Probability Theory 
for Data Analysis 
and Decision-Making

ArrowHead’s Decision Analysis training course will provide you with a comprehensive grasp of essential concepts drawn from the famed Stanford Decision Analysis course that Dr. Nesbitt has been teaching. This session gives you a practical understanding of the key concepts designed for pencil and paper calculation by covering fundamental topics like alternatives, probabilities, decision trees, influence diagrams, Bayesian networks, and values and risk attitude.

In this module, you'll delve into the art of harnessing computer-generated samples to infer probability. We will explore Monte Carlo integration, generating densities from shapes, sampling from univariate and multivariate densities, and deriving distributions from samples. Additionally, we'll navigate the challenges and pitfalls associated with applying simulation techniques to economic models.

In this module, we'll explore the intricacies of obtaining probability distributions for different variables, such as price. We'll cover various techniques, including the probability wheel, data-driven probability assessment using the Nesbitt Bayesian Linear Regression method, the Keelin meta-log method, and the discretization of continuous probabilities to create decision trees.

Dr. Nesbitt's definitive text and course on Bayesian regression serve as the foundation for this module. Here, you'll learn to leverage prior probability estimates and data to construct sophisticated, valid probability distributions. We'll explore "zero information" priors and harness probability distributions for accurate forecasting. Patterned after Dr. Nesbitt's renowned Stanford course, this world-class statistical analysis method and course that supersedes classical linear regression, equipping you with easily programmable methods for both large and small data sets.

You will learn to harness the power of Markov and semi-Markov decision processes, which excel at representing dynamic probabilities and outcomes over time, enabling you to adapt and mitigate risks effectively. We cover both transient and recurrent processes, including decision trees and long-term state transitions, enabling you to analyze scenarios such as preventive maintenance, rehabilitation, and replacement.