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We study production planning in a multi‐product setting, in which demand for each product depends on multiple financial assets (such as commodities, market indices, etc). In addition to the production quantity decision at the beginning of the planning horizon, there is also a real‐time hedging decision throughout the horizon; and we optimize both decisions jointly. With a mean–variance problem formulation, we first derive the optimal hedging strategy, given the production quantities. This leads to an explicit objective function with which bounds on optimal production quantities are identified. Thus, optimization of the production policies can be readily solved numerically as a static minimization problem. This way, we are able to give a complete characterization of the mean–variance efficient frontier, and quantify the contribution of the hedging strategy by the variance reduction it achieves. Furthermore, the model and results are extended to allow dynamic production control that tracks the demand rates.

The propensity methodology is widely used in medical research to compare different treatments in designs with a nonrandomized treatment allocation. The inverse probability weighted (IPW) estimators are a primary tool for estimating the average treatment effect but the large variance of these estimators is often a significant concern for their reliable use in practice. Inspired by Rao-Blackwellization, this paper proposes a method to smooth an IPW estimator by replacing the weights in the original estimator by their mean over a distribution of the potential treatment assignment. In our simulation study, the smoothed IPW estimator achieves a substantial variance reduction over its original version with only a small increased bias, for example two-to-sevenfold variance reduction for the three IPW estimators in Lunceford and Davidian [Statistics in Medicine, 23(19), 2937-2960]. In addition, our proposed smoothing can also be applied to the locally efficient and doubly robust estimator for added protection against model misspecification. An implementation in R is provided.

International audience; In this paper we examine a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic forces. The control variate is the expectation of the same functional for the limit diffusion process that approximates the original process when the mean-reversion time goes to zero. To get an efficient control variate estimator, we propose a coupling method to build the original process and the limit diffusion process. We show that the correlation between the two processes indeed goes to one when the mean reversion time goes to zero and we quantify the convergence rate, which makes it possible to characterize the variance reduction of the proposed control variate method. The efficiency of the method is illustrated on a few examples.

Chance imbalance in baseline characteristics is common in randomized clinical trials. Regression adjustment such as the analysis of covariance (ANCOVA) is often used to account for imbalance and increase precision of the treatment effect estimate. An objective alternative is through inverse probability weighting (IPW) of the propensity scores. Although IPW and ANCOVA are asymptotically equivalent, the former may demonstrate inferior performance in finite samples. In this article, we point out that IPW is a special case of the general class of balancing weights, and advocate to use overlap weighting (OW) for covariate adjustment. The OW method has a unique advantage of completely removing chance imbalance when the propensity score is estimated by logistic regression. We show that the OW estimator attains the same semiparametric variance lower bound as the most efficient ANCOVA estimator and the IPW estimator for a continuous outcome, and derive closed-form variance estimators for OW when estimating additive and ratio estimands. Through extensive simulations, we demonstrate OW consistently outperforms IPW in finite samples and improves the efficiency over ANCOVA and augmented IPW when the degree of treatment effect heterogeneity is moderate or when the outcome model is incorrectly specified. We apply the proposed OW estimator to the Best Apnea Interventions for Research (BestAIR) randomized trial to evaluate the effect of continuous positive airway pressure on patient health outcomes. All the discussed propensity score weighting methods are implemented in the R package PSweight., 18 pages, 1 figure, 3 tables

Purpose Radiation doses accumulated during very complicated image-guided x-ray procedures have the potential to cause stochastic, but also deterministic effects, such as skin rashes or even hair loss. To monitor and reduce radiation-related risks to patients' skin, x-ray imaging devices are equipped with online air kerma monitoring components. Traditionally, such measurements have been used to estimate skin entrance dose by (a) estimating air kerma at the interventional reference point (IRP), (b) forward projecting the dose distribution, and (c) considering a backscatter factor among other correction factors. Unfortunately, the complicated interaction between incident x-ray photons, secondary electrons, and skin tissue cannot be properly accounted for by assuming a linear relationship between forward projected air kerma and a backscatter factor. Gold standard skin dose models are therefore determined using Monte Carlo (MC) techniques. However, MC simulations are computationally complex in general and possible acceleration mainly depends on the employed hardware and variance reduction techniques. To obtain reliable and fast dose estimates, we propose to combine MC-based simulations with learning-based methods. Methods The basic idea of our method is to approximate the radiation physics to calculate a first-order exposure estimate quickly. This initial estimate is then refined using prior knowledge derived from MC simulations. To this end, the primary photon propagation inside a voxelized patient model is estimated using a less accurate but fast photon ray casting (RC) simulation based on the Beer-Lambert law. The results of the RC simulation are then fed into a convolutional neural network (CNN), which maps the propagation of primary photons to the dose deposition inside the patient model. Additionally, the patient model itself including anatomy and material properties, such as mass density and mass energy-absorption coefficients, are fed into the CNN as well. The CNN is trained using smoothed results of MC simulations as output and RC simulations of identical imaging settings and patient models as input. Results In total, 163 MC and associated RC simulations are carried out for the head, thorax, abdomen, and pelvis in three different voxel phantoms. We used 10 8 or 10 9 primarily emitted photons sampled from a 125 kV peak voltage spectrum, respectively. Edge-preserving smoothing (EPS) is applied to reduce (a) general stochastic uncertainties and (b) stochastic uncertainty concerning MC simulations of less primary photons. The CNN is trained using seven imaging settings of the abdomen in a single phantom. Testing its performance on the remaining datasets, the CNN is capable of estimating skin dose with an error of below 10% for the majority of test cases. Conclusion The combination of deep neural networks and MC simulation of particle physics has the potential to decrease the computational complexity of accurate skin dose estimation. The proposed approach can provide dose distributions in under one second when running on high-end hardware. On lower cost hardware, it took up to 2 min to arrive at the same result. This makes our approach applicable in high-end environments as well as in budget solutions. Furthermore, the number of primary photons only affects the training time, while the execution time is independent of the number of primary photons.

