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Introductory Mathematics

Update the two possible causes of an alarm

The alarm rate stays fixed; faults become common

An alarm is common enough among working components that Botie must consider the starting shares of both causes.

BOTIE

The alarm rates remain 0.9 for faults and 0.1 for working components. Why can the faulty share among alarms change when the fault prior rises to 0.2?
The inputs we are comparing

Faulty and working priors

Rare faults

  1. 00.01
  2. 10.99

More common faults

  1. 00.2
  2. 10.8

Alarm rates given each cause

Same in both cases

  1. 00.9
  2. 10.1
Result for rare faults
  1. 00.0833
  2. 10.9167
Choose an explanation to test
A rarer false alarm

This check uses the pieces from “Change the reference group to alarms”.

BOTIE

Faults account for five percent of components. The revised alarm catches eighty percent of faults and activates on two percent of working components. Predict the faulty and working shares among alarms, in that order.
Faulty and working priors
  1. 00.05
  2. 10.95
Alarm rates given each cause
  1. 00.8
  2. 10.02

Use a number, text, or an array matching the requested result. For a matrix, put each row in brackets. Saving your prediction runs your current construction on these inputs and checks the earlier examples too.

Build a construction in the workspace above first. This case will test those pieces.

Which part of your construction distinguishes the probability of an alarm given a fault from the probability of a fault given an alarm?

Multiply each possible cause's prior by its evidence likelihood before normalising across causes.

These invented rates are known inputs. This calculation neither estimates their uncertainty nor decides whether an inspection is worth its cost.

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