On avoiding statistical bias in linkage-based counselling

Using the Succession Rule of Laplace (1795) and related reasoning, this paper shows how to give unbiased counselling to patients when predictions are to be based on small samples. The recombination fraction can be regarded as a probability parameter, theta, which itself has a probability distribution between the limits of 0 and 1/2. The probability of a recombinant, P(Rec), is not numerically equal to the maximum likelihood estimate of theta, nor is it numerically equal to the maximum posterior probability estimate in Bayesian inference. Rather it is equal to the infinite sum of all possible theta values, each weighted according to its probability density p(theta) which denotes the relative probability that that theta value is the true one. The various published proposals for obtaining an unbiased estimate of theta are shown to be equivalent one to another, except for the simplifying approximations used.