We consider the problem of sequential learning from categorical observations bounded in [0, 1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0, 1) noise. We establish that, conditioned upon identical data with at least two observations, the posterior mean of the categorical distribution will always second-o...

Simulation models are widely used for studying and predicting dynamic behaviors of complex systems. Inaccurate simulation results are often inevitable due to imperfect model and inaccurate inputs. With the advances of sensor technology, it is possible to collect large amount of real time observation data from real systems during simulations. This gives rise to a new paradigm of Dynamic Data Dri...

‎We extend the method of adaptive two-stage sequential sampling to‎‎include designs where there is more than one criteria is used in‎‎deciding on the allocation of additional sampling effort‎. ‎These‎‎criteria‎, ‎or conditions‎, ‎can be a measure of the target‎‎population‎, ‎or a measure of some related population‎. ‎We develop‎‎Murthy estimator for the design that is unbiased estimators for‎‎t...

A deep Gaussian process (DGP) is a deep network in which each layer is modelled with a Gaussian process (GP). It is a flexible model that can capture highly-nonlinear functions for complex data sets. However, the network structure of DGP often makes inference computationally expensive. In this paper, we propose an efficient sequential inference framework for DGP, where the data is processed seq...

Sequential sampling strategies have been developed for managing complexity when using computationally expensive computer simulations in engineering design. However, much of the literature has focused on objective-oriented sequential sampling methods for deterministic optimization. These methods cannot be directly applied to robust design which must account for uncontrollable variations in certa...

This article presents a method for simulation of continuous and discrete fracture parameters distributions in hydrocarbon reservoirs using Sequential Indicator Simulation (SIS) and Sequential Gaussian Simulation (SGS) methods. Fracture parameters including azimuth, dip and density are integrated with the porosity and permeability values determined in the models. Based on this study we have iden...

Estimation of a dynamical system’s latent state subject to sensor noise and model inaccuracies remains critical yet difficult problem in robotics. While Kalman filters provide the optimal solution least squared sense for linear Gaussian problems, general nonlinear non-Gaussian case is significantly more complicated, typically relying on sampling strategies that are limited low-dimensional space...