Journal of Data Science

Abstract: A statistical approach, based on artificial neural networks, is pro posed for the post-calibration of weather radar rainfall estimation. Tested artificial neural networks include multilayer feedforward networks and radial basis functions. The multilayer feedforward training algorithms consisted of four variants of the gradient descent method, four variants of the conju gate gradient method, Quasi-Newton, One Step Secant, Resilient backprop agation, Levenberg-Marquardt method and Levenberg-Marquardt method using Bayesian regularization. The radial basis networks were the radial basis functions and the generalized regression networks. In general, results showed that the Levenberg-Marquardt algorithm using Bayesian regulariza tion can be introduced as a robust and reliable algorithm for post-calibration of weather radar rainfall estimation. This method benefits from the conver gence speed of the Levenberg-Marquardt algorithm and from the over fitting control of Bayes’ theorem. All the other multilayer feedforward training al gorithms result in failure since they often lead to over fitting or converged to a local minimum, which prevents them from generalizing the data. Radial basis networks are also problematic since they are very sensitive when used with sparse data.

Abstract: A new approach for analyzing state duration data in brand-choice studies is explored. This approach not only incorporates the correlation among repeated purchases for a subject, it also models the purchase timing and the brand decision jointly. The former is accomplished by applying transition model approaches from longitudinal studies while the latter is done by conditioning on the brand choice variable. Then mixed multinomial logit models and Cox proportional hazards models are employed to model the marginal densities of the brand choice and the conditional densities of the interpurchase time given the brand choice. We illustrate the approach using a Nielsen household scanner panel data set