In the simple bootstrap, the n observations are resampled with replacement to produce a bootstrap sample of size n. Note that some observations might not appear in the bootstrap sample, and others might appear multiple times. The number of times that an observation occurs in the bootstrap sample is called its bootstrap weight. For each bootstrap iteration, the entire analysis that produced the statistic of interest is rerun with these changes:

However, the simple bootstrap can sometimes be inadequate. For example, suppose your data set is small or you have a logistic regression setting where you can encounter separation issues. In such cases, JMP enables you to conduct Bayesian bootstrapping using fractional weights. When fractional weights are used, a fractional weight is associated with each observation. The fractional weights sum to n. The statistic of interest is computed by treating the fractional weights as a frequency variable in the analysis platform. For information about fractional weights, see Fractional Weights and Calculation of Fractional Weights.