The effect of prior information in Bayesian estimation is considered, mainly from the standpoint of objective testing. In the estimation of a parameter belonging to an individual, the prior information is, in most cases, the density function of the population to which the individual belongs. Bayesian estimation was compared with maximum likelihood estimation, a population-free estimation. Using several different types of tests, including both paper-and-pencil tests and computerized adaptive tests, the effect of priors on the resultant estimate was observed. It was pointed out that the use of priors in Bayesian estimation results in biases which favor certain individuals over certain other individuals, even though they are exactly equal with respect to their ability levels. An alternative method of using the maximum likelihood estimation with the replacement of positive and negative infinities for the two extreme response patterns, by a pair of new estimates, was proposed, and the resulting regression shows less bias then that of the Bayes modal estimate. (RL)