Importance sampling is one of the most widely used variance reduction strategies in Monte Carlo rendering. In this paper, we propose a novel importance sampling technique that uses a neural network to learn how to sample from a desired density represented by a set of samples. Our approach considers an existing Monte Carlo rendering algorithm as a black box. During a scene-dependent training phase, we learn to generate samples with a desired density in the primary sample space of the rendering algorithm using maximum likelihood estimation. We leverage a recent neural network architecture that was designed to represent real-valued non-volume preserving ('Real NVP') transformations in high dimensional spaces. We use Real NVP to non-linearly warp primary sample space and obtain desired densities. In addition, Real NVP efficiently computes the determinant of the Jacobian of the warp, which is required to implement the change of integration variables implied by the warp. A main advantage of our approach is that it is agnostic of underlying light transport effects, and can be combined with many existing rendering techniques by treating them as a black box. We show that our approach leads to effective variance reduction in several practical scenarios., Submitted to SIGGRAPH ASIA'18

PURPOSE The purpose of this work is threefold: First, to obtain the phase space of an electronic brachytherapy (eBT) system designed for surface skin treatments. Second, to explore the use of some efficiency enhancing (EFEN) strategies in the determination of the phase space. Third, to use the phase space previously obtained to perform a dosimetric characterization of the Esteya eBT system. METHODS The Monte Carlo study of the 69.5 kVp x-ray beam of the Esteya® unit (Elekta Brachytherapy, Veenendaal, The Netherlands) was performed with PENELOPE2014. The EFEN strategies included the use of variance reduction techniques and mixed Class II simulations, where transport parameters were fine-tuned. Four source models were studied varying the most relevant parameters characterizing the electron beam impinging the target: the energy spectrum (mono-energetic or Gaussian shaped), and the electron distribution over the focal spot (uniform or Gaussian shaped). Phase spaces obtained were analyzed to detect differences in the calculated data due to the EFEN strategy or the source configuration. Depth dose curves and absorbed dose profiles were obtained for each source model and compared to experimental data previously published. RESULTS In our EFEN strategy, the interaction forcing variance reduction (VRIF) technique increases efficiency by a factor ~20. Tailoring the transport parameters values (C1 and C2) does not increase the efficiency in a significant way. Applying a universal cutoff energy EABS of 10 keV saves 84% of CPU time while showing negligible impact on the calculated results. Disabling the electron transport by imposing an electron energy cutoff of 70 keV (except for the target) saves an extra 8% (losing in the process 1.2% of the photons). The Gaussian energy source (FWHM = 10%, centered at the nominal kVp, homogeneous electron distribution) shows characteristic K-lines in its energy spectrum, not observed experimentally. The average photon energy using an ideal source (mono-energetic, homogeneous electron distribution) was 36.19 ± 0.09 keV, in agreement with the published measured data of 36.2 ± 0.2 keV. The use of a Gaussian-distributed electron source (mono-energetic) increases the penumbra by 50%, which is closer to the measurement results. The maximum discrepancy of the calculated percent depth dose with the corresponding measured values is 4.5% (at the phantom surface, less than 2% beyond 1 mm depth) and 5% (for the 80% of the field) in the dose profile. Our results agree with the findings published by other authors and are consistent within the expected Type A and B uncertainties. CONCLUSIONS Our results agree with the published measurement results within the reported uncertainties. The observed differences in PDD, dose profiles, and photon spectrum come from three main sources of uncertainty: intermachine variations, measurements, and Monte Carlo calculations. It has been observed that a mono-energetic source with a Gaussian electron distribution over the focal spot is a suitable choice to reproduce the experimental data.

International audience; Staged local optimized permutations Our optimized scrambled sequence Sobol sequence Our sequence Ground truth Figure 1: Left: our staged per-tile optimized scrambling, applied to a Sobol sequence of sampling points, produces a power spectrum close to Blue Noise. Right: Rendering of a challenging scene featuring depth of field and high specularity (jewels). The sampling was done with the Sobol sequence (top) and our sampler (bottom); both use 256 samples per pixel and 3 light bounces. Note the improvement in aliasing when using our method in comparison to the original Sobol sequence. Abstract Distributions of samples play a very important role in rendering, affecting variance, bias and aliasing in Monte-Carlo and Quasi-Monte Carlo evaluation of the rendering equation. In this paper, we propose an original sampler which inherits many important features of classical low-discrepancy sequences (LDS): a high degree of uniformity of the achieved distribution of samples, computational efficiency and progressive sampling capability. At the same time, we purposely tailor our sampler in order to improve its spectral characteristics, which in turn play a crucial role in variance reduction, anti-aliasing and improving visual appearance of rendering. Our sampler can efficiently generate sequences of multidimensional points, whose power spectra approach so-called Blue-Noise (BN) spectral property while preserving low discrepancy (LD) in certain 2-D projections. In our tile-based approach, we perform permutations on subsets of the original Sobol LDS. In a large space of all possible permutations, we select those which better approach the target BN property, using pair-correlation statistics. We pre-calculate such " good " permutations for each possible Sobol pattern, and store them in a lookup table efficiently accessible in runtime. We provide a complete and rigorous proof that such permutations preserve dyadic partitioning and thus the LDS properties of the point set in 2-D projections. Our construction is computationally efficient, has a relatively low memory footprint and supports adaptive sampling. We validate our method by performing spectral/discrepancy/aliasing analysis of the achieved distributions, and provide variance analysis for several target integrands of theoretical and practical interest.

