Laplace

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understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

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Laplace's law of succession

Submitted by david on Sun, 28/12/2008 - 5:27pm

Suppose that every time there is an opportunity for an event to happen, then it occurs with unknown probability [math]p[/math]. Laplace's law of succession states that, if before we observed any events we thought all values of [math]p [/math] were equally likely, then after observing [math]r[/math] events out of [math]n[/math] opportunities a good estimate of [math]p[/math] is [math]\hat{p} = (r+1)/(n+2)[/math].

The classical approach

Submitted by hauke on Mon, 28/01/2008 - 9:35am

Due to our ignorance about the outcome of, say, a cast die, and because there is no indication for us to think one outcome more likely than any other, we must give them all an equal probability.

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