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It is shown that the Poisson binomial distribution function can be efficiently calculated using simple convolution based methods. The Poisson binomial distribution describes how the sum of independent but not identically distributed Bernoulli random variables is distributed. Due to the intractability of the Poisson binomial distribution function, efficient methods for computing it have been of particular interest in past Statistical literature. First, it is demonstrated that simply and directly using the definition of the distribution function of a sum of random variables can calculate the Poisson binomial distribution function efficiently. A modified, tree structured Fourier transform convolution scheme is then presented, which provides even greater gains in efficiency. Both approaches are shown to outperform the current state of the art methods in terms of accuracy and speed. The methods are then evaluated on a real data image processing example in order to demonstrate the efficiency advantages of the proposed methods in practical cases. Finally, possible extensions for using convolution based methods to calculate other distribution functions are discussed. [ABSTRACT FROM AUTHOR]

Multivariate regression has many applications, ranging from time series prediction to genomics. Borrowing information across the outcomes can improve prediction error, even when outcomes are statistically independent. Many methods exist to implement this strategy, for example the multiresponse lasso, but choosing the optimal method for a given dataset is difficult. These issues are addressed by establishing a connection between multivariate linear regression and compound decision problems. A nonparametric empirical Bayes procedure that can learn the optimal regression method from the data itself is proposed. Furthermore, the proposed procedure is free of tuning parameters and performs well in simulations and in a multiple stock price prediction problem. [ABSTRACT FROM AUTHOR]

Objective. To evaluate the clinical outcomes of a publicly funded cataract elimination program. Methods. Outcomes of all patients (186) who received extracapsular cataract extraction (ECCE) surgery free of charge at the Instituto Regional de Oftalmología in northern Peru in the first year (August 2008 to July 2009) of the Peruvian National Cataract Elimination Plan were compared retrospectively with the outcomes of all patients (68) who paid in the highest charge tier for ECCE surgery during the same period. Preoperatively, the median uncorrected visual acuity (UCVA) of National Plan patients was Hand Motion; the UCVA of paying patients was Counting Fingers (P = 0.09). Complication frequency and visual acuity (uncorrected visual acuity, pinhole visual acuity, and best correct visual acuity) were the primary outcome measures. The World Health Organization (WHO) Vision 2020 goal is for 85% of operated eyes to achieve 20/60 vision; the Ministerio de Salud del Perú goal is for 75% of eyes to achieve 20/50. Results. One month postoperatively, only 24% of National Plan patients achieved a UCVA of 20/60. The median UCVA for both groups was 20/100 (P = 0.23). Intraoperative complications occurred in 27% of all patients; postoperative complications occurred in 39%. Patients more likely to have a poor outcome (UCVA < 20/200) were those who experienced a postoperative complication (odds ratio [OR] 3.3, P = 0.002), who experienced an intraoperative complication (OR 2.5, P = 0.01), and who were 75 years or older (OR 2.7, P = 0.008). National Plan patients were more likely to have an OCTET Grade II intraoperative complication (OR 4.2, P = 0.03) and were less likely to receive refractive services (OR 1.5, P = 0.002). Conclusions. Neither WHO nor Peruvian benchmarks for surgical outcome were achieved in the first year of the Peruvian National Cataract Elimination Plan. Providing more comprehensive services to patients and addressing variables correlated with poor outcomes may improve interventions and help achieve Vision 2020 goals. [ABSTRACT FROM AUTHOR]