How do you update the probability of rain using the observation of cloudiness in the picnic example?
Conditions
- Cloudiness is the observed event (B).
- Rain is the event of interest (A).
- Prior probabilities and likelihoods are supplied.
- .
Reasoning, step by step
- Identify the event of interest (Rain) and the observed event (Cloudiness).
- Retrieve the prior probability of Rain, .
- Retrieve the likelihood of Cloudiness given Rain, .
- Retrieve or calculate the marginal probability of Cloudiness, .
- Apply Bayes' formula: .
- Interpret the result as the updated (posterior) probability of rain.
Example
The script states: 'In the picnic example, cloudiness is the observed event and rain is the event of interest. Substitute the supplied prior and likelihood values, then normalize by the probability of the observed cloudiness.'
Common misconceptions
- Confusing the likelihood with the posterior .
- Forgetting to normalize by dividing by .
- Treating cloudiness as the event of interest instead of the evidence.
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