Prior Probability

A certain kind of PROBABILISTIC reasoning uses the observed data to update probabilities that existed before the data were collected, the so-called prior probabilities. This approach is called BAYESIAN INFERENCE and is in sharp contrast to the other existing approach, which is called frequentist. In the frequentist approach, the probabilities themselves are considered fixed but unknown quantities that can be observed through the RELATIVE FREQUENCIES. If the Bayesian approach is applied to a certain event, the researcher is assumed to have some knowledge regarding the probability of the event—the prior probability—and this is converted, using the BAYES THEOREM, into a posterior probability. The prior probability expresses the knowledge available before the actual observations become known, and the posterior probability is a combination of the prior probability with the information in the data. This updating procedure uses the BAYES FACTOR.

The prior probabilities are similar to ordinary probabilities, and they are called prior only if the goal is to update them using new data. One situation when this approach seems appropriate is when the prior probability comes from a census or an earlier large survey and updating is based on a recent, smaller survey. Although census data, in most cases, are considered more reliable than survey data, they may become outdated, and a newer survey may reflect changes in the society that have taken place since the census was conducted. In such cases, a combination of the old and new pieces of information is achieved by considering the probability of a certain fact, computed from the census, as a prior probability and updating it using the recent survey information. A similar situation occurs when the prior information is taken from a large survey.

For example, suppose that the efficiency of a retraining program for unemployed people is investigated, in terms of the chance (probability) that someone who finishes the program will find employment within a certain period of time. When the program is launched, its efficiency is monitored in great detail, and the data are used to determine employment probabilities for different groups of unemployed people. After the first year of operation, to cut costs, complete monitoring is stopped, and only small-scale surveys are conducted to provide figures for the efficiency of the program. In this case, the probabilities from the complete monitoring are more reliable than those computed from the later surveys. On the other hand, the efficiency of the program may have changed in the meantime for a number of reasons, and the survey results may reflect this change. Therefore, it is appropriate to consider the original probabilities as prior probabilities and to update them using the new data.

The simplest updating procedure uses the so-called BAYES THEOREM and may be applied to update the prior probabilities of certain events that cannot occur at the same time (e.g., different religious affiliations) and may all be compatible with a further event (e.g., agreeing with a certain statement about the separation of state and church). If the former events have known (prior) probabilities (e.g., taken from census data) and it is known what the conditional probability is for someone belonging to one of the religions to agree with the statement, then if agreement with the statement is observed for a respondent, the probabilities of the different religious affiliations may be updated to produce new probabilities for the respondent.

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