I propose an exact finite sample test of the risk reduction of the global minimum variance (GMV) portfolio. The GMV test statistic is proportional to the reduction in the variance of the GMV portfolio and has a straightforward geometric and portfolio interpretation and complements the celebrated GRS test in Gibbons et al. (1989). In practical applications, the GMV test leads to a rejection of the null hypothesis of no improvement in the GMV portfolio more often than the GRS test rejects the null hypothesis of no improvement in the risk‐return profile of the tangent portfolio. The power of the GMV test increases with the variance reduction of the GMV portfolio. Using test asset returns scaled by predetermined predictive variables is equivalent to increasing the overall number of test assets and leads to substantial power gains.

In the past several decades, many ranking-and-selection (R&S) procedures have been developed to select the best simulated system with the largest (or smallest) mean performance measure from a finite number of alternatives. A major issue to address in these R&S problems is to balance the trade-off between the effectiveness (ie, making a correct selection with a high probability) and the efficiency (ie, using a small total number of observations). In this paper, we take a frequentist's point of view by setting a predetermined probability of correct selection while trying to reduce the total sample size, that is, to improve the efficiency but also maintain the effectiveness. In particular, in order to achieve this goal, we investigate combining various variance reduction techniques into the fully sequential framework, resulting in different R&S procedures with either finite-time or asymptotic statistical validity. Extensive numerical experiments show great improvement in the efficiency of our proposed procedures as compared with several existing procedures.

We introduce a metric based on Bayesian probability theory to evaluate the determinants of scientific discovery, and use it to assess an international aquacultural research program consisting of a large number of highly varied projects. The metric accommodates not only project variety but a detailed breakdown of the sources of research productivity, accounting, for example, for the contributions of “failed” as well as “successful” investigations. A mean-absolute-deviation loss functional form permits decomposition of knowledge gain into an outcome probability shift (mean surprise) and outcome variance reduction (statistical precision), allowing productivity to be estimated for each of them separately, then combined into a single knowledge production relationship. Laboratory size is found to moderately boost mean surprise but has no effect on statistical precision, while investigator education greatly improves precision but has no effect on mean surprise. Returns to research scale are decreasing in the size dimension alone but increasing when size and education are taken together, suggesting the importance of measuring human capital at both the quantitative and qualitative margins.

A new nonparametric approach is developed to estimate the time-dependent accuracy measure curves, which are defined on the cumulative cases and dynamic controls, for censored survival data. Based on an estimable survival process, the main intention of this study is to reduce the finite-sample biases of nearest neighbor estimators. The asymptotic variances of some retrospective accuracy measure estimators are further reduced by applying a smoothing technique to the underlying process of a marker. Meanwhile, practically feasible and theoretically valid procedures are proposed for bandwidth selection in the presented estimators. In addition, the proposed methodology can be reasonably extended to accommodate stratified survival data and survival data with multiple markers. As shown in the simulations, our new estimators outperform the nearest neighbor and inverse censoring weighted estimators. Data from the AIDS Clinical Trials Group study 175 and an angiographic coronary artery disease study are also used to illustrate the proposed methodology. Copyright © 2016 John Wiley & Sons, Ltd.

Summary Fluorescence enhancement in samples irradiated in a scanning electron microscope or an electron microprobe should be appropriately assessed in order not to distort quantitative analyses. Several models have been proposed to take into account this effect and current quantification routines are based on them, many of which have been developed under the assumption that bremsstrahlung fluorescence correction is negligible when compared to characteristic enhancement; however, no concluding arguments have been provided in order to support this assumption. As detectors are unable to discriminate primary from secondary characteristic X-rays, Monte Carlo simulation of radiation transport becomes a determinant tool in the study of this fluorescence enhancement. In this work, bremsstrahlung fluorescence enhancement in electron probe microanalysis has been studied by using the interaction forcing routine offered by penelope 2008 as a variance reduction alternative. The developed software allowed us to show that bremsstrahlung and characteristic fluorescence corrections are in fact comparable in the studied cases. As an extra result, the interaction forcing approach appears as a most efficient method, not only in the computation of the continuum enhancement but also for the assessment of the characteristic fluorescence correction.

Three flawed practices associated with model averaging coefficients for predictor variables in regression models commonly occur when making multimodel inferences in analyses of ecological data. Model-averaged regression coefficients based on Akaike information criterion (AIC) weights have been recommended for addressing model uncertainty but they are not valid, interpretable estimates of partial effects for individual predictors when there is multicollinearity among the predictor variables. Multicollinearity implies that the scaling of units in the denominators of the regression coefficients may change across models such that neither the parameters nor their estimates have common scales, therefore averaging them makes no sense. The associated sums of AIC model weights recommended to assess relative importance of individual predictors are really a measure of relative importance of models, with little information about contributions by individual predictors compared to other measures of relative importance based on effects size or variance reduction. Sometimes the model-averaged regression coefficients for predictor variables are incorrectly used to make model-averaged predictions of the response variable when the models are not linear in the parameters. I demonstrate the issues with the first two practices using the college grade point average example extensively analyzed by Burnham and Anderson. I show how partial standard deviations of the predictor variables can be used to detect changing scales of their estimates with multicollinearity. Standardizing estimates based on partial standard deviations for their variables can be used to make the scaling of the estimates commensurate across models, a necessary but not sufficient condition for model averaging of the estimates to be sensible. A unimodal distribution of estimates and valid interpretation of individual parameters are additional requisite conditions. The standardized estimates or equivalently the t statistics on unstandardized estimates also can be used to provide more informative measures of relative importance than sums of AIC weights. Finally, I illustrate how seriously compromised statistical interpretations and predictions can be for all three of these flawed practices by critiquing their use in a recent species distribution modeling technique developed for predicting Greater Sage-Grouse (Centrocercus urophasianus) distribution in Colorado, USA. These model averaging issues are common in other ecological literature and ought to be discontinued if we are to make effective scientific contributions to ecological knowledge and conservation of natural resources.

