Index
A
- AI
- AI systems based on models, The Need for Probabilistic Machine Learning
- dangers of conventional AI, The Dangers of Conventional AI Systems
- description of AI, Financial AI and ML-Financial AI and ML
- evolution crossroads of AI, Why I Wrote This Book
- generative AI
- about, Probabilistic ML
- about generative ensembles, Generative Ensembles, Making Probabilistic Decisions with Generative Ensembles
- about probabilistic ML, Preface, Probabilistic ML
- characteristic of probabilistic ML, Generative Ensembles
- continually learning and revising parameters, Making Probabilistic Decisions with Generative Ensembles
- generating data with predictive probability distributions, Generating Data with Predictive Probability Distributions-Generating Data with Predictive Probability Distributions
- market model, Market Model
- market model assumptions, Model Assumptions
- MLE regression models, MLE Regression Models-Predicting and Simulating Model Outputs
- probabilistic linear ensembles, Probabilistic Linear Ensembles-Posterior Probability Distributions P(a, b, e| X, Y)
- PyMC library, Probabilistic Machine Learning with Generative Ensembles, Assembling PLEs with PyMC and ArviZ-Evaluate, revise, or deploy ensemble
- residual, MLE Regression Models
- simulating new data and counterfactual knowledge, Making Probabilistic Decisions with Generative Ensembles
- symbolic AI, Financial AI and ML
- aleatory uncertainty, Analyzing and Quantifying Uncertainty, Aleatory Uncertainty
- algorithmic uncertainty and ML epistemic uncertainty, Epistemic Uncertainty
- alpha (α) as expected stock-specific return, Single-Factor Market Model for Equities
- alpha for significance level, NHST Is Guilty of the Prosecutor’s Fallacy
- Apple Inc. (AAPL)
- arbitrage pricing model (APT), Probabilistic Machine Learning with Generative Ensembles
- arithmetic mean, Mean and Variance
- asymmetry of information, Epistemic Uncertainty
- axioms of probability, Axioms of Probability-Axioms of Probability
B
- Bayes, Thomas, Inverting Probabilities, NHST Is Guilty of the Prosecutor’s Fallacy
- Bayesian inference referred to as probabilistic inference, Inverting Probabilities
- Bayesian statistics referred to as epistemic statistics, Inverting Probabilities, Epistemic Probability
- “Bayes’s theorem”
- Bernoulli distribution, An MLE Model for Earnings Expectations
- Bernoulli, Daniel, Inverting Probabilities
- beta (β) as systemic risk exposure, Single-Factor Market Model for Equities
- bias as underfitting the training data, Epistemic Uncertainty
- bias-free and optimal for all problems as free lunch, Epistemic Probability, The No Free Lunch Theorems
- binomial distribution to model interest rates, Errors in Model Parameter Estimates, Errors from the Failure of a Model to Adapt to Structural Changes
- Black, Fischer, Risk Versus Uncertainty: A Useless Distinction
- Black-Scholes options pricing model, Risk Versus Uncertainty: A Useless Distinction
- Black-Scholes-Merton option pricing formula, All Financial Models Are Wrong, Most Are Useless
- book web page, How to Contact Us
- Box, George, The Need for Probabilistic Machine Learning
- Buffet, Warren, Why Volatility Is a Nonsensical Measure of Risk, Capital Preservation, Modern Portfolio Theory
- Buffon, Georges Louis Leclerc, comte de, Monte Carlo Simulation: Proof of Concept
C
- capital allocation
- capital asset pricing model (CAPM), Single-Factor Market Model for Equities
- Carvaka philosophy, Investing and the Problem of Induction
- cash flows and DCF model, Investing and the Problem of Induction
- Cauchy distribution, Risk Versus Uncertainty: A Useless Distinction, Skewness and Kurtosis
- central limit theorem (CLT), The Central Limit Theorem-Theoretical Underpinnings of MCS
- central tendency measures, Mean and Variance
- ChatGPT as deep neural network, Preface
- coin tosses as predictable physics, Frequentist Probability, Aleatory Uncertainty
- common sense lacking from AI, AI Systems: A Dangerous Lack of Common Sense-AI Systems: A Dangerous Lack of Common Sense
- conditional probabilities, Inverting Probabilities
- confidence intervals (CIs)
- constants versus variables, Axioms of Probability
- conventional AI dangers (see dangers of conventional AI)
- conventional view of probability, Analyzing and Quantifying Uncertainty
- (see also dangers of conventional statistical methods; frequentist view of probability)
- cost of equity capital, Financial activities
- credit card interest rate estimation errors, Errors in Model Parameter Estimates-Errors in Model Parameter Estimates
- cross-hedging, Financial activities
D
- dangers of conventional AI
- dangers of conventional statistical methods
- about, The Dangers of Conventional Statistical Methodologies
- confidence intervals
- alpha and beta estimation code, Simple Linear Regression with Statsmodels-Simple Linear Regression with Statsmodels
- alpha and beta estimation confidence intervals, Confidence Intervals for Alpha and Beta
- capital asset pricing model assumptions wrecked, Errors in Making Probabilistic Claims About Sampling Distributions
- central limit theorem assumptions violated, The Dangers of Conventional Statistical Methodologies, Errors in Making Probabilistic Claims About Sampling Distributions
