# Why need frequentist considered "a distribution of possible data sets D" in likelihood function p(D|w)?

There some words in PRML:

In a frequentist setting, w is considered to be a fixed parameter, whose value is determined by some form of ‘estimator’, and error bars on this estimate are obtained by considering the distribution of possible data sets D. By contrast, from the Bayesian viewpoint there is only a single data set D (namely the one that is actually observed), and the uncertainty in the parameters is expressed through a probability distribution over w.

I wonder what`s the meaning of "the distribution of possible data sets D". Why is it a distribution of data sets for frequentist?

• Maybe it helps if you first consider a data set with only one column, 'male' say with $1=$ male and $0=$ female. Oct 5, 2015 at 14:58
• I think this quotation may be a little misleading. It's a distribution of datasets for both schools of statistics. For the Bayesian, the probability distribution over $w$ is determined by a prior distribution over $w$, by the data, and by a model that associates every value of $w$ with a distribution of possible datasets.
– whuber
Oct 5, 2015 at 19:49