The paper by Seymour Geisser, titled "A Predictive Approach to the Random Effect Model," published in April 1973, explores two Bayesian methods for estimating treatment means in a randomized experiment. The first method uses the sample treatment mean as an estimator, while the second method employs a weighted combination of the treatment mean and a grand mean, akin to Stein's method. These methods are derived from linear normal models with different prior distributions. The paper discusses the limitations of Lindley's objections to the variance priors and proposes two predictive methods for evaluating these models. The first method involves omitting observations from each group and computing a predictor based on the remaining data, followed by evaluating the mean squared prediction error. The second method simultaneously omits observations from each group and calculates the squared deviation of the predicted value from the actual value for all possible configurations of the data. Both methods aim to find the "best" estimate of the parameter μ, which can be used to predict new observations or estimate the treatment means. The paper includes an example using dyestuff data to illustrate the application of these methods and compares the results with those from the Box-Tiao and Lindley approaches. It concludes that the predictive methods yield close estimates and are robust to variations in the weighting coefficient, making them suitable for evaluating different prior models and generating "best" predictors. The methods are also extended to the mixed model case, where columns are not necessarily independent.The paper by Seymour Geisser, titled "A Predictive Approach to the Random Effect Model," published in April 1973, explores two Bayesian methods for estimating treatment means in a randomized experiment. The first method uses the sample treatment mean as an estimator, while the second method employs a weighted combination of the treatment mean and a grand mean, akin to Stein's method. These methods are derived from linear normal models with different prior distributions. The paper discusses the limitations of Lindley's objections to the variance priors and proposes two predictive methods for evaluating these models. The first method involves omitting observations from each group and computing a predictor based on the remaining data, followed by evaluating the mean squared prediction error. The second method simultaneously omits observations from each group and calculates the squared deviation of the predicted value from the actual value for all possible configurations of the data. Both methods aim to find the "best" estimate of the parameter μ, which can be used to predict new observations or estimate the treatment means. The paper includes an example using dyestuff data to illustrate the application of these methods and compares the results with those from the Box-Tiao and Lindley approaches. It concludes that the predictive methods yield close estimates and are robust to variations in the weighting coefficient, making them suitable for evaluating different prior models and generating "best" predictors. The methods are also extended to the mixed model case, where columns are not necessarily independent.