The regression-based Monte Carlo methods for backward stochastic differential equations (BSDEs) have been the object of considerable research, particularly for solving nonlinear partial differential equations (PDEs). Unfortunately, such methods often become unstable when implemented with small time steps because the variance of gradient estimates is inversely proportional to the time step (σ2∼ 1/Δ t). Recently new variance reduction techniques were introduced to address this problem in~a paper by the author and Avellaneda. The purpose of this paper is to provide a rigorous justification for these techniques in the context of the discrete-time BSDE scheme of Bouchard and Touzi. We also suggest a new higher-order scheme that makes the variance proportional to the time step (σ2∼Δ t). These techniques are easy to implement. Numerical examples strongly indicate that they render the regression-based Monte Carlo methods stable for small time steps and thus viable for numerical solution of nonlinear PDEs.© 2016 Wiley Periodicals, Inc.

Suppliers of consumer packaged goods are facing an increasingly challenging situation as they work to fulfill orders from their retail partners’ distribution facilities. Traditionally these suppliers have generated forecasts of a given retailer's orders using records of that retailer's past orders. However, it is becoming increasingly common for retail firms to collect and share large volumes of point-of-sale (POS) data, thus presenting an alternative data signal for suppliers to use in generating forecasts. A question then arises as to which data produce the most accurate forecasts. Compounding this question is the fact that forecasters often temporally aggregate data for consolidation or to produce forecasts in larger time buckets. Extant literature prescribes two countervailing statistical effects, information loss and variance reduction, that could play significant roles in determining the impact of temporal aggregation on forecast accuracy. Utilizing a large set of paired order and POS data, this study examines these relationships.

We consider the variance estimation of the weighted likelihood estimator (WLE) under two-phase stratified sampling without replacement. Asymptotic variance of the WLE in many semiparametric models contains unknown functions or does not have a closed form. The standard method of the inverse probability weighted (IPW) sample variances of an estimated influence function is then not available in these models. To address this issue, we develop the variance estimation procedure for the WLE in a general semiparametric model. The phase I variance is estimated by taking a numerical derivative of the IPW log likelihood. The phase II variance is estimated based on the bootstrap for a stratified sample in a finite population. Despite a theoretical difficulty of dependent observations due to sampling without replacement, we establish the (bootstrap) consistency of our estimators. Finite sample properties of our method are illustrated in a simulation study.

Purpose: While significant progress has been made in speeding up Monte Carlo (MC) dose calculation methods, they remain too time-consuming for the purpose of inverse planning. To achieve clinically usable calculation speeds, a precalculated Monte Carlo (PMC) algorithm for proton and electron transport was developed to run on graphics processing units (GPUs). The algorithm utilizes pregenerated particle track data from conventional MC codes for different materials such as water, bone, and lung to produce dose distributions in voxelized phantoms. While PMC methods have been described in the past, an explicit quantification of the latent uncertainty arising from the limited number of unique tracks in the pregenerated track bank is missing from the paper. With a proper uncertainty analysis, an optimal number of tracks in the pregenerated track bank can be selected for a desired dose calculation uncertainty. Methods: Particle tracks were pregenerated for electrons and protons using EGSnrc and GEANT4 and saved in a database. The PMC algorithm for track selection, rotation, and transport was implemented on the Compute Unified Device Architecture (CUDA) 4.0 programming framework. PMC dose distributions were calculated in a variety of media and compared to benchmark dose distributions simulated from the corresponding general-purpose MC codes inmore » the same conditions. A latent uncertainty metric was defined and analysis was performed by varying the pregenerated track bank size and the number of simulated primary particle histories and comparing dose values to a “ground truth” benchmark dose distribution calculated to 0.04% average uncertainty in voxels with dose greater than 20% of D{sub max}. Efficiency metrics were calculated against benchmark MC codes on a single CPU core with no variance reduction. Results: Dose distributions generated using PMC and benchmark MC codes were compared and found to be within 2% of each other in voxels with dose values greater than 20% of the maximum dose. In proton calculations, a small (≤1 mm) distance-to-agreement error was observed at the Bragg peak. Latent uncertainty was characterized for electrons and found to follow a Poisson distribution with the number of unique tracks per energy. A track bank of 12 energies and 60000 unique tracks per pregenerated energy in water had a size of 2.4 GB and achieved a latent uncertainty of approximately 1% at an optimal efficiency gain over DOSXYZnrc. Larger track banks produced a lower latent uncertainty at the cost of increased memory consumption. Using an NVIDIA GTX 590, efficiency analysis showed a 807 × efficiency increase over DOSXYZnrc for 16 MeV electrons in water and 508 × for 16 MeV electrons in bone. Conclusions: The PMC method can calculate dose distributions for electrons and protons to a statistical uncertainty of 1% with a large efficiency gain over conventional MC codes. Before performing clinical dose calculations, models to calculate dose contributions from uncharged particles must be implemented. Following the successful implementation of these models, the PMC method will be evaluated as a candidate for inverse planning of modulated electron radiation therapy and scanned proton beams.« less

