Estimation of Quantities of Drugs Handled and the Burden of Proof

A person is convicted for the handling of drugs. In the USA, the sentence must be determined partly on the total quantity of drugs handled. The determination of this quantity is a controversial estimation problem. Moreover, there is confusion concerning the relationship of this problem and the burden of proof. Various aspects of this problem are discussed in the context of three cases, each of which requires a different approach. In the first, a product of two uniform distributions is determined. In the second, there is simulation based on resampling from a training set. In the third, a predictive distribution based on independent priors for the mean and variance of a normal distribution is derived.