If you’re feeling a bit lost, read this introduction to Bayes Theorem, which shows when and where to use the Math.

## Comparing Two Hypotheses

You’ve seen your colleague, Alice, be late 3 days, and on time 4 days the past week.

Hypothesis: They’re almost always late, i.e. they’re late 95% of the time.

Alternate Hypothesis: They’re almost never late, i.e they’re late about 5% of the time.

$Posterior \hspace{2mm} Odds = Prior \hspace{2mm} Odds * Likelihood \hspace{2mm} Odds$

 Main Hypothesis success rate % Alternative hypothesis success rate % Number of Successes Number of Failures Total Likelihood Ratio (rounded)

Everyone has their own prior odds. I used 1:1 for the being late case. But, you can play around with these too.

 Prior Odds : Posterior Odds

In the being late example, this gives us that our current hypothesis is $$\frac{1}{19}$$ times likely as the other one.

## Comparing Two Hypotheses - known likelihoods

 Prior Odds : Likelihood Odds : Posterior Odds

## Comparing infinite Hypotheses

To come soon.

Have another use case I’m not covering? Let me know.

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