We present a theoretical analysis of error of combinations of Monte Carlo estimators used in image synthesis. Importance sampling and multiple importance sampling are popular variance-reduction strategies. Unfortunately, neither strategy improves the rate of convergence of Monte Carlo integration. Jittered sampling (a type of stratified sampling), on the other hand is known to improve the convergence rate. Most rendering software optimistically combine importance sampling with jittered sampling, hoping to achieve both. We derive the exact error of the combination of multiple importance sampling with jittered sampling. In addition, we demonstrate a further benefit of introducing negative correlations (antithetic sampling) between estimates to the convergence rate. As with importance sampling, antithetic sampling is known to reduce error for certain classes of integrands without affecting the convergence rate. In this paper, our analysis and experiments reveal that importance and antithetic sampling, if used judiciously and in conjunction with jittered sampling, may improve convergence rates. We show the impact of such combinations of strategies on the convergence rate of estimators for direct illumination.

This article introduces a method for estimating performability metrics built upon non-binary network states, determined by the hop distances between distinguished nodes. The estimation is performed by a Monte Carlo simulation where the sampling space is reduced using edge sets known as d-pathsets and d-cutsets. Numerical experiments over two mesh-like networks are presented. They show significant efficiency improvements relative to the crude Monte Carlo method, in particular as link failures become rarer events, which is usually the case in most real communication networks.

For fixed size sampling designs with high entropy it is well known that the variance of the Horvitz-Thompson estimator can be approximated by the Hajek formula. The interest of this asymptotic variance approximation is that it only involves the first order inclusion probabilities of the statistical units. We extend this variance formula when the variable under study is functional and we prove, under general conditions on the regularity of the individual trajectories and the sampling design, that it asymptotically provides a uniformly consistent estimator of the variance function of the Horvitz-Thompson estimator of the mean function. Rates of convergence to the true variance function are given for rejective sampling. We deduce, under conditions on the entropy of the sampling design, that it is possible to build confidence bands whose coverage is asymptotically the desired one via simulation of Gaussian processes whose variance function is given by the Hajek formula. Finally, the accuracy of the proposed variance estimator is evaluated on samples of electricity consumption data measured every half an hour over a period of one week.

In this paper, we investigate a method based on risk minimization to hedge observable but non-tradable source of risk on financial or energy markets. The optimal portfolio strategy is obtained by minimizing dynamically the Conditional Value-at-Risk (CVaR) using three main tools: stochastic approximation algorithm, optimal quantization and variance reduction techniques (importance sampling (IS) and linear control variable (LCV)) as the quantities of interest are naturally related to rare events. As a first step, we investigate the problem of CVaR regression, which corresponds to a static portfolio strategy where the number of units of each tradable assets is fixed at time 0 and remains unchanged till time $T$. We devise a stochastic approximation algorithm and study its a.s. convergence and rate of convergence. Then, we extend to the dynamic case under the assumption that the process modelling the non-tradable source of risk and financial assets prices are Markov. Finally, we illustrate our approach by considering several portfolios in the incomplete energy market.

In individually randomised controlled trials, adjustment for baseline characteristics is often undertaken to increase precision of the treatment effect estimate. This is usually performed using covariate adjustment in outcome regression models. An alternative method of adjustment is to use inverse probability-of-treatment weighting (IPTW), on the basis of estimated propensity scores. We calculate the large-sample marginal variance of IPTW estimators of the mean difference for continuous outcomes, and risk difference, risk ratio or odds ratio for binary outcomes. We show that IPTW adjustment always increases the precision of the treatment effect estimate. For continuous outcomes, we demonstrate that the IPTW estimator has the same large-sample marginal variance as the standard analysis of covariance estimator. However, ignoring the estimation of the propensity score in the calculation of the variance leads to the erroneous conclusion that the IPTW treatment effect estimator has the same variance as an unadjusted estimator; thus, it is important to use a variance estimator that correctly takes into account the estimation of the propensity score. The IPTW approach has particular advantages when estimating risk differences or risk ratios. In this case, non-convergence of covariate-adjusted outcome regression models frequently occurs. Such problems can be circumvented by using the IPTW adjustment approach. © 2013 The authors. Statistics in Medicine published by John Wiley & Sons, Ltd.

In this paper, we consider the design for comparing the performance of two binary classification rules, for example, two record linkage algorithms or two screening tests. Statistical methods are well developed for comparing these accuracy measures when the gold standard is available for every unit in the sample, or in a two-phase study when the gold standard is ascertained only in the second phase in a subsample using a fixed sampling scheme. However, these methods do not attempt to optimize the sampling scheme to minimize the variance of the estimators of interest. In comparing the performance of two classification rules, the parameters of primary interest are the difference in sensitivities, specificities, and positive predictive values. We derived the analytic variance formulas for these parameter estimates and used them to obtain the optimal sampling design. The efficiency of the optimal sampling design is evaluated through an empirical investigation that compares the optimal sampling with simple random sampling and with proportional allocation. Results of the empirical study show that the optimal sampling design is similar for estimating the difference in sensitivities and in specificities, and both achieve a substantial amount of variance reduction with an over-sample of subjects with discordant results and under-sample of subjects with concordant results. A heuristic rule is recommended when there is no prior knowledge of individual sensitivities and specificities, or the prevalence of the true positive findings in the study population. The optimal sampling is applied to a real-world example in record linkage to evaluate the difference in classification accuracy of two matching algorithms. Copyright © 2013 John Wiley & Sons, Ltd.

