Persistency Model and Its Applications in Choice Modeling



Given a discrete optimization problem with random objective coefficients, we would like to approximate the likelihood function of the optimal solution value, using only partial information of the objective coefficients. We call this the persistency problem, and the corresponding probabilities of the likelihood function the persistence values of the variables.We solve various classes of these problems, using marginal moments or marginal distribution information of the objective coefficients. We demonstrate how the approach can be used to obtain insights to problems in discrete choice modeling. Using a set of survey data from a transport choice modeling study, we calibrate the random utility model with choice probabilities obtained from the persistency model. Numerical results suggest that the proposed persistency model is capable of obtaining estimates which perform as well, if not better, than classical methods such as logit and cross nested logit models. We can also use the persistency model to obtain choice probability estimates for more complex choice problems. We illustrate this on a stochastic knapsack problem, which is essentially a discrete choice problem under budget constraint. Numerical results again suggest that our model is able to obtain good estimates of the choice probabilities for this problem. 
Contact information:
Wilco van den Heuvel