In reasoning from a sample to the population from which it is drawn the mathematical likelihood, which is proportional to the a posteriori probability that the observed sample shall be drawn from a given population, generally takes the place of probability as a measure of rational belief. An estimate of a parameter of the population which, as the size of sample increases without limit, tends to the value of the parameter is a consistent estimate. The limit of 1/nV, where n is size of sample and V is variance of estimate, is necessarily less than or equal to a quantity, i, which is independent of the method of estimation used. If the limit of l/nV = i, the estimate is efficient. The method of maximum likelihood leads to efficient estimates. Some estimates, which are called sufficient, contain, even from finite samples, the whole of the information supplied by the data. In other cases ancillary statistics may be calculated, which tell us nothing about the value of the parameter, but, instead, tell us how good an estimate we have made of it.