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2025-08-09

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Navigating This resource The contents of this resource may be divided into two logical parts interwoven unevenly throughout each chapter. One
part examines the appalling uselessness of the prevailing economics, statistical, and machine learning models for finance and investing domains. The other part examines why probabilistic machine learning is a less wrong, more useful model for these problem domains. The singular focus of this primer is on understanding the foundations of this
complex, multidisciplinary field. Only pivotal concepts and applications are covered. Sometimes less is indeed more. The resource is organized as follows, with each chapter having
at least one of the main concepts in finance and investing applied in a hands-on Python code exercise: Chapter 1, “The Need for Probabilistic Machine Learning” examines some of the woeful inadequacies of theoretical finance, how all financial models are afflicted with a trifecta of errors, and why we nee d asystematic way of quantifying the uncertainty of our inferences and predictions. The chapter explains why robabilistic ML provides a useful framework for
finance and investing. Chapter 2, “Analyzing and Quantifying Uncertainty”
uses the Monty Hall problem to review the basic rules
of probability theory, examine the meanings of
probability, and explore the trinity of uncertainties that
pervade our world. The chapter also explores the
problem of induction and its algorithmic restatement,
the no free lunch (NFL) theorems, and how they
underpin finance, investing, and probabilistic ML.
Chapter 3, “Quantifying Output Uncertainty with Monte
Carlo Simulation” reviews important statistical
concepts to explain why Monte Carlo simulation (MCS),
one of the most important numerical techniques, works
by generating approximate probabilistic solutions to
analytically intractable problems.
Chapter 4, “The Dangers of Conventional Statistical
Methodologies” exposes the skullduggery of
conventional statistical inference methodologies
commonly used in research and industry, and explains
why they are the main cause of false research findings
that plague the social and economic sciences.
Chapter 5, “The Probabilistic Machine Learning
Framework” explores the probabilistic machine
framework and demonstrates how inference from data
and simulation of new data are logically and seamlessly
integrated in this type of generative model.
Chapter 6, “The Dangers of Conventional AI Systems”
exposes the dangers of conventional AI systems,
especially their lack of basic common sense and how
they are unaware of their own limitations, which pose
massive risks to all their stakeholders and society at
large. Markov chain Monte Carlo simulations are
introduced as a dependent sampling method for solving
complex problems in finance and investing.
Chapter 7, “Probabilistic Machine Learning with
Generative Ensembles” explains how probabilistic
machine learning is essentially a form of ensemble
machine learning. It shows readers how to develop a
prototype of a generative linear ensemble for
regression problems in finance and investing using
PyMC, Xarray, and ArviZ Python libraries.
Chapter 8, “Making Probabilistic Decisions with
Generative Ensembles” shows how to apply generative
ensembles to risk management and capital allocation
decisions in finance and investing. The implications of
ergodicity and the pitfalls of using ensemble averages
for financial decision making are explored. The
strengths and weaknesses of capital allocation
algorithms, including the Kelly criterion, are examined


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