AROME-France is an operational convective-scale numerical weather prediction system which uses a 3D-Var assimilation scheme in order to determine its initial conditions. In addition to conventional and satellite observations, regional high-resolution observations are assimilated, such as screen-level observations, total zenith delays from ground-based GPS stations and radar measurements (radial winds and reflectivities). The impact of the various observation types on AROME-France analyses is assessed using an a posteriori diagnostic, the reduction of the estimation error variance. This diagnostic, estimated using a randomization technique, allows one to investigate observation impact depending on the control variable field, model levels, date, analysis time, and spatial scales considered. This highlights the importance of screen-level observations (2 m temperature and relative humidity, 10 m wind) for the lowest layers, of aircraft measurements for temperature and wind field analyses and of radar observations for wind and specific humidity in middle and high troposphere. Only the last mentioned observations appear to be informative regarding the horizontal length-scale below 200 km, while all observations are mostly informative for length-scales above 200 km. The results from two diagnostics, namely the variance reduction and the Degrees of Freedom for Signal (DFS), are compared and found to be largely similar. The variance reduction appears to be an interesting diagnostic to improve the understanding of how observations are used.

The Sequential Importance Resampling method is introduced to a two dimensional hydraulic model to estimate inflow and Manning roughness coefficient (Manning's n) simultaneously. The equifinality problem between the Manning's n and the inflow is considered using the proposed method. To solve the problem, we introduce the variance reduction factor and the correction factor in the perturbation step of the proposed method. The perturbed inflow and Manning's n were updated according to the observed water stage with state variables. The result of the proposed method shows good agreement with the observed discharge, which enabled us to estimate the Manning's n and inflow discharge at the same time considering the uncertainties of the existing rating curve. Finally, it showed that the methodology not only estimates the appropriate Manning's n but also improves the existing rating curve.

Stability of feature selection is an important but under-addressed issue in knowledge discovery from high-dimensional data. In this study, we present a theoretical framework about the relationship between the stability and the accuracy of feature selection based on a formal bias-variance decomposition of feature selection error. The framework also reveals the connection between stability and sample size and suggests a variance reduction approach for improving the stability of feature selection algorithms under small sample size. Following the theoretical framework, we propose an empirical variance reduction framework, margin-based instance weighting, which weights training instances according to their importance to feature evaluation. Our extensive experimental study first verifies the theoretical and empirical frameworks based on synthetic data sets and a popular feature selection algorithm SVM-RFE. Experiments based on real-world microarray data sets further verify that the empirical framework is effective at reducing the variance and improving the subset stability of two representative feature selection algorithms, SVM-RFE and ReliefF, while maintaining comparable predictive accuracy based on the selected features. The proposed instance weighting framework is also shown to be more effective and efficient than the ensemble framework at improving the subset stability of the feature selection algorithms under study. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012 © 2012 Wiley Periodicals, Inc.

We consider the problem of identifying the simulated system with the best expected performance measure when the number of alternatives is finite and small (often < 500). Recently, more research efforts in the simulation community have been directed to develop ranking and selection (R&S) procedures capable of exploiting variance reduction techniques (especially the control variates). In this article, we propose new R&S procedures that can jointly use control variates and correlation induction techniques (including antithetic variates and Latin hypercube sampling). Empirical results and a realistic illustration show that the proposed procedures outperform the conventional procedures using sample means or control variates alone. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

To determine k Q msr, Q o f msr, f o correction factors for machine-specific reference (msr) conditions by Monte Carlo (MC) simulations for reference dosimetry of TomoTherapy static beams for ion chambers Exradin A1SL, A12; PTW 30006, 31010 Semiflex, 31014 PinPoint, 31018 microLion; NE 2571. Methods: For the calibration of TomoTherapy units, reference conditions specified in current codes of practice like IAEA/TRS-398 and AAPM/TG-51 cannot be realized. To cope with this issue, Alfonso [Med. Phys. 35, 5179-5186 (2008)] described a new formalism introducing msr factors k Q msr, Q o f msr, f o for reference dosimetry, applicable to static TomoTherapy beams. In this study, those factors were computed directly using MC simulations for Q 0 corresponding to a simplified 60Co beam in TRS-398 reference conditions (at 10 cm depth). The msr conditions were a 10 × 5 cm 2 TomoTherapy beam, source-surface distance of 85 cm and 10 cm depth. The chambers were modeled according to technical drawings using the egs++ package and the MC simulations were run with the egs-chamber user code. Phase-space files used as the source input were produced using PENELOPE after simulation of a simplified 60Co beam and the TomoTherapy treatment head modeled according to technical drawings. Correlated sampling, intermediate phase-space storage, and photon cross-section enhancement variance reduction techniques were used. The simulations were stopped when the combined standard uncertainty was below 0.2%. Results: Computed k Q msr, Q o f msr, f o values were all close to one, in a range from 0.991 for the PinPoint chamber to 1.000 for the Exradin A12 with a statistical uncertainty below 0.2%. Considering a beam quality Q defined as the TPR 20,10 for a 6 MV Elekta photon beam (0.661), the additional correction k Q msr, Q f msr, f ref to kQ, Q o defined in Alfonso [Med. Phys. 35, 5179-5186 (2008)] formalism was in a range from 0.997 to 1.004. Conclusion: The MC computed factors in this study are in agreement with measured factors for chamber types already studied in literature. This work provides msr correction factors for additional chambers used in reference dosimetry. All of them were close to one (within 1%).

