Abstract We present the Optimizing Control Variate (OCV) estimator, a new estimator for Monte Carlo rendering. Based upon a deterministic sampling framework, OCV allows multiple importance sampling functions to be combined in one algorithm. Its optimizing nature addresses a major problem with control variate estimators for rendering: users supply a generic correlated function which is optimized for each estimate, rather than a single highly tuned one that must work well everywhere. We demonstrate OCV with both direct lighting and irradiance‐caching examples, showing improvements in image error of over 35% in some cases, for little extra computation time. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism Color, shading, shadowing, and texture G.3 [Probability and Statistics]: Probabilistic Algorithms Keywords: direct lighting, deterministic mixture sampling, control variates

Abstract Motivation: The classification of samples using gene expression profiles is an important application in areas such as cancer research and environmental health studies. However, the classification is usually based on a small number of samples, and each sample is a long vector of thousands of gene expression levels. An important issue in parametric modeling for so many gene expression levels is the control of the number of nuisance parameters in the model. Large models often lead to intensive or even intractable computation, while small models may be inadequate for complex data. Methodology: We propose a two-step empirical Bayes classification method as a solution to this issue. At the first step, we use the model-based cluster algorithm with a non-traditional purpose of assigning gene expression levels to form abundance groups. At the second step, by assuming the same variance for all the genes in the same group, we substantially reduce the number of nuisance parameters in our statistical model. Results: The proposed model is more parsimonious, which leads to efficient computation under an empirical Bayes estimation procedure. We consider two real examples and simulate data using our method. Desired low classification error rates are obtained even when a large number of genes are pre-selected for class prediction. Availability: Supplemental materials including technical details are available at “http://odin.mdacc.tmc.edu/~yuanj/papers/sup.pdf”. An R program for computation is available upon request by email to Yuan Ji ([email protected]) Contact: [email protected]