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STATLAB Academy | Learn Statistics with R and Real-World Data

Lesson 14 of 16

General Bayes Updating and Decision Analysis

Home/Modules/Module 5/General Bayes Updating and Decision Analysis

Update several possible causes using weighted likelihoods and connect posterior shares to decisions.

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46 minutes88% path

Learning objectivesBy the end of this lesson, students will be able to:

1Define the events and probability quantities used in general bayes updating and decision analysis.
2Select and calculate an appropriate probability rule with a visible denominator or assumption.
3Interpret the result for a business decision without overstating certainty or causation.

Theory

Core probability reasoning

Update several possible causes using weighted likelihoods and connect posterior shares to decisions.

Explanation 1

Prior categories: Mutually exclusive and exhaustive possible sources.

Explanation 2

Weighted likelihood: Prior share multiplied by evidence likelihood.

Explanation 3

Posterior share: One weighted likelihood divided by their total.

Terminology

Concept map

Prior categories

Mutually exclusive and exhaustive possible sources.

Three suppliers.

Weighted likelihood

Prior share multiplied by evidence likelihood.

Supplier share x alert rate.

Posterior share

One weighted likelihood divided by their total.

Updated supplier probability after an alert.

Notation and formulas

General Bayes update

Key relationship

posterior_i = prior_i x likelihood_i / sum(prior_j x likelihood_j)

Define every event before substituting values, then validate the result and denominator.

Step 1Validate priors sum to one.
Step 2Calculate every weighted likelihood.
Step 3Normalize and verify posteriors sum to one.

Interactive Mission

multi category bayes updater

Category 1 priorEvidence likelihood

Posterior

0.3418

Category 2 priorEvidence likelihood

Posterior

0.3544

Category 3 priorEvidence likelihood

Posterior

0.3038

Prior total: 1. Priors must sum to 1; posterior shares are normalized weighted likelihoods.

Worked example

Supplier review

Scenario

Three suppliers have different shares and alert likelihoods.

A posterior supports prioritization but does not prove responsibility.

R connection

R note: General Bayes Updating

Run and edit the code, inspect intermediate output, and use the movable R Code Guide while practising.

Live R Lab

General Bayes Updating

Update several mutually exclusive source probabilities with one piece of evidence.

Editable R code

Results

Ready to run

Ready to run

Ready to run. Results, errors, tables, plots, and fallback messages will appear here.

Validate prior categories.

Calculate weighted likelihoods.

Normalize posterior shares.

Dataset provenance

Original synthetic data generated for STATLAB Academy. No textbook data used.

Interpretation safeguard

Posterior probabilities depend on both the evidence model and the prior distribution.

Reflection

Pause and write

Where could an unclear event definition or assumption change the conclusion in general bayes updating and decision analysis?

Name the event, denominator, probability interpretation, and one operational limitation.

Assistant

Ask your probability coach

Help me reason through General Bayes Updating and Decision Analysis by asking questions about my event definitions, denominator, formula choice, assumptions, and interpretation. Do not give a quiz answer before I submit.

Exit check

Lesson checkpoint

Use a hint before submitting if needed. Full calculations and interpretations appear after submission.

Checkpoint

Module 5 Lesson 14 Checkpoint

Question 1 of 2. Answered 0/2. Passing score: 70%.

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Question 1: Choose one

easyCalculate and responsibly interpret probability for a defined event.

Three prior categories are mutually exclusive and exhaustive. Their prior probabilities must:

All exceed 0.5All be equalMultiply to 1Sum to 1

Resource

Recommended reading

Explore additional probability explanations and exercises from properly licensed or publisher resources.

Resource

Module 5 learning material

Download an original worksheet or guide for this lesson.

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