Recently, many Bayesian methods have been developed for dose finding when simultaneously modeling both toxicity and efficacy outcomes in a blended phase I/II fashion. A further challenge arises when all the true efficacy data cannot be obtained quickly after the treatment so that surrogate markers are instead used (e.g., in cancer trials). We propose a framework to jointly model the probabiliti...

In this paper, we establish sharp bounds on the distribution of the treatment effect in switching regimes models or generalized sample selection models in Heckman (1990). These bounds depend on the identified model parameters only and hence are themselves identified. Their estimation is straightforward once the identified model parameters are estimated. We compare our bounds when the identified...

The strategic technical vision of this thesis proposal is to seek to systematically trailblaze a novel vol-umetric modeling framework/methdology to represent 3D solids. The rapid advances in 3D scanning and acquisition techniques have given rise to the explosive increase of volumetric digital models in recent years. The strong need to explore more efficient and robust 3D modeling techniques has...

We propose a new stochastic frontier model with sample selection, in which the dependencies between selection mechanism, inefficiency term and two-sided error production equation are modeled by trivariate Gaussian copula. This is compared to Greene's original an alternative based on two bivariate copulas. The relative performances of three models analyzed using simulated data cross-sectional ab...

In this paper we introduce and study random Cox-Ross-Rubinstein (CRR) model. The CRR model is a natural bridge, overture to continuous models for which it is possible to derive the Black Scholes option pricing formula. An attractive property of CRR model is that the binomial tree for geometric Brownian motion is consistent with the standard Black-Scholes formula for European options in that no ...

Interrogative visualization refers to the process of interactive computer graphics display and accurate quantitative querying of physical data. Quantitative querying includes search for metric, combinato-rial and topological information. To support this paradigm, we build uniform, compact, co-registered representations (spline models) of multiple physical data elds over the same domain. Dense, ...

In this paper, assuming that (X, Y1, Y2)T has a trivariate normal distribution, we derive the exact joint distribution of ( X, Y(1), Y(2))^T, where Y(1) and Y(2) are order statistics arising from (Y1, Y2)T . We show that this joint distribution is a mixture of truncated trivariate normal distributions and then use this mixture representation to derive the best (nonlinear) predictiors of X...