Conditional information using copulas with an application to decision making
We focus on the task of calculating conditional probabilities of the form Prob(U?x|V?y) Prob ( U ? x | V ? y ) . We point out that in this case the relevant probabilities, Prob(U?x) Prob ( U ? x ) and Prob(V?y) Prob ( V ? y ) , have the nature of a cumulative distribution. This enables us to use the Sklar theorem to directly calculate the required joint probability as a simple binary aggregation of these marginals using a copula. Here the choice of copula reflects the type of correlation between U and V . We study in considerable detail the effects of using different copulas. We also show that this enables us to simply and directly calculate the probability that U=x U = x conditioned on the knowledge of the Prob(V?y) Prob ( V ? y ) . We use this result to aid in decision-making where we compare alternative's expected payoffs based on the conditioned probabilities.
copula conditional probabilities uncertain decision making