Must the frequentist refuse to assign probabilities to one-off events? Consider the question 'will it rain tomorrow'. The frequentist can define some abstract class of events, say the class of possible weathers. She can then assume that every day the actual weather is randomly sampled from this imaginary population. She can then look at some past weather records and calculate a random sample from this hypothetical population. Suppose there that in this large sample 30% of days were sunny; we can then say that approximately 30% of the hypothetical weathers in this population are sunny and hence the probability of drawing a sunny day tomorrow is approx 30%.
Must the frequentist refuse to assign probabilities to one-off events? Consider the question 'will it rain tomorrow'. The frequentist can define some abstract class of events, say the class of possible weathers. She can then assume that every day the actual weather is randomly sampled from this imaginary population. She can then look at some past weather records and calculate a random sample from this hypothetical population. Suppose there that in this large sample 30% of days were sunny; we can then say that approximately 30% of the hypothetical weathers in this population are sunny and hence the probability of drawing a sunny day tomorrow is approx 30%.
Obviously the answer she gets... (read more)