Modelling Conditional Probability

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Abstract
Many studies of the joint frequency of the initial and final conditions of weather elements such as cloud cover, visibility, rainfall or temperature attest to the importance of the initial event as a predictor of the later event. Most efforts have involved the actual collection of the data in contingency tables but there is a strong need for an analytical tool to estimate the conditional probabilities from more readily available climatic frequencies. By assuming the Markov process, and with the help of published tables detailing the bivariate normal distribution, a succinct two-parameter model, using the climatic frequencies in a single equation, has been developed to estimate conditional probabilities, of both frequent and rare events, within a few percentage points. The two parameters have been charted as direct functions of the probability of the initial event and the temporal persistence of the element.

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