- CI theory as predata, The Confidence Game
- errors from CI theory used postdata, The Confidence Game, Unveiling the Confidence Game-Errors in Making Probabilistic Claims About Sampling Distributions
- market model assumptions wrecked, Errors in Making Probabilistic Claims About Sampling Distributions
- single-factor market model for equities, Single-Factor Market Model for Equities
- frequentist view worse than useless, Analyzing and Quantifying Uncertainty, NHST Is Guilty of the Prosecutor’s Fallacy
- inverse fallacy, The Inverse Fallacy-The Inverse Fallacy
- NHST committing prosecutor’s fallacy, NHST Is Guilty of the Prosecutor’s Fallacy-NHST Is Guilty of the Prosecutor’s Fallacy
- dangers of modern portfolio theory, Modern Portfolio Theory
- data generated with predictive probability distributions, Generating Data with Predictive Probability Distributions-Generating Data with Predictive Probability Distributions
- data uncertainty and ML epistemic uncertainty, Epistemic Uncertainty
- DCF (see discounted cash flow model)
- de Moivre, Abraham, Inverting Probabilities
- debt default probability estimation via PML, Estimating the Probability of Debt Default-Estimating the Probability of Debt Default
- decision making
- probabilistic versus nonprobabilistic, Preface
- probabilistic with generative ensembles
- about, Making Probabilistic Decisions with Generative Ensembles
- capital allocation, Capital Allocation-Kelly Investor’s Ruin
- capital preservation, Capital Preservation
- ergodicity, Ergodicity-Ergodicity
- estimating losses, Estimating Losses-Minimizing Losses
- expected shortfall, Generative Expected Shortfall
- expected valuer’s ruin, Expected Valuer’s Ruin-Expected Valuer’s Ruin
- gamblers, Capital Allocation
- gamblers’ ruin, Gambler’s Ruin
- integrating subjectivity, Integrating Subjectivity
- Kelly criterion, Kelly Criterion-Kelly Criterion
- Kelly investor’s ruin, Kelly Investor’s Ruin
- loss functions defined, Making Probabilistic Decisions with Generative Ensembles, Probabilistic Decision-Making Framework
- minimizing losses, Minimizing Losses
- modern portfolio theory, Modern Portfolio Theory-Modern Portfolio Theory
- MPT/CAPM investor’s ruin, Markowitz Investor’s Ruin-Markowitz Investor’s Ruin
- probabilistic decision-making framework, Probabilistic Decision-Making Framework
- probabilistic inference and prediction framework, Probabilistic Inference and Prediction Framework-Probabilistic Inference and Prediction Framework
- risk management, Risk Management-Generative Tail Risk
- tail risk, Generative Tail Risk
- value at risk, Generative Value at Risk-Generative Value at Risk
- psychology of financial decision making, The Monty Hall Problem
- deductive and inductive reasoning, Investing and the Problem of Induction
- deep learning as supervised learning, Financial AI and ML
- deep neural networks
- deep Q-learning as reinforcement learning, Financial AI and ML
- defense attorney’s fallacy, The Inverse Fallacy
- degrees of freedom in variance calculation, Mean and Variance
- dependent/output variables, The Need for Probabilistic Machine Learning
- deterministic models versus probabilistic, The Need for Probabilistic Machine Learning, Financial AI and ML
- Diaconis, Persi, Aleatory Uncertainty
- discounted cash flow model (DCF), Investing and the Problem of Induction
- The Doctrine of Chances (de Moivre), Inverting Probabilities
- drunkard’s search and normal distribution, Errors in Model Specification
- “Dyuta Sukta” (“Ode to Dice”), Capital Allocation
E
- earnings expectations
- economic recessions and prosecutor’s fallacy, The Inverse Fallacy-The Inverse Fallacy
- Einstein, Albert, Relative Probability
- Eisenhower, Dwight, Risk Versus Uncertainty: A Useless Distinction
- endowment effect, The Monty Hall Problem
- epistemic statistics, Epistemic Probability-Epistemic Probability
- about, Inverting Probabilities
- frequentist versus, Epistemic Probability
- image processing requiring probabilistic algorithms, Epistemic Probability
- not “Bayesian”, Inverting Probabilities, Epistemic Probability
- probabilistic ML foundation, Inverting Probabilities
- probabilities assigned to any uncertain event, Risk Versus Uncertainty: A Useless Distinction
- problem of induction, The Problem of Induction, NFL Theorems, and Probabilistic Machine Learning
- risk versus uncertainty, Risk Versus Uncertainty: A Useless Distinction-Risk Versus Uncertainty: A Useless Distinction
- subjective probabilities of, Epistemic Probability
- epistemic uncertainty, Epistemic Uncertainty-Epistemic Uncertainty
- epsilon (ε) as unexpected stock-specific return, Single-Factor Market Model for Equities
- equity single-factor market model, Single-Factor Market Model for Equities
- Erdos, Paul, The Monty Hall Problem
- ergodicity, Ergodicity-Ergodicity
- ETF (exchange-traded fund), Why Volatility Underestimates Financial Risk
- excess returns for excess risk, Single-Factor Market Model for Equities
- expected shortfall (ES), Generative Expected Shortfall
- expected stock-specific return (α), Single-Factor Market Model for Equities
- expected value, Expected Value: Probability-Weighted Arithmetic Mean, Investigating the Inverse Probability Rule