Purpose: Highly constrained backprojection-local reconstruction (HYPR-LR) has made a dramatic impact on magnetic resonance angiography (MRA) and shows promise for positron emission tomography (PET) because of the improvements in the signal-to-noise ratio (SNR) it provides dynamic images. For PET in particular, HYPR-LR could improve kinetic analysis methods that are sensitive to noise. In this work, the authors closely examine the performance of HYPR-LR in the context of kinetic analysis, they develop an implementation of the algorithm that can be tailored to specific PET imaging tasks to minimize bias and maximize improvement in variance, and they provide a framework for validating the use of HYPR-LR processing for a particular imaging task. Methods: HYPR-LR can introduce errors into non sparse PET studies that might bias kinetic parameter estimates. An implementation of HYPR-LR is proposed that uses multiple temporally summed composite images that are formed based on the kinetics of the tracer being studied (HYPR-LR-MC). The effects of HYPR-LR-MC and of HYPR-LR using a full composite formed with all the frames in the study (HYPR-LR-FC) on the kinetic analysis of Pittsburgh compound-B ([11C]-PIB) are studied. HYPR-LR processing is compared to spatial smoothing. HYPR-LR processing was evaluated using both simulated and human studies. Nondisplaceable binding potential (BPND) parametric images were generated from fifty noise realizations of the same numerical phantom and eight [11C]-PIB positive human scans before and after HYPR-LR processing or smoothing using the reference region Logan graphical method and receptor parametric mapping (RPM2). The bias and coefficient of variation in the frontal and parietal cortex in the simulated parametric images were calculated to evaluate the absolute performance of HYPR-LR processing. Bias in the human data was evaluated by comparing parametric image BPND values averaged over large regions of interest (ROIs) to Logan estimates of the BPND from TACs averaged over the same ROIs. Variance was assessed qualitatively in the parametric images and semiquantitatively by studying the correlation between voxel BPND estimates from Logan analysis and RPM2. Results: Both the simulated and human data show that HYPR-LR-FC overestimates BPND values in regions of high [11C]-PIB uptake. HYPR-LR-MC virtually eliminates this bias. Both implementations of HYPR-LR reduce variance in the parametric images generated with both Logan analysis and RPM2, and HYPR-LR-FC provides a greater reduction in variance. This reduction in variance nearly eliminates the noise-dependent Logan bias. The variance reduction is greater for the Logan method, particularly for HYPR-LR-MC, and the variance in the resulting Logan images is comparable to that in the RPM2 images. HYPR-LR processing compares favorably with spatial smoothing, particularly when the data are analyzed with the Logan method, as it provides a reduction in variance with no loss of spatial resolution. Conclusions: HYPR-LR processing shows significant potential for reducing variance in parametric images, and can eliminate the noise-dependent Logan bias. HYPR-LR-FC processing provides the greatest reduction in variance but introduces a positive bias into the BPND of high-uptake border regions. The proposed method for forming HYPR composite images, HYPR-LR-MC, eliminates this bias at the cost of less variance reduction.

Systematic sampling is frequently used in surveys, because of its ease of implementation and its design efficiency. An important drawback of systematic sampling, however, is that no direct estimator of the design variance is available. We describe a new estimator of the model-based expectation of the design variance, under a non-parametric model for the population. The non-parametric model is sufficiently flexible that it can be expected to hold at least approximately in many situations with continuous auxiliary variables observed at the population level. We prove the model consistency of the estimator for both the anticipated variance and the design variance under a non-parametric model with a univariate covariate. The broad applicability of the approach is demonstrated on a dataset from a forestry survey.

Purpose: Power spectral analysis in radiographic images is conventionally performed using a windowed overlapping averaging periodogram. This study describes an alternative approach using a multitaper technique and compares its performance with that of the standard method. This tool will be valuable in power spectrum estimation of images, whose content deviates significantly from uniform white noise. The performance of the multitaper approach will be evaluated in terms of spectral stability, variance reduction, bias, and frequency precision. The ultimate goal is the development of a useful tool for image quality assurance. Methods: A multitaper approach uses successive data windows of increasing order. This mitigates spectral leakage allowing one to calculate a reduced-variance power spectrum. The multitaper approach will be compared with the conventional power spectrum method in several typical situations, including the noise power spectra (NPS) measurements of simulated projection images of a uniform phantom, NPS measurement of real detectorimages of a uniform phantom for two clinical digital mammographysystems, and the estimation of the anatomic noise in mammographicimages (simulated images and clinical mammograms). Results: Examination of spectrum variance versus frequency resolution and bias indicates that the multitaper approach is superior to the conventional single taper methods in the prevention of spectrum leakage and variance reduction. More than four times finer frequency precision can be achieved with equivalent or less variance and bias. Conclusions: Without any shortening of the image data length, the bias is smaller and the frequency resolution is higher with the multitaper method, and the need to compromise in the choice of regions of interest size to balance between the reduction of variance and the loss of frequency resolution is largely eliminated.

The CEARXRF GUI-Based Monte Carlo–Library Least-Squares (MCLLS) Code is demonstrated with results from a micro-focused EDXRF analyzer, which can be used to calculate elemental weight fractions in metal alloys or rock samples accurately by library least-squares regression of the measured X-ray spectrum with computer-generated elemental library spectra. An elemental stratified sampling variance reduction technique has been implemented in the CEARXRF5 code, which equalizes the statistical precision of the elemental libraries within the measured sample independent of the relative elemental amounts that are present. Also, an improved Si(Li) detector response function (DRF) has been obtained for micro-focused X-ray fluorescence (XRF) analyzers, and the DRF parameters are obtained based on regression from pure elemental experimental spectra. It is demonstrated that the resulting MCLLS approach can greatly improve the accuracy of elemental XRF analysis results. Copyright © 2011 John Wiley & Sons, Ltd.

