You input the low and high values of each proportion on PROGRAM pp_disc - Finds posterior distribution for (p1, p2) when a uniform prior Posterior probabilities of the intervals are displayed in the output. Midpoints of the subintervals, the corresponding prior probabilities,Īnd the data (number of successes and failures). The interval of plausible p values into equally spaced subintervalsĪnd assign a probability to each subinterval. PROGRAM p_hist_p - For a histogram prior for p, finds posterior probabilities of The output is theīayes factor and the posterior probability that the proportion is equal to the specific Hypothesis, and the number of successes and failures in the experiment.

Probability of this value, the parameters of the beta distribution under the alternative You input the value of p that you wish to test, the prior PROGRAM p_beta_t - Tests the hypothesis that p is equal to a specific value. Is stored in the columns 'SUCC' and 'PRED'. The range of numbers of successes that you are interested in.

You input the beta parameters, the number of trials, and Number of successes in future experiment. PROGRAM p_beta_p - For beta prior or posterior, computes predictive distribution for Graph of the density, compute cumulative probabilities for a list of values of interest, and After inputting the beta parameters a and b, you can see a PROGRAM p_beta - Summarizes beta distribution for p. Matching values of the beta parameters a and b. Probability of a second success conditional on a first success. You input the probability of a future success, and the PROGRAM beta_sel - Finds parameters of beta distribution which matches two Predictive distribution is stored in the columns 'SUCC' and 'PRED'. Probabilities for p, and the range of number of successes that you are interested in. Number of trials in the future experiment, if you want to use prior or posterior To run: The values of p are contained in a column 'P' and the probabilities are containedĮither in the columns 'PRIOR' or 'POST'. PROGRAM p_disc_p - Computes predictive distribution for number of successes in To run: Name two Minitab columns 'P' and 'PRIOR'. PROGRAM p_disc - Computes the posterior distribution for p when there is a discrete set of models. SAMPLE MINITAB OUTPUT FROM 'bayes_se' AND 'bayes' Run first.) You input the sequence of independent observations and PROGRAM bayes - Implements Bayes' rule sequentially for independent sequence of outcomes. The number of observations and names, and the likelihoods. You input the number of models, the prior probabilities, PROGRAM bayes_se - Sets up models, prior probabilities, and likelihoods for Bayes' Team with the first strength value, etc.) The place finishes for all teams are stored in the ('NWIN_1' contains the number of games won by the The number of wins for all teams are stored in theĬolumns 'NWIN_1', 'NWIN_2', etc.

(The program 'bball' must be run first.) The number of games won for all To run: Type exec 'bball_re' K, where K is the number of times you wish to repeat the The results of all of the gamesĪre displayed in a 2-way contingency table. Played where each team plays every other team 8 games.

One inputs the strength values for the teams. PROGRAM bball - Simulates a baseball season using a Bradley-Terry model. The column 'F_ROLL' contains the results of the final The results of the first three rolls are placed in the columns (The program 'yahtz_au' must be run first.) The results for each game in codedįorm are displayed. To run: Type exec 'yahtz_re' K, where K is the number of times you wish to repeat the PROGRAM yahtz_re - Play the computer version of Yahtzee repeatedly. The computer will decide which dice to keep. PROGRAM yahtz_au - Computer plays Yahtzee using a particular strategy. After each roll, the result is printed (two of a kind, small straight, etc.) Which dice to keep (if you wish to keep the first, second and fourth dice, you type 1 1 0 1Ġ). PROGRAM yahtzee - Plays simplified version of Yahtzee. The end of the games, some summary statistics are displayed. The program will let you play the game a number of times. CHAPTER 3 - Introduction to Inference Using Bayes' RuleĬHAPTER 7 - Learning About Two Normal MeansĬHAPTER 9 - Learning About Discrete ModelsĬHAPTER 10 - Learning About Continuous ModelsĬHAPTER 11 - Summarizing Posterior Distributions

Minitab output