- expected valuer’s ruin, Expected Valuer’s Ruin-Expected Valuer’s Ruin
- expert systems described, Financial AI and ML
F
- fat-tailed probability distributions
- FCF (free cash flows) in valuing a software project, Valuing a Software Project-Valuing a Software Project
- feature uncertainty and ML epistemic uncertainty, Epistemic Uncertainty
- the Fed (Federal Open Market Committee) interest rate estimation errors, Errors in Model Parameter Estimates-Errors in Model Parameter Estimates
- feedback in reinforcement learning, Financial AI and ML
- Fermi, Enrico, Monte Carlo Simulation: Proof of Concept
- financial data signal-to-noise ratios, Learning Parameters Using MLE
- financial theory
- financial markets non-ergodic, Markov Chains, Kelly Investor’s Ruin
- flaws of, Why I Wrote This Book
- linear regression’s pivotal role, Probabilistic Machine Learning with Generative Ensembles
- models wrong but useful, The Need for Probabilistic Machine Learning
- models wrong, even dangerous, All Financial Models Are Wrong, Most Are Useless
- probabilistic financial models, Probabilistic Financial Models
- psychology of financial decision making, The Monty Hall Problem
- risk versus uncertainty, Risk Versus Uncertainty: A Useless Distinction-Risk Versus Uncertainty: A Useless Distinction
- S&P 500 index normally distributed, Why Volatility Underestimates Financial Risk
- what is considered impossible, Investigating the Inverse Probability Rule
- Fisher, Ronald A., Inverting Probabilities, The Dangers of Conventional Statistical Methodologies, NHST Is Guilty of the Prosecutor’s Fallacy, NHST Is Guilty of the Prosecutor’s Fallacy, The Confidence Game
- forward propagation quantifying output uncertainty, Probabilistic Financial Models, Generating Data with Predictive Probability Distributions
- free cash flows (FCF) in valuing a software project, Valuing a Software Project-Valuing a Software Project
- frequentist view of probability, Frequentist Probability, Unveiling the Confidence Game
- about, Analyzing and Quantifying Uncertainty, Inverting Probabilities
- confidence intervals for alpha and beta, Confidence Intervals for Alpha and Beta
- dangerous (see dangers of conventional statistical methods)
- disparaging epistemic school, Epistemic Probability
- epistemic versus, Epistemic Probability
- free lunch of bias-free and optimal for all problems, Epistemic Probability, The No Free Lunch Theorems
- image processing requiring probabilistic algorithms, Epistemic Probability
- long-run frequencies of repeatable events, Errors in Making Probabilistic Claims About a Specific Confidence Interval, Errors in Making Probabilistic Claims About Sampling Distributions
- maximum likelihood estimation used by, Epistemic Probability
- population parameters constants with “true” values, Errors in Making Probabilistic Claims About Population Parameters
- regularizations to reduce variance, Learning Parameters Using MLE
- worse than useless, Analyzing and Quantifying Uncertainty
- fundamental analysis, Investing and the Problem of Induction, Investing and the Problem of Induction
G
- gambler’s ruin, Gambler’s Ruin
- gambling in history, Capital Allocation
- game theory and Monty Hall problem, Axioms of Probability
- Gaus, Carl, Probabilistic Machine Learning with Generative Ensembles
- Gaus-Markov theorem assumptions, Model Assumptions
- Gaussian distribution (see normal distribution)
- generalizing learnings inability in conventional AI, AI Systems: A Dangerous Lack of Common Sense-AI Systems: A Dangerous Lack of Common Sense
- generating data with predictive probability distributions, Generating Data with Predictive Probability Distributions-Generating Data with Predictive Probability Distributions
- generative AI
- about, Probabilistic ML
- about probabilistic ML, Preface, Probabilistic ML
- generating data with predictive probability distributions, Generating Data with Predictive Probability Distributions-Generating Data with Predictive Probability Distributions
- generative ensembles
- about, Generative Ensembles, Making Probabilistic Decisions with Generative Ensembles
- continually learning and revising parameters, Making Probabilistic Decisions with Generative Ensembles
- market model, Market Model
- market model assumptions, Model Assumptions
- MLE regression models, MLE Regression Models-Predicting and Simulating Model Outputs
- probabilistic linear ensembles, Probabilistic Linear Ensembles-Posterior Probability Distributions P(a, b, e| X, Y)
- PyMC library, Probabilistic Machine Learning with Generative Ensembles, Assembling PLEs with PyMC and ArviZ-Evaluate, revise, or deploy ensemble
- residual, MLE Regression Models
- simulating new data and counterfactual knowledge, Making Probabilistic Decisions with Generative Ensembles
- geometric Brownian motion (GBM), Mean and Variance
- goal of financial modeling, The Need for Probabilistic Machine Learning
- Google TensorFlow Probability, Probabilistic ML
- gradient-boosted machines as supervised learning, Financial AI and ML
- Great Financial Crisis, Why Volatility Underestimates Financial Risk, Generative Expected Shortfall
I