Stratification is common in clinical trials because it can reduce the variance of the estimated treatment effect. The traditional demonstration of variance reduction relies on the assumption of stratum sizes being fixed quantities. However, in practice, to speed up enrollment, and to obtain a study population with a similar distribution as the overall population, the stratum sizes are allowed to vary. Under the condition that the total sample size is fixed and that the stratum sizes have a multinomial distribution, the criterion changes for achieving a reduction in variance. The relationship between the stratified and unstratified variances is established and shown to be approximately the same for prestratified and post-stratified trials. It is demonstrated why stratification may actually increase the variance compared with no stratification even when the mean square error is reduced on account of stratification. Data from a real clinical trial will be used for illustration. The benefit attributed to stratification needs to be re-examined in light of the findings presented, particularly given its widespread use. Copyright © 2011 John Wiley & Sons, Ltd.

Summary In spatial surveys for estimating the density of objects in a survey region, systematic designs will generally yield lower variance than random designs. However, estimating the systematic variance is well known to be a difficult problem. Existing methods tend to overestimate the variance, so although the variance is genuinely reduced, it is over-reported, and the gain from the more efficient design is lost. The current approaches to estimating a systematic variance for spatial surveys are to approximate the systematic design by a random design, or approximate it by a stratified design. Previous work has shown that approximation by a random design can perform very poorly, while approximation by a stratified design is an improvement but can still be severely biased in some situations. We develop a new estimator based on modeling the encounter process over space. The new “striplet” estimator has negligible bias and excellent precision in a wide range of simulation scenarios, including strip-sampling, distance-sampling, and quadrat-sampling surveys, and including populations that are highly trended or have strong aggregation of objects. We apply the new estimator to survey data for the spotted hyena (Crocuta crocuta) in the Serengeti National Park, Tanzania, and find that the reported coefficient of variation for estimated density is 20% using approximation by a random design, 17% using approximation by a stratified design, and 11% using the new striplet estimator. This large reduction in reported variance is verified by simulation.

This study investigates the hedging effectiveness of a dynamic moving-window OLS hedging model, formed using wavelet decomposed time-series. The wavelet transform is applied to calculate the appropriate dynamic minimum-variance hedge ratio for various hedging horizons for a number of assets. The effectiveness of the dynamic multiscale hedging strategy is then tested, both in- and out-of-sample, using standard variance reduction and expanded to include a downside risk metric, the scale-dependent Value-at-Risk. Measured using variance reduction, the effectiveness converges to one at longer scales, while a measure of VaR reduction indicates a portion of residual risk remains at all scales. Analysis of the hedge portfolio distributions indicate that this unhedged tail risk is related to excess portfolio kurtosis found at all scales.

A novel technique for estimating the optical fibre PPM frame phase and eliminating the pattern dependent jitter is proposed while practical implementations and a mathematical characterisation for the technique are reported. Use is made of naturally occurring sequences thus avoiding the sensitivity and bit rate penalties associated with the previous methods. Tracking additional sequences is demonstrated and shown to be beneficial resulting in a frame rate discrete component enhancement of 10.8 dB and timing variance reduction from 12 × 10−3rad2 to 3.6 × 10−3rod2. Utilising the systematic jitter rejection method proposed resulted in a measured timing variance reduction from 3.6 × 10−3rad2 to 4.2 × 10−5rod2. The limit is imposed by the PLL performance while good correlation is depicted with the theoretical model.

Variance reduction ratio (VRR) is generally considered as an important index in characterizing the continuous powder mixing. Although the capacity of the mixer to smooth out feeder fluctuations can be expressed by the VRR, few studies are performed quantitatively in this area. The feeder effects are investigated on the solid mixer through the Fourier series analysis. The VRR is deduced quantitatively using the Fourier series of the feed rate variability and the residence time distribution (RTD), which facilitate the explicit decomposition of VRR into intensities of different frequency components. It provides a novel model to determine whether the integrated feeder-mixer system satisfies specific solid mixing performance criteria, and provides guidelines of system improvement. © 2010 American Institute of Chemical Engineers AIChE J, 2011

Bollerslev's (1990, Review of Economics and Statistics, 52, 5–59) constant conditional correlation and Engle's (2002, Journal of Business & Economic Statistics, 20, 339–350) dynamic conditional correlation (DCC) bivariate generalized autoregressive conditional heteroskedasticity (BGARCH) models are usually used to estimate time-varying hedge ratios. In this study, we extend the above model to more flexible ones to analyze the behavior of the optimal conditional hedge ratio based on two (BGARCH) models: (i) adopting more flexible bivariate density functions such as a bivariate skewed-t density function; (ii) considering asymmetric individual conditional variance equations; and (iii) incorporating asymmetry in the conditional correlation equation for the DCC-based model. Hedging performance in terms of variance reduction and also value at risk and expected shortfall of the hedged portfolio are also conducted. Using daily data of the spot and futures returns of corn and soybeans we find asymmetric and flexible density specifications help increase the goodness-of-fit of the estimated models, but do not guarantee higher hedging performance. We also find that there is an inverse relationship between the variance of hedge ratios and hedging effectiveness. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:71–99, 2010

Two forced detection (FD) variance reduction Monte Carlo algorithms for image simulations of tissue-embedded objects with matched refractive index are presented. The principle of the algorithms is to force a fraction of the photon weight to the detector at each and every scattering event. The fractional weight is given by the probability for the photon to reach the detector without further interactions. Two imaging setups are applied to a tissue model including blood vessels, where the ID algorithms produce identical results as traditional brute force simulations, while being accelerated with two orders of magnitude. Extending the methods to include refraction mismatches is discussed. The principle of forced detection; a part of the photon weight. based on the probability of reaching the detector without further interactions, is forced to the detector at each and every scattering event. This is the pre-peer reviewed version of the following article:Ingemar Fredriksson, Marcus