Stats 5.5Concept7 parts

Bayesian Estimation and Credible Intervals

Update uncertainty about an unknown rate as new outcomes arrive, and distinguish a credible interval from a confidence interval.

In this lesson7 parts

  1. 01Why the starting distribution matters
  2. 02Put two explicit priors on the same question
  3. 03Count observed labels and update each curve
  4. 04Read uncertainty from posterior curves
  5. 05Watch more sampled evidence accumulate
  6. 06Keep interval interpretations separate
  7. 07Predict conditionally and test the limitation

Key terms

The words this lesson introduces, each in one line. The module’s glossary collects them all.

sampling without replacement
A selected row ID cannot be selected again.
Bernoulli rate (narration)
The probability that a transaction has fraud label one.
prior distribution (narration)
Assigns probability across the possible rates before the reviewed rows supply any evidence.
Beta distribution
A probability distribution over a rate from 0 to 1, with mean a / (a + b).
shape parameter
A number defining an assumed Beta curve before sampled evidence.
posterior distribution
Uncertainty over the rate after updating the declared prior with observed labels.
prior sensitivity
A change in posterior results caused by changing the assumed prior while keeping evidence fixed.
credible interval
A rate range containing a stated share of posterior probability under the stated prior and likelihood.
confidence interval
Interval from a procedure designed for repeated-sample coverage under its assumptions.
posterior predictive probability
The model's chance of one next outcome after averaging over posterior rate uncertainty.

Quiz 5 questions

Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.

Practice

Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.

The self-checking notebook for this lesson is Stats 5.5 (optional) · Bayesian estimation and credible intervals.

Common mistakes

What you will see when it goes wrong, why it happens, and the fix.

Where it’s used

Where this lesson’s ideas turn up in real work.