Probabilistic Machine Learning for Finance and Investing: A Primer to Generative AI with Python (Final)

Preface
   Who Should Read This Book?
   Why I Wrote This Book
   Navigating This Book
   Conventions Used in This Book
   Using Code Examples
   O’Reilly Online Learning
   How to Contact Us
   Acknowledgments
1. The Need for Probabilistic Machine Learning
   Finance Is Not Physics
   All Financial Models Are Wrong, Most Are Useless
   The Trifecta of Modeling Errors
      Errors in Model Specification
      Errors in Model Parameter Estimates
      Errors from the Failure of a Model to Adapt to Structural Changes
   Probabilistic Financial Models
   Financial AI and ML
   Probabilistic ML
      Probability Distributions
      Knowledge Integration
      Parameter Inference
      Generative Ensembles
      Uncertainty Awareness
   Summary
   References
   Further Reading
2. Analyzing and Quantifying Uncertainty
   The Monty Hall Problem
   Axioms of Probability
   Inverting Probabilities
   Simulating the Solution
   Meaning of Probability
      Frequentist Probability
      Epistemic Probability
      Relative Probability
   Risk Versus Uncertainty: A Useless Distinction
   The Trinity of Uncertainty
      Aleatory Uncertainty
      Epistemic Uncertainty
      Ontological Uncertainty
   The No Free Lunch Theorems
   Investing and the Problem of Induction
   The Problem of Induction, NFL Theorems, and Probabilistic Machine Learning
   Summary
   References
3. Quantifying Output Uncertainty with Monte Carlo Simulation
   Monte Carlo Simulation: Proof of Concept
   Key Statistical Concepts
      Mean and Variance
      Expected Value: Probability-Weighted Arithmetic Mean
      Why Volatility Is a Nonsensical Measure of Risk
      Skewness and Kurtosis
      The Gaussian or Normal Distribution
      Why Volatility Underestimates Financial Risk
      The Law of Large Numbers
      The Central Limit Theorem
   Theoretical Underpinnings of MCS
   Valuing a Software Project
   Building a Sound MCS
   Summary
   References
4. The Dangers of Conventional Statistical Methodologies
   The Inverse Fallacy
   NHST Is Guilty of the Prosecutor’s Fallacy
   The Confidence Game
      Single-Factor Market Model for Equities
      Simple Linear Regression with Statsmodels
      Confidence Intervals for Alpha and Beta
   Unveiling the Confidence Game
      Errors in Making Probabilistic Claims About Population Parameters
      Errors in Making Probabilistic Claims About a Specific Confidence Interval
      Errors in Making Probabilistic Claims About Sampling Distributions
   Summary
   References
   Further Reading
5. The Probabilistic Machine Learning Framework
   Investigating the Inverse Probability Rule
   Estimating the Probability of Debt Default
   Generating Data with Predictive Probability Distributions
   Summary
   Further Reading
6. The Dangers of Conventional AI Systems
   AI Systems: A Dangerous Lack of Common Sense
   Why MLE Models Fail in Finance
      An MLE Model for Earnings Expectations
      A Probabilistic Model for Earnings Expectations
   Markov Chain Monte Carlo Simulations
      Markov Chains
      Metropolis Sampling
   Summary
   References
7. Probabilistic Machine Learning with Generative Ensembles
   MLE Regression Models
      Market Model
      Model Assumptions
      Learning Parameters Using MLE
      Quantifying Parameter Uncertainty with Confidence Intervals
      Predicting and Simulating Model Outputs
   Probabilistic Linear Ensembles
      Prior Probability Distributions P(a, b, e)
      Likelihood Function P(Y| a, b, e, X)
      Marginal Likelihood Function P(Y|X)
      Posterior Probability Distributions P(a, b, e| X, Y)
   Assembling PLEs with PyMC and ArviZ
      Define Ensemble Performance Metrics
         Financial activities
         Objective function
         Performance metrics
      Analyze Data and Engineer Features
         Data exploration
            Feature engineering
         Data analysis
      Develop and Retrodict Prior Ensemble
         Specify distributions and their parameters
         Sample distributions and simulate data
         Evaluate and revise untrained model
      Train and Retrodict Posterior Model
         Train and sample posterior
         Retrodict and simulate training data
         Evaluate and revise trained model
      Test and Evaluate Ensemble Predictions
         Swap data and resample posterior predictive distribution
         Predict and simulate test data
         Evaluate, revise, or deploy ensemble
   Summary
   References
   Further Reading
8. Making Probabilistic Decisions with Generative Ensembles
   Probabilistic Inference and Prediction Framework
   Probabilistic Decision-Making Framework
      Integrating Subjectivity
      Estimating Losses
      Minimizing Losses
   Risk Management
      Capital Preservation
      Ergodicity
      Generative Value at Risk
      Generative Expected Shortfall
      Generative Tail Risk
   Capital Allocation
      Gambler’s Ruin
      Expected Valuer’s Ruin
      Modern Portfolio Theory
      Markowitz Investor’s Ruin
      Kelly Criterion
      Kelly Investor’s Ruin
   Summary
   References
   Further Reading
Index