in the understanding and development of AI and Machine Learning, among many other things. This book seeks to act as a tool for proselytising the benefits and limits of Bayesianism to a wider public. Features Presents the Bayesian approach as a unifying scientific method for a wide range of topics Suitable for a broad audience, including professionals, students, and academics Provides a more accessible, philosophical introduction to the subject that is offered elsewhere

The Equation of Knowledge From Bayes Rule to a Unified Philosophy of Science 1st Table of contents:

Section I: Pure Bayesianism
Chapter 1: On A Transformative Journey
1.1 STUMPED BY A STUDENT
1.2 MY PATH TOWARDS BAYESIANISM
1.3 A UNIFIED PHILOSOPHY OF KNOWLEDGE
1.4 AN ALTERNATIVE TO THE SCIENTIFIC METHOD
1.5 THE OBJECTIVITY MYTH
1.6 THE GOALS OF THE BOOK
Chapter 2: Bayes’ Theorem
2.1 THE TROLL STUDENT PUZZLE
2.2 THE MONTY HALL PROBLEM
2.3 THE TRIAL OF SALLY CLARK
2.4 THE LEGAL CONVICTION OF BAYESIANISM
2.5 BAYES’ THEOREM
2.6 THE COMPONENTS OF BAYES’ RULE
2.7 BAYES TO THE RESCUE OF DIAGNOSIS
2.8 BAYES TO THE RESCUE OF SALLY CLARK
2.9 BAYES TO THE RESCUE OF THE TROLL STUDENT PROBLEM
2.10 A FEW WORDS OF ENCOURAGEMENT
Chapter 3: Logically Speaking…
3.1 TWO THINKING PROCESSES
3.2 THE RULES OF LOGIC
3.3 ARE ALL QUEENS BLUE?
3.4 QUANTIFIERS AND PREDICATES
3.5 ARISTOTLE’S SYLLOGISM REINTERPRETED
3.6 AXIOMATIZATION
3.7 PLATONISTS VERSUS INTUITIONISTS
3.8 BAYESIAN LOGIC*
3.9 BEYOND TRUE OR FALSE
3.10 THE COHABITATION OF INCOMPATIBLE THEORIES
Chapter 4: Let’s Generalize!
4.1 THE SCOTTISH BLACK SHEEP
4.2 A BRIEF HISTORY OF EPISTEMOLOGY
4.3 A BRIEF HISTORY OF PLANETOLOGY
4.4 SCIENCE AGAINST POPPER?
4.5 FREQUENTISM*
4.6 STATISTICIANS AGAINST THE p-VALUE
4.7 p-HACKING
4.8 WHAT A STATISTICS TEXTBOOK SAYS
4.9 THE EQUATION OF KNOWLEDGE
4.10 CUMULATIVE LEARNING
4.11 BACK TO EINSTEIN
Chapter 5: All Hail Prejudices
5.1 THE LINDA PROBLEM
5.2 PREJUDICES TO THE RESCUE OF LINDA*
5.3 LONG LIVE PREJUDICES
5.4 xkcd’s SUN
5.5 PREJUDICES TO THE RESCUE OF xkcd
5.6 PREJUDICES TO THE RESCUE OF SALLY CLARK
5.7 PREJUDICES AGAINST PSEUDO-SCIENCES
5.8 PREJUDICES TO THE RESCUE OF SCIENCE
5.9 THE BAYESIAN HAS AN OPINION ON EVERYTHING
5.10 ERRONEOUS PREJUDICES
5.11 PREJUDICES AND MORAL QUESTIONS
Chapter 6: The Bayesian Prophets
6.1 A THRILLING HISTORY
6.2 THE ORIGINS OF PROBABILITY
6.3 THE MYSTERIOUS THOMAS BAYES
6.4 LAPLACE, THE FATHER OF BAYESIANISM
6.5 LAPLACE’S SUCCESSION RULE
6.6 THE GREAT BAYESIAN WINTER
6.7 BAYES TO THE RESCUE OF ALLIES
6.8 BAYESIAN ISLANDS IN A FREQUENTIST OCEAN
6.9 BAYES TO THE RESCUE OF PRACTITIONERS
6.10 BAYES’ TRIUMPH, AT LAST!
6.11 BAYES IS UBIQUITOUS
Chapter 7: Solomonoff’s Demon
7.1 NEITHER HUMAN NOR MACHINE
7.2 THE THEORY OF COMPUTATION
7.3 WHAT’S A PATTERN?
7.4 THE SOLOMONOFF COMPLEXITY*
7.5 THE MARRIAGE OF ALGORITHMICS AND PROBABILITIES
7.6 THE SOLOMONOFF PRIOR*
7.7 BAYES TO THE RESCUE OF SOLOMONOFF’S DEMON*
7.8 SOLOMONOFF’S COMPLETENESS
7.9 SOLOMONOFF’S INCOMPUTABILITY
7.10 SOLOMONOFF’S INCOMPLETENESS
7.11 LET’S BE PRAGMATIC
Section II: Applied Bayesianism
Chapter 8: Can You Keep A Secret?
