I. J. Good (1916–2009) was a prolific scientist who contributed to many fields, mostly from a Bayesian standpoint. This column explains his idea of quasi-Bayes (a.k.a. pseudo-Bayes) estimation or smoothing of categorical frequencies in a contingency table, which is especially useful as a way of dealing with awkward sampling or random zeros. It shows how the method can be implemented, almost calculator-style, using a combination of Stata and Mata. Convenience commands qsbayesi and qsbayes are also introduced.
AgrestiA.2002. Categorical Data Analysis. 2nd ed. Hoboken, NJ: Wiley.
2.
BanksD.2008. A conversation with I. J. Good. In The Good Book: Thirty Years of Comments, Conjectures, and Conclusions by I. J. Good, ed. BanksD., and SmithE. P., 13–34. Houston, TX: Rice University Press. Article originally published in 1996, Statistical Science 11: 1–19.
BanksD., and SmithE. P.2008. The Good Book: Thirty Years of Comments, Conjectures, and Conclusions by I. J. Good.Houston, TX: Rice University Press.
5.
BishopY. M. M., FienbergS. E., and HollandP. W.1975. Discrete Multivariate Analysis: Theory and Practice.Cambridge, MA: MIT Press. Reissue, New York: Springer, 2007.
6.
CoxN. J.2004. Speaking Stata: Graphing categorical and compositional data. Stata Journal4: 190–215.
7.
CoxN. J.2008. Stata tip 59: Plotting on any transformed scale. Stata Journal8: 142–145.
8.
FienbergS. E.2008. I. J. Good-An appreciation. In The Good Book: Thirty Years of Comments, Conjectures, and Conclusions by I. J. Good, ed. BanksD., and SmithE. P., 1–4. Houston, TX: Rice University Press.
9.
FienbergS. E., and HollandP. W.1970. Methods for eliminating zero counts in contingency tables. In Random Counts in Scientific Work, Volume 1: Random Counts in Models and Structures, ed. PatilG. P., 233–260. University Park, PA: Pennsylvania State University Press.
10.
FienbergS. E.1972. On the choice of flattening constants for estimating multinomial probabilities. Journal of Multivariate Analysis2: 127–134.
11.
FienbergS. E.1973. Simultaneous estimation of multinomial cell probabilities. Journal of the American Statistical Association68: 683–691.
12.
GoodI. J. ed. 1962. The Scientist Speculates: An Anthology of Partly-Baked Ideas.London: Heinemann.
13.
GoodI. J.1965. The Estimation of Probabilities: An Essay on Modern Bayesian Methods.Cambridge, MA: MIT Press.
14.
GoodI. J.1979. Studies in the history of probability and statistics. XXXVII: A. M. Turing's statistical work in World War II. Biometrika66: 393–396.
15.
GoodI. J.1983. Good Thinking: The Foundations of Probability and Its Applications.Minneapolis, mn: University of Minnesota Press.
16.
GoodI. J.2008. Terminology for various kinds of Bayesian methods. In The Good Book: Thirty Years of Comments, Conjectures, and Conclusions by I. J. Good, ed. BanksD., and SmithE. P., 76–78. Houston, TX: Rice University Press. Article originally published in 1980, Journal of Statistical Computation and Simulation 11: 309–313.
17.
SimonoffJ. S.1996. Smoothing Methods in Statistics.New York: Springer.
18.
SutherlandM., HollandP. W., and FienbergS. E.1975. Combining Bayes and frequency approaches to estimate a multinomial parameter. In Studies in Bayesian Econometrics and Statistics: In Honor of Leonard J. Savage, ed. FienbergS. E., and ZellnerA., 585–617. Amsterdam: North-Holland.