- image processing requiring probabilistic algorithms, Epistemic Probability
- implementation uncertainty and ML epistemic uncertainty, Epistemic Uncertainty
- inaccuracies accommodated by probabilistic models, Probabilistic Financial Models
- independent/input variables, The Need for Probabilistic Machine Learning
- induction problem, Investing and the Problem of Induction-Investing and the Problem of Induction
- information (see knowledge integration)
- information asymmetry, Epistemic Uncertainty
- input uncertainty quantified via inverse propagation, Probabilistic Financial Models
- input/independent variables, The Need for Probabilistic Machine Learning
- interest rates
- inverse fallacy, The Inverse Fallacy-The Inverse Fallacy
- inverse probability rule, Inverting Probabilities, Investigating the Inverse Probability Rule-Investigating the Inverse Probability Rule
- application to real-world problems, The Probabilistic Machine Learning Framework
- Bayes’s theorem misnomer, Parameter Inference, Inverting Probabilities-Inverting Probabilities, NHST Is Guilty of the Prosecutor’s Fallacy
- dangers of conventional statistical methods, The Inverse Fallacy-The Inverse Fallacy
- debt default probability estimation, Estimating the Probability of Debt Default
- Monty Hall problem, Inverting Probabilities
- probabilistic ML foundation, Inverting Probabilities, The Probabilistic Machine Learning Framework
- product rule reformulation, Inverting Probabilities, The Inverse Fallacy, The Probabilistic Machine Learning Framework
- inverse propagation quantifying input uncertainty, Probabilistic Financial Models
- inverting conditional probabilities for Monty Hall problem, Inverting Probabilities-Inverting Probabilities
K
- k-means clustering algorithm as unsupervised learning, Financial AI and ML
- Kelly criterion, Kelly Criterion-Kelly Criterion
- Kelly, John, Gambler’s Ruin, Kelly Criterion
- Keynes, Maynard, Errors in Making Probabilistic Claims About Sampling Distributions
- Kipling, Rudyard, The No Free Lunch Theorems
- knowledge integration
- debt default probability estimation via PML, Estimating the Probability of Debt Default-Estimating the Probability of Debt Default
- epistemic uncertainty and, Epistemic Uncertainty
- fundamental analysis, Investing and the Problem of Induction, Investing and the Problem of Induction
- Markov chains memoryless, Markov Chains
- MLE ignoring prior domain knowledge, Why MLE Models Fail in Finance
- no free lunch requiring prior knowledge, Knowledge Integration, The No Free Lunch Theorems, Investigating the Inverse Probability Rule
- null hypothesis significance testing prohibiting, Knowledge Integration
- prior knowledge and bias-variance balance, Epistemic Uncertainty
- probabilistic ML system characteristic, Knowledge Integration
- problem of induction, Investing and the Problem of Induction-Investing and the Problem of Induction
- technical analysis, Investing and the Problem of Induction, Investing and the Problem of Induction
- kurtosis, Skewness and Kurtosis
L
- L1 regularization, Learning Parameters Using MLE
- L2 regularization, Learning Parameters Using MLE
- Laplace, Pierre-Simon, Inverting Probabilities, The Probabilistic Machine Learning Framework
- lasso regularization, Learning Parameters Using MLE
- law of large numbers (LLN), The Law of Large Numbers, Theoretical Underpinnings of MCS
- LCTM (Long-Term Capital Management), All Financial Models Are Wrong, Most Are Useless
- learning dynamically via PML, Estimating the Probability of Debt Default
- Legendre, Adrien-Marie, Probabilistic Machine Learning with Generative Ensembles
- likelihood function P(D|H), Investigating the Inverse Probability Rule
- linear regression
- logistic regression as supervised learning, Financial AI and ML
- Long-Term Capital Management (LTCM), All Financial Models Are Wrong, Most Are Useless
- Lorentzian distribution (see Cauchy distribution)
- loss aversion and endowment effect, The Monty Hall Problem
- loss functions, Making Probabilistic Decisions with Generative Ensembles, Probabilistic Decision-Making Framework
M
- machine learning (ML) models
- Macready, William, The No Free Lunch Theorems
- Mahabharata on gambling, Capital Allocation
- marginal likelihood function P(D), Inverting Probabilities, Investigating the Inverse Probability Rule
- marginal probability
- marginal probability distribution complexity, The Dangers of Conventional AI Systems
- market bull, bear, stagnant Markov chain, Markov Chains
- market model for equities (MM), Single-Factor Market Model for Equities
- market neutral strategies, Financial activities
- Markov chain Monte Carlo (MCMC) simulations, The Dangers of Conventional AI Systems
- Markowitz, Harry, Modern Portfolio Theory, Modern Portfolio Theory
- maximum likelihood estimation (MLE)
- MCS (see Monte Carlo simulation)
- mean, Mean and Variance
- measurement uncertainty and ML aleatory uncertainty, Aleatory Uncertainty
- median, Mean and Variance
- method uncertainty and ML epistemic uncertainty, Epistemic Uncertainty
- Metropolis MCMC algorithm, Markov Chains-Metropolis Sampling
- Metropolis, Nicholas, Monte Carlo Simulation: Proof of Concept, Markov Chains
- Metropolis-Hastings MCMC algorithm, Metropolis Sampling
