In an invitational address to the Victorian Institute of Educational Research, the author discussed Bayesian theory and its relationship to the design and construction of tailored or adaptive tests. Bayesian thinking involves recognizing the role of prior probabilities and using these probabilities in combination with new data to arrive at future probabilities. These prior probabilities should be viewed as beliefs held in common agreement by individuals, based on data which has been carefully gathered, thoughtfully analyzed, and widely disseminated. Bayesian statistics quantify the prior probabilities, and these probabilities combined with subsequent data, such as test scores, can be used to arrive at a valid posterior judgment. By using Bayesian concepts and computers, tailored tests can be geared to individual examinees' estimated ability levels. Even without computer-assisted testing and large item banks, testing can be made more efficient by: (1) using a multi-level test format; (2) allowing the examinee to select the difficulty level of the test; or (3) employing a two-stage test, in which a routing test is given first to determine the difficulty level of the main test. Stradaptive testing was a method once considered, but was abandoned as too difficult to administer. (MH)