Laplace

Laplace's law of succession

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

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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