- Mitchell, Tom, Financial AI and ML
- MLE (see maximum likelihood estimation)
- mode, Mean and Variance
- models
- about, The Need for Probabilistic Machine Learning
- bias-variance balance, Epistemic Uncertainty
- goal of financial modeling, The Need for Probabilistic Machine Learning
- limitations must be known, The Dangers of Conventional AI Systems
- (see also dangers of conventional AI)
- ML and AI explained, Financial AI and ML-Financial AI and ML
- model uncertainty and ML epistemic uncertainty, Epistemic Uncertainty
- PML models
- probabilistic financial models, Probabilistic Financial Models
- stochastic processes modeled by Markov chains, Markov Chains
- uncertainty incorporated, Ontological Uncertainty
- uncertainty must be quantified, Probabilistic Financial Models, The Dangers of Conventional Statistical Methodologies
- wrong but useful, The Need for Probabilistic Machine Learning, Risk Versus Uncertainty: A Useless Distinction
- wrong, even dangerous, All Financial Models Are Wrong, Most Are Useless
- modern portfolio theory (MPT)
- Moivre, Abraham de, Inverting Probabilities
- Monte Carlo simulation (MCS)
- about, Probabilistic Financial Models, Simulating the Solution
- building a sound MCS, Building a Sound MCS
- history of, Monte Carlo Simulation: Proof of Concept
- importance of, Quantifying Output Uncertainty with Monte Carlo Simulation
- Markov chain Monte Carlo simulations
- Monty Hall solution via, Simulating the Solution-Simulating the Solution
- output uncertainty quantified via forward propagation, Probabilistic Financial Models, Quantifying Output Uncertainty with Monte Carlo Simulation
- pi estimation, Monte Carlo Simulation: Proof of Concept
- statistical concepts of, Key Statistical Concepts-The Central Limit Theorem
- theoretical underpinnings of, Theoretical Underpinnings of MCS
- valuing a software project, Valuing a Software Project-Valuing a Software Project
- Monty Hall problem, The Monty Hall Problem-The Monty Hall Problem
- about, Analyzing and Quantifying Uncertainty
- axioms of probability, Axioms of Probability-Axioms of Probability
- epistemic uncertainty, Epistemic Uncertainty
- game theory and, Axioms of Probability
- inverting conditional probabilities, Inverting Probabilities-Inverting Probabilities
- Monte Carlo simulation for solution, Simulating the Solution-Simulating the Solution
- ontological uncertainty, Ontological Uncertainty
- psychology of financial decision making, The Monty Hall Problem
- relative probability, Relative Probability-Relative Probability
- types of uncertainty, Analyzing and Quantifying Uncertainty
- MPT (see modern portfolio theory)
- multicollinearity, Learning Parameters Using MLE
N
- naive diversification strategy, Modern Portfolio Theory
- Nash equilibrium, Axioms of Probability
- Nash, John, Axioms of Probability
- net present value (NPV), Valuing a Software Project-Valuing a Software Project
- Newton, Isaac, Finance Is Not Physics, Finance Is Not Physics
- Neyman, Jerzy, The Dangers of Conventional Statistical Methodologies, NHST Is Guilty of the Prosecutor’s Fallacy, The Confidence Game
- NFL (see no free lunch (NFL) theorems)
- NHST (see null hypothesis significance testing)
- no free lunch (NFL) theorems, The No Free Lunch Theorems-The No Free Lunch Theorems
- about, Analyzing and Quantifying Uncertainty
- bias-free and optimal for all problems as free lunch, Epistemic Probability
- free lunch per Rudyard Kipling, The No Free Lunch Theorems
- frequentist claims disputed by, Epistemic Probability
- prior knowledge necessary for optimization, Knowledge Integration, The No Free Lunch Theorems, Investigating the Inverse Probability Rule
- problem of induction in probabilistic framework, The Problem of Induction, NFL Theorems, and Probabilistic Machine Learning
- “Nobel Prize in Economics”, Finance Is Not Physics
- Nobel, Alfred, Finance Is Not Physics
- nonprobabilistic ML models described, Preface
- normal (Gaussian) distribution, The Gaussian or Normal Distribution
- null hypothesis (H0) in NHST, NHST Is Guilty of the Prosecutor’s Fallacy
- null hypothesis significance testing (NHST)
- NumPy random number generator, Why Volatility Underestimates Financial Risk
O
- objective function, Objective function
- objectivity per NHST, Knowledge Integration
- “Ode to Dice” (“Dyuta Sukta”), Capital Allocation
- ontological uncertainty, Ontological Uncertainty-Ontological Uncertainty
- optimal capital growth algorithm, Gambler’s Ruin
- option pricing models, Thorp versus Black and Scholes, Risk Versus Uncertainty: A Useless Distinction
- ordinary least squares (OLS), Probabilistic Machine Learning with Generative Ensembles
- outliers, Mean and Variance
- output uncertainty quantified via forward propagation, Probabilistic Financial Models
- output/dependent variables, The Need for Probabilistic Machine Learning
P
- p-values
- parameters of a model, The Need for Probabilistic Machine Learning
- Pareto distribution not having finite mean or variances, Errors in Making Probabilistic Claims About Sampling Distributions
- Pascal, Blaise, Gambler’s Ruin
- Pearson, Egon, NHST Is Guilty of the Prosecutor’s Fallacy
- Pearson, Karl, NHST Is Guilty of the Prosecutor’s Fallacy
