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If you believe that 1% of people want your foobar, odds are good that you'd have a sale within your first 70 offers (0.99 70 = approx. 0.495) . A Bayesian wou
by aamar 17y ago
If you believe that 1% of people want your foobar, odds are good that you'd have a sale within your first 70 offers (0.99 70 = approx. 0.495) .
A Bayesian would say that if your prior expectation of sale was 1%, 99 consecutive nos would suggest you update your future expectation of sale to around 0.36%.
- waldrews 17y agoMight need a better specifed prior for that Bayesian calculation - prior expectation of 1% gets you the mean of the prior distribution of the success probability of each Bernoulli trial, but you also need a variance or other measure of the uncertainty of your belief. Otherwise, if you have a degenerate prior based on a belief that the prob of sale is 1% - you just stay at that probability no matter how many successes and failures you observe. Presumably you'd want a Beta distribution prior for the computational convenience of the conjugate property - unless you have reason to prefer something else. Then you take the mean and variance of the prior for p, or two ends of a confidence interval for p, and use them to find the alpha and beta parameters for the Beta distribution. Then you update those parameters for the 99 failure events, and read off the new expectation - that's the probability of the 100'th sale being a success.