First Lecture: Introduction to Probabilistic Models

Overview

• Subject Focus: Dive directly into the core of probabilistic models.
• Goals for this Lecture: Understand all elements of a probabilistic model.

Probabilistic Models

• Definition: A quantitative description of a situation, phenomenon, or experiment with uncertain outcomes.
• Key Steps to Create a Model:
  1. Describe Possible Outcomes: Specifying a sample space.
  2. Specify Probability Law: Assigns probabilities to outcomes or collections of outcomes.

Probability Laws

• Function: Indicates likelihood of outcomes.
• Basic Properties/Axioms: Must adhere to certain properties to be meaningful (e.g., probabilities cannot be negative).
• Powerful Consequences: Few axioms but lead to many other important properties.

Examples

• Simple Examples: Both discrete and continuous outcomes.
• Discrete Models: Conceptually easier.
• Continuous Models: Require more sophisticated concepts and highlight subtle issues.

Big Picture

• Role of Probability Theory: Its relationship with the real world and its significance.