- performance of a model
- physics
- pi estimation via Monte Carlo simulation, Monte Carlo Simulation: Proof of Concept
- plans useless, planning indespensable, Risk Versus Uncertainty: A Useless Distinction
- PML (see probabilistic machine learning)
- policy-gradient methods as reinforcement learning, Financial AI and ML
- population parameters
- posterior predictive distribution P(D**|D), Generating Data with Predictive Probability Distributions
- posterior probability distribution P(H|D), Investigating the Inverse Probability Rule
- predictions
- Price, Richard, Inverting Probabilities
- principal component analysis as unsupervised learning, Financial AI and ML
- prior and posterior distributions, Generating Data with Predictive Probability Distributions
- prior and posterior predictive distributions
- prior knowledge (see knowledge integration)
- prior predictive distribution P(D*), Generating Data with Predictive Probability Distributions
- prior probability distributions P(a, b, e), Prior Probability Distributions P(a, b, e)
- probabilistic decision making with generative ensembles
- probabilistic financial models, Probabilistic Financial Models
- debt default probability estimation, Estimating the Probability of Debt Default-Estimating the Probability of Debt Default
- deterministic versus, The Need for Probabilistic Machine Learning, Financial AI and ML
- earnings expectations, A Probabilistic Model for Earnings Expectations-A Probabilistic Model for Earnings Expectations
- as generative models, Probabilistic ML, Generating Data with Predictive Probability Distributions
- about, Making Probabilistic Decisions with Generative Ensembles
- generating data with predictive probability distributions, Generating Data with Predictive Probability Distributions-Generating Data with Predictive Probability Distributions
- market model, Market Model
- market model assumptions, Model Assumptions
- MLE regression models, MLE Regression Models-Predicting and Simulating Model Outputs
- probabilistic linear ensembles, Probabilistic Linear Ensembles-Posterior Probability Distributions P(a, b, e| X, Y)
- residual, MLE Regression Models
- inaccuracies accommodated by, Probabilistic Financial Models
- ingesting data one point at a time or all at once, Estimating the Probability of Debt Default
- model uncertainty quantified, Probabilistic Financial Models
- probabilistic linear ensembles, Probabilistic Linear Ensembles-Posterior Probability Distributions P(a, b, e| X, Y)
- about, Probabilistic Linear Ensembles
- assembling with PyMC and ArviZ, Assembling PLEs with PyMC and ArviZ-Evaluate, revise, or deploy ensemble
- likelihood function P(Y|a, b, e, X), Likelihood Function P(Y| a, b, e, X)
- marginal likelihood function P(Y|X), Marginal Likelihood Function P(Y|X)
- posterior probability distributions P(a, b, e|X, Y), Posterior Probability Distributions P(a, b, e| X, Y)
- prior probability distributions P(a, b, e), Prior Probability Distributions P(a, b, e)
- PyMC library for assembling probabilistic linear ensembles, Assembling PLEs with PyMC and ArviZ-Evaluate, revise, or deploy ensemble
- probabilistic inference, not “Bayesian”, Inverting Probabilities
- probabilistic linear ensembles
- assembling with PyMC and ArviZ, Assembling PLEs with PyMC and ArviZ-Evaluate, revise, or deploy ensemble
- frequentist linear regression versus probabilistic, Making Probabilistic Decisions with Generative Ensembles
- likelihood function P(Y|a, b, e, X), Likelihood Function P(Y| a, b, e, X)
- marginal likelihood function P(Y|X), Marginal Likelihood Function P(Y|X)
- posterior probability distributions P(a, b, e|X, Y), Posterior Probability Distributions P(a, b, e| X, Y)
- prior probability distributions P(a, b, e), Prior Probability Distributions P(a, b, e)
- probabilistic machine learning (PML)
- about, Preface, Probabilistic ML
- aleatory uncertainty generation, Aleatory Uncertainty
- characteristics of, Probabilistic ML-Uncertainty Awareness
- debt default probability estimation, Estimating the Probability of Debt Default-Estimating the Probability of Debt Default
- epstemic statistics foundation, Inverting Probabilities
- finance is not physics, Finance Is Not Physics-Finance Is Not Physics
- generating data with predictive probability distributions, Generating Data with Predictive Probability Distributions-Generating Data with Predictive Probability Distributions
- generative ensembles
- about, Generative Ensembles, Making Probabilistic Decisions with Generative Ensembles
- continually learning and revising parameters, Making Probabilistic Decisions with Generative Ensembles
- market model, Market Model
- market model assumptions, Model Assumptions
- MLE regression models, MLE Regression Models-Predicting and Simulating Model Outputs
- probabilistic linear ensembles, Probabilistic Linear Ensembles-Posterior Probability Distributions P(a, b, e| X, Y)
- PyMC library, Probabilistic Machine Learning with Generative Ensembles, Assembling PLEs with PyMC and ArviZ-Evaluate, revise, or deploy ensemble
- residual, MLE Regression Models
- simulating new data and counterfactual knowledge, Making Probabilistic Decisions with Generative Ensembles