8.1 CLASSIFIED
8.2 TODAY’S CRYPTOGRAPHY
8.3 BAYES BREAKS CODES
8.4 RANDOMIZED SURVEY
8.5 THE PRIVACY OF THE RANDOMIZED SURVEY
8.6 THE DEFINITION OF DIFFERENTIAL PRIVACY*
8.7 THE LAPLACIAN MECHANISM
8.8 ROBUSTNESS TO COMPOSITION
8.9 THE ADDITION OF PRIVACY LOSSES
8.10 IN PRACTICE, IT’S NOT GOING WELL!
8.11 HOMOMORPHIC ENCRYPTION
Chapter 9: Game, Set and Math
9.1 THE MAGOUILLEUSE
9.2 SPLIT OR STEAL?
9.3 BAYESIAN PERSUASION
9.4 SCHELLING’S POINTS
9.5 MIXED EQUILIBRIUM
9.6 BAYESIAN GAMES
9.7 BAYESIAN MECHANISM DESIGN*
9.8 MYERSON’S AUCTION
9.9 THE SOCIAL CONSEQUENCES OF BAYESIANISM
Chapter 10: Will Darwin Select Bayes?
10.1 THE SURVIVOR BIAS
10.2 CALIFORNIA’S COLORED LIZARDS
10.3 THE LOTKA-VOLTERRA DYNAMIC*
10.4 GENETIC ALGORITHMS
10.5 MAKE UP YOUR OWN MIND?
10.6 AARONSON’S BAYESIAN DEBATING
10.7 SHOULD YOU TRUST A SCIENTIST?
10.8 THE ARGUMENT OF AUTHORITY
10.9 THE SCIENTIFIC CONSENSUS
10.10 CLICKBAIT
10.11 THE PREDICTIVE POWER OF MARKETS
10.12 FINANCIAL BUBBLES
Chapter 11: Exponentially Counterintuitive
11.1 SUPER LARGE NUMBERS
11.2 THE GLASS CEILING OF COMPUTATION
11.3 EXPONENTIAL EXPLOSION
11.4 THE MAGIC OF ARABIC NUMERALS
11.5 BENFORD’S LAW
11.6 LOGARITHMIC SCALES
11.7 LOGARITHMS
11.8 BAYES WINS A GO¨ DEL PRIZE
11.9 BAYES ON HOLIDAY
11.10 THE SINGULARITY
Chapter 12: Ockham Cuts to the Chase
12.1 LAST THURSDAY
12.2 IN FOOTBALL, YOU NEVER KNOW
12.3 THE CURSE OF OVERFITTING
12.4 THE COMPLEX QUEST OF SIMPLICITY
12.5 NOT ALL IS SIMPLE
12.6 CROSS VALIDATION
12.7 TIBSCHIRANI’S REGULARIZATION
12.8 ROBUST OPTIMIZATION
12.9 BAYES TO THE RESCUE OF OVERFITTING*
12.10 ONLY BAYESIAN INFERENCES ARE ADMISSIBLE*
12.11 OCKHAM’S RAZOR AS A BAYESIAN THEOREM!
Chapter 13: Facts Are Misleading
13.1 HOSPITAL OR CLINIC
13.2 CORRELATION IS NOT CAUSALITY
13.3 LET’S SEARCH FOR CONFOUNDING VARIABLES!
13.4 REGRESSION TO THE MEAN
13.5 STEIN’S PARADOX
13.6 THE FAILURE OF ENDOGENOUS STRATIFICATION
13.7 RANDOMIZE!
13.8 CAVEATS ABOUT RANDOMIZED CONTROLLED TRIALS
13.9 THE RETURN OF THE SCOTTISH BLACK SHEEP
13.10 WHAT’S A CAT?
13.11 POETIC NATURALISM
Section III: Pragmatic Bayesianism
Chapter 14: Quick And Not Too Dirty
14.1 THE MYSTERY OF PRIMES
14.2 THE PRIME NUMBER THEOREM
14.3 APPROXIMATING T
14.4 LINEARIZATION
14.5 THE CONSTRAINTS OF PRAGMATISM
14.6 TURING’S LEARNING MACHINES
14.7 PRAGMATIC BAYESIANISM
14.8 SUBLINEAR ALGORITHMS
14.9 DIFFERENT THINKING MODES
14.10 BECOME POST-RIGOROUS!
14.11 BAYESIAN APPROXIMATIONS
Chapter 15: Wish Me Luck
15.1 FIVETHIRTYEIGHT AND THE 2016 US ELECTION
15.2 IS QUANTUM MECHANICS PROBABILISTIC?
15.3 CHAOS THEORY
15.4 UNPREDICTABLE DETERMINISTIC AUTOMATA
15.5 THERMODYNAMICS
15.6 SHANNON’S ENTROPY
15.7 SHANNON’S OPTIMAL COMPRESSION
15.8 SHANNON’S REDUNDANCY
15.9 THE KULLBACK-LEIBLER DIVERGENCE
15.10 PROPER SCORING RULES
15.11 WASSERSTEIN’S METRIC
15.12 GENERATIVE ADVERSARIAL NETWORKS (GANS)
