Unit 3 of 13
Conditioning, Independence and Evidence
- 9 lessons
- Videos 16 to 24
New information changes the reference group. This unit covers conditional probability, independence, probability trees, the law of total probability, Bayes’ theorem and odds.
Two-way tables make the denominator of a conditional probability visible and show why reversing a condition generally changes the answer. Independence is defined by a product rule and kept apart from disjointness, which only says that two events cannot occur together. Trees and the chain rule handle experiments in stages, and total probability combines groups with their actual weights. Bayes’ theorem then updates a prior probability with evidence, in probability form, in odds form and over several conditionally independent observations.
Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.
Conditional Probability
Conditional Probability
How conditional probability restricts a model to a conditioning event, why that reference group sets the denominator, why reversing the condition generally changes the answer, and why the condition needs positive probability.
Video 16
Conditional Probability Tables
How to read a two-way table, with joint probabilities from the grand total, marginal probabilities from the margins, conditional probabilities from row and column percentages, and natural frequencies that keep group sizes in view.
Video 17
Independence
Independent Events
What it means for events to be independent, how the product criterion tests it, why disjoint events with positive probability are dependent, why complements keep independence, and how pairwise and mutual independence differ.
Video 18
Disjoint Events and Independence
Why disjoint events with positive probability are dependent, why overlapping events can be independent or dependent, and how zero-probability events and nested events behave under the product test.
Video 19
Trees, Total Probability and Bayes’ Theorem
Probability Trees and the Chain Rule
How a probability tree maps a staged experiment with conditional branches, how the multiplication and chain rules give path probabilities, how adding terminal paths gives event probabilities, and how branch sums check the tree.
Video 20
The Law of Total Probability
How the law of total probability combines conditional rates across a partition, why each rate is multiplied by its group weight, why the result is a weighted average, and how to treat a zero-weight group.
Video 21
Bayes’ Theorem and Base Rates
How Bayes’ theorem reverses a conditional probability using a prior probability and likelihoods, why base rates matter, and what sensitivity, specificity and the false positive rate measure.
Video 22
Combining Evidence
Conditional Independence and Sequential Evidence
What conditional independence given a latent state means, how a shared cause can make observations marginally dependent, and how to update one observation at a time without counting duplicated evidence twice.
Video 23
Probability and Odds
How odds in favor and odds against compare an event with its complement, how to convert between odds and probability, and how the odds form of Bayes’ theorem multiplies prior odds by a likelihood ratio.
Video 24