- inverse probability rule foundation, Inverting Probabilities, The Probabilistic Machine Learning Framework
- ML and AI explained, Financial AI and ML-Financial AI and ML
- point estimate zero probability for probability density functions, Axioms of Probability
- prior and posterior distributions, Generating Data with Predictive Probability Distributions
- prior and posterior predictive distributions
- PyMC library for assembling probabilistic linear ensembles, Assembling PLEs with PyMC and ArviZ-Evaluate, revise, or deploy ensemble
- training a linear ML system, Financial AI and ML
- probability
- axioms of, Axioms of Probability-Axioms of Probability
- common sense reduced to calculation, The Probabilistic Machine Learning Framework
- conditional probabilities, Inverting Probabilities
- deterministic and random variables, Axioms of Probability
- epistemic school of thought, Epistemic Probability-Epistemic Probability
- frequentist conventional view, Frequentist Probability, Unveiling the Confidence Game
- about, Analyzing and Quantifying Uncertainty, Inverting Probabilities
- coin tosses, Frequentist Probability
- confidence intervals for alpha and beta, Confidence Intervals for Alpha and Beta
- dangerous (see dangers of conventional statistical methods)
- disparaging epistemic school, Epistemic Probability
- epistemic versus, Epistemic Probability
- free lunch of bias-free and optimal for all problems, Epistemic Probability, The No Free Lunch Theorems
- impact on financial economics, The Confidence Game
- long-run frequencies of repeatable events, Errors in Making Probabilistic Claims About a Specific Confidence Interval, Errors in Making Probabilistic Claims About Sampling Distributions
- maximum likelihood estimation used by, Epistemic Probability
- null hypothesis significance testing, The Dangers of Conventional Statistical Methodologies, NHST Is Guilty of the Prosecutor’s Fallacy
- population parameters constants with “true” values, Errors in Making Probabilistic Claims About Population Parameters
- regularizations to reduce variance, Learning Parameters Using MLE
- using prosecutor’s fallacy, Epistemic Probability, The Inverse Fallacy
- violating product and inverse probability rules, Epistemic Probability
- meaning of, Meaning of Probability
- probability density functions, Axioms of Probability
- probability mass functions, Axioms of Probability
- relative probability, Relative Probability-Relative Probability
- risk versus uncertainty, Risk Versus Uncertainty: A Useless Distinction-Risk Versus Uncertainty: A Useless Distinction
- subjective probabilities, Epistemic Probability
- uncertainty quantification and analysis, Analyzing and Quantifying Uncertainty
- probability density functions (PDF), Axioms of Probability
- probability distributions
- Bernoulli same as binomial for single trial, An MLE Model for Earnings Expectations
- errors from model not adapting to structural changes, Errors from the Failure of a Model to Adapt to Structural Changes
- errors in model parameter estimations, Errors in Model Parameter Estimates
- fat-tailed Cauchy distribution, Risk Versus Uncertainty: A Useless Distinction, Skewness and Kurtosis
- generating data with predictive probability distributions, Generating Data with Predictive Probability Distributions-Generating Data with Predictive Probability Distributions
- Markov chain Monte Carlo simulation, The Dangers of Conventional AI Systems
- Monte Carlo simulations sampling randomly from, Simulating the Solution
- prior and posterior distributions, Generating Data with Predictive Probability Distributions
- prior and posterior predictive distributions
- probabilistic ML system characteristic, Probability Distributions
- probability distribution functions, Axioms of Probability
- zero probability parameter value, Investigating the Inverse Probability Rule
- probability mass functions (PMF), Axioms of Probability
- probability-weighted average sum, Expected Value: Probability-Weighted Arithmetic Mean, Investigating the Inverse Probability Rule
- product rule for conditional probabilities, Inverting Probabilities
- proof by contrapositive, NHST Is Guilty of the Prosecutor’s Fallacy
- prosecutor’s fallacy, The Inverse Fallacy-The Inverse Fallacy
- psychology of financial decision making, The Monty Hall Problem
- PyMC library
- Pyro extending PyTorch platform, Probabilistic ML
R
- random forests as supervised learning, Financial AI and ML
- random number generator (NumPy), Why Volatility Underestimates Financial Risk
- random sampling
- recessions and prosecutor’s fallacy, The Inverse Fallacy-The Inverse Fallacy
- regression (see linear regression)
- regularizations to reduce variance, Learning Parameters Using MLE
- reinforcement learning ML systems, Financial AI and ML
- relative probability, Relative Probability-Relative Probability
- Renaissance Technologies, All Financial Models Are Wrong, Most Are Useless
- residual, MLE Regression Models
- reward-to-risk ratio, Expected Value: Probability-Weighted Arithmetic Mean
- ridge regularization, Learning Parameters Using MLE
- risk
- Rosenbluth, Arianna W., Markov Chains
- Rosenbluth, Marshall, Markov Chains
