Multi Predictor Conditional Probabilities

A predictand's probability distribution is modified by information on one or more of its predictors. If linear dependence is assumed between the predictand and the predictors transformed into normal Gaussian variates, then a model algorithm is possible for the conditional probability of the predictand. It is given as the probability that a Gaussian variable (eta) will equal or exceed a threshold value (eta sub c) where (eta sub c) is expressed linearly in terms of specific normalized values of the predictors. The predictor coefficients, known as partial regression coefficients, are functions of the correlations between predictors and the correlations between each predictor and the predictand. This stochastic model was tested on regular 3-hourly observations of precipitation-produced radar echoes at five widely scattered stations in the eastern half of the United States. The results revealed strong evidence of the validity of the probability estimates, but more importantly revealed that the model can yield sharp estimates of the conditional probability with as many as seven predictors.