توضیح 1
Prior: Probability before the new signal.
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درس 13 از 16
Update a prior probability after observing a signal and explain the base-rate effect.
Theory
Update a prior probability after observing a signal and explain the base-rate effect.
توضیح 1
Prior: Probability before the new signal.
توضیح 2
Likelihood: Probability of the signal under a stated condition.
توضیح 3
Posterior: Updated probability after the signal.
اصطلاحات
Probability before the new signal.
Baseline quality-issue rate.
Probability of the signal under a stated condition.
Alert given an issue.
Updated probability after the signal.
Issue given an alert.
نمادگذاری و فرمولها
P(B given A) = P(A given B)P(B) / [P(A given B)P(B) + P(A given not B)P(not B)]
Define every event before substituting values, then validate the result and denominator.
فعالیت تعاملی
P(event given positive)
0.3191
True-positive contribution / all positive contributions
| Actual group | Positive | Negative |
|---|---|---|
| Event | 360 | 40 |
| No event | 768 | 8832 |
A rare base rate can leave many false positives even when sensitivity is high.
مثال حلشده
سناریو
An automated alert is sensitive, but confirmed issues are rare.
Sensitivity is not positive predictive probability.
ارتباط با R
Run and edit the code, inspect intermediate output, and use the movable R Code Guide while practising.
Live R Lab
Update a prior event probability using sensitivity and false-positive probability.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
A highly accurate signal can still have a low positive predictive value when the event is rare.
بازاندیشی
Name the event, denominator, probability interpretation, and one operational limitation.
دستیار
Help me reason through Bayes' Theorem: From Prior to Posterior Probability by asking questions about my event definitions, denominator, formula choice, assumptions, and interpretation. Do not give a quiz answer before I submit.
ارزیابی پایانی
منبع
Explore additional probability explanations and exercises from properly licensed or publisher resources.
دریافتمنبع
Download an original worksheet or guide for this lesson.
دریافت