- Rumsfeld, Donald, Analyzing and Quantifying Uncertainty
- Russian government default on local currency bonds, All Financial Models Are Wrong, Most Are Useless
S
- S&P 500
- SAI (symbolic AI), Financial AI and ML
- sampling distributions of sample mean, Errors in Making Probabilistic Claims About Sampling Distributions
- sampling error of Monte Carlo simulations, Theoretical Underpinnings of MCS
- sampling uncertainty and ML aleatory uncertainty, Aleatory Uncertainty
- scenario analysis, Probabilistic Financial Models
- Scholes, Myron, All Financial Models Are Wrong, Most Are Useless, Risk Versus Uncertainty: A Useless Distinction
- Selvin, Steve, The Monty Hall Problem
- sensitivity analysis, Probabilistic Financial Models
- Sharpe ratio, Why Volatility Is a Nonsensical Measure of Risk
- Sharpe, William, Modern Portfolio Theory
- significance level (alpha)
- Simpson, O. J., The Inverse Fallacy
- single-factor market model for equities, Single-Factor Market Model for Equities
- skewness, Skewness and Kurtosis
- Smith, Adam, Finance Is Not Physics
- software project valuation via MCS, Valuing a Software Project-Valuing a Software Project
- Stan library
- standard deviation, Mean and Variance
- stationary ergodic as time invariant, Why Volatility Underestimates Financial Risk
- stationary ergodic stochastic process, Markov Chains
- statistical decision theory of Neyman, The Confidence Game
- statistical inference
- Statsmodels linear regression to estimate alpha and beta, Simple Linear Regression with Statsmodels-Simple Linear Regression with Statsmodels
- stochastic processes
- stock single-factor market model, Single-Factor Market Model for Equities
- Student’s t-distribution MCMC simulation, Metropolis Sampling-Metropolis Sampling
- subjective probabilities of epistemic probabilities, Epistemic Probability
- subjectivity integrated into probabilistic decision making, Integrating Subjectivity
- sum rule of probability, Axioms of Probability
- supervised learning ML systems, Financial AI and ML
- Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, Finance Is Not Physics
- symbolic AI (SAI), Financial AI and ML
- systematic risk of CAPM, Modern Portfolio Theory
- systemic risk exposure (β), Single-Factor Market Model for Equities
T
- t-distribution MCMC simulation, Metropolis Sampling-Metropolis Sampling
- target distribution equal probabilities, The No Free Lunch Theorems
- technical analysis, Investing and the Problem of Induction, Investing and the Problem of Induction
- Teller, Augusta H., Markov Chains
- Teller, Edward, Markov Chains
- TensorFlow Probability (Google), Probabilistic ML
- Thorp, Edward O., Risk Versus Uncertainty: A Useless Distinction, Making Probabilistic Decisions with Generative Ensembles, Gambler’s Ruin
- time
- time-variant distribution parameter values from historical data, Errors from the Failure of a Model to Adapt to Structural Changes
- total probability rule for Monty Hall problem, Inverting Probabilities
- training a linear ML system, Financial AI and ML
- training data overfit as variance, Epistemic Uncertainty
- training data underfit as bias, Epistemic Uncertainty
- transposed conditional fallacy (see prosecutor’s fallacy)
- type I and type II error control by Neyman, The Confidence Game
U
- Ulam, Stanisław, Monte Carlo Simulation: Proof of Concept
- uncertainty quantification and analysis
- all models should quantify uncertainty, Probabilistic Financial Models
- input uncertainty via inverse propagation, Probabilistic Financial Models
- MLE models failing in finance, Why MLE Models Fail in Finance
- Monty Hall problem, The Monty Hall Problem-The Monty Hall Problem
- about, Analyzing and Quantifying Uncertainty
- axioms of probability, Axioms of Probability-Axioms of Probability
- epistemic uncertainty, Epistemic Uncertainty
- game theory and, Axioms of Probability
- inverting conditional probabilities, Inverting Probabilities-Inverting Probabilities
- inverting conditional probabilities detail, Investigating the Inverse Probability Rule-Investigating the Inverse Probability Rule
- Monte Carlo simulation for solution, Simulating the Solution-Simulating the Solution
- ontological uncertainty, Ontological Uncertainty
- psychology of financial decision making, The Monty Hall Problem
- relative probability, Relative Probability-Relative Probability
- types of uncertainty, Analyzing and Quantifying Uncertainty, The Trinity of Uncertainty-Ontological Uncertainty
- output uncertainty via forward propagation
- probability for, Analyzing and Quantifying Uncertainty
- problem of induction, Investing and the Problem of Induction-Investing and the Problem of Induction
- risk versus uncertainty, Risk Versus Uncertainty: A Useless Distinction-Risk Versus Uncertainty: A Useless Distinction
- types of uncertainty, Analyzing and Quantifying Uncertainty, The Trinity of Uncertainty-Ontological Uncertainty
- unconditional probability
- unexpected stock-specific return (ε), Single-Factor Market Model for Equities
- uniform distributions have no tails, Skewness and Kurtosis
- unsupervised learning ML systems, Financial AI and ML
- unsystematic risk of CAPM, Modern Portfolio Theory
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