# Frequencies

A number of observations in a class of events. Frequencies can be expressed as relative frequencies, absolute frequencies, or natural frequencies.

## Natural frequencies

Numbers that correspond to the way humans encountered information before the invention of probability theory. Unlike probabilities and relative frequencies, they are raw observations that have not been normalised with respect to the base rates of the event in question.

For instance, a physician has observed 100 persons, 10 of whom show a new disease. Of these 10 persons, 8 show a symptom, whereas 4 of the 90 without the disease also show the symptom. Breaking these 100 cases down into four numbers:

- disease and symptom 8
- disease and no symptom 2
- no disease and symptom 4
- no disease and no symptom 86

results in four natural frequencies 8, 2, 4, and 86. Natural frequencies facilitate Bayesian inferences. For instance, if the physician observes a new person with the symptom, the physician can easily see that the chance that this patient also has the disease is 8/(8+4), that is 2/3. If the physician's observations, however, are transformed into conditional probabilities or relative frequencies (for example, by dividing the natural frequency 4 by the base rate 90, resulting in .044, or 4.4 percent,) then the computation of this probability becomes more difficult and requires Bayes's rule for probabilities. Natural frequencies help people to make sound conclusions, whereas conditional probabilities tend to cloud minds.

The use of natural frequencies can be seen for :

## Relative frequencies

One of the three major interpretations of probability (the others are degrees of belief and propensities). The probability of an event is defined as its relative frequency in a reference class. Historically, frequencies entered probability theory through mortality tables that provided the basis for calculating life insurance rates. Relative frequencies are constrained to repeated events that can be observed in large numbers.