To Laplace, the (shaded) area under the posterior pdf curve between \( m_1 \) and \( m_2 \) was a measure of how much he believed that the mass of Saturn lay in the range \( m_1 \le M \le m_2 \). As such, the position of the maximum of the posterior pdf represents a best estimate of the mass; its width, or spread, about this optimal value gives an indication of the uncertainty in the estimate. Laplace stated that: ‘ . . . it is a bet of 11,000 to 1 that the error of this result is not 1/100th of its value.’ He would have won the bet, as another 150 years’ accumulation of data has changed the estimate by only 0.63%!