Statistical Engineering Division
Seminar Series

Don Malec
The YS Bureau of the Census

Experiments are often expensive and time-consuming with resulting conclusions being based on relatively small sample sizes. Often, however, data from related experiments or from pre-experiments are available and their combined use may help arrive at more confident conclusions. A way to combine related data, while simultaneously estimating how much borrowing among data sets should take place, is through the use of hierarchical models and Bayesian inference. This approach is illustrated using a series of examples combining two binomial experiments. The effect of a hierarchical model on estimates of rates and on the degree to which data is combined is illustrated. In addition, the phenomenon in which combining data reduces overall precision is explained. Simpler models based on finite mixtures are shown to work as well as more computationally intensive, continuous mixtures. Lastly, an example combining three concurrent experiments is illustrated.