Chapter 16: Down Memory Lane
16.1 THE VALUE OF DATA
16.2 THE DELUGE OF DATA
16.3 THE TOILET PROBLEM
16.4 EFFICIENT BIG DATA PROCESSING
16.5 THE KALMAN FILTER
16.6 OUR BRAINS FACED WITH BIG DATA
16.7 REMOVING TRAUMATIC SOUVENIRS
16.8 FALSE MEMORY
16.9 BAYES TO THE RESCUE OF MEMORY
16.10 SHORTER AND LONGER-TERM MEMORIES
16.11 RECURRENT NEURAL NETWORKS
16.12 ATTENTION MECHANISMS
16.13 WHAT SHOULD BE TAUGHT AND LEARNED?
Chapter 17: Let’s Sleep on It
17.1 WHERE DO IDEAS COME FROM?
17.2 CREATIVE ART BY ARTIFICIAL INTELLIGENCES
17.3 LATENT DIRICHLET ALLOCATION (LDA)
17.4 THE CHINESE RESTAURANT
17.5 MONTE CARLO SIMULATIONS
17.6 STOCHASTIC GRADIENT DESCENT (SGD)
17.7 PSEUDO-RANDOM NUMBERS
17.8 IMPORTANCE SAMPLING
17.9 IMPORTANCE SAMPLING FOR LDA
17.10 THE ISING MODEL*
17.11 THE BOLTZMANN MACHINE
17.12 MCMC AND GOOGLE PAGERANK
17.13 METROPOLIS-HASTING SAMPLING
17.14 GIBBS SAMPLING
17.15 MCMC AND COGNITIVE BIASES
17.16 CONSTRASTIVE DIVERGENCE
Chapter 18: The Unreasonable Effectiveness of Abstraction
18.1 DEEP LEARNING WORKS!
18.2 FEATURE LEARNING
18.3 WORD VECTOR REPRESENTATION
18.4 EXPONENTIAL EXPRESSIVITY*
18.5 THE EMERGENCE OF COMPLEXITY
18.6 THE KOLMOGOROV SOPHISTICATION*
18.7 SOPHISTICATION IS A SOLOMONOFF MAP!*
18.8 THE BENNETT LOGICAL DEPTH
18.9 THE DEPTH OF MATHEMATICS
18.10 THE CONCISION OF MATHEMATICS
18.11 THE MODULARITY OF MATHEMATICS
Chapter 19: The Bayesian Brain
19.1 THE BRAIN IS FORMIDABLE
19.2 MOUNTAIN OR VALLEY?
19.3 OPTICAL ILLUSIONS
19.4 THE PERCEPTION OF MOTION
19.5 BAYESIAN SAMPLING
19.6 THE SCANDAL OF INDUCTION
19.7 LEARNING TO LEARN
19.8 THE BLESSING OF ABSTRACTION
19.9 THE BABY IS A GENIUS
19.10 LEARNING TO TALK
19.11 LEARNING TO COUNT
19.12 THE THEORY OF MIND
19.13 NATURE VERSUS NURTURE
Section IV: Beyond Bayesianism
Chapter 20: It’s All Fiction
20.1 PLATO’S CAVE
20.2 ANTIREALISM
20.3 DOES LIFE EXIST?
20.4 DOES MONEY EXIST?
20.5 IS TELEOLOGY A SCIENTIFIC DEAD END?
20.6 THE CHURCH-TURING THESIS VERSUS REALITY
20.7 IS (INSTRUMENTAL) ANTIREALISM USEFUL?
20.8 IS THERE A WORLD OUTSIDE OUR BRAIN?
20.9 A CAT IN A BINARY CODE?
20.10 SOLOMONOFF DEMON’S ANTIREALISM
Chapter 21: Exploring The Origins of Beliefs
21.1 THE SCANDAL OF DIVERGENT SERIES
21.2 BUT THIS IS FALSE, RIGHT?
21.3 CADET OFFICER
21.4 MY ASIAN JOURNEY
21.5 ARE WE ALL POTENTIAL MONSTERS?
21.6 STORIES OVER STATISTICS
21.7 SUPERSTITIONS
21.8 THE DARWINIAN EVOLUTION OF IDEOLOGIES
21.9 BELIEVING SUPERSTITIONS CAN BE USEFUL
21.10 THE MAGIC OF YOUTUBE
21.11 THE JOURNEY GOES ON
Chapter 22: Beyond Bayesianism
22.1 THE BAYESIAN HAS NO MORAL
22.2 THE NATURAL MORAL
22.3 UNAWARE OF OUR MORALS
22.4 CARROT AND STICK
22.5 THE MORAL OF THE MAJORITY
22.6 DEONTOLOGICAL MORAL
22.7 SHOULD KNOWLEDGE BE A GOAL?
22.8 UTILITARIANISM
22.9 BAYESIAN CONSEQUENTIALISM
22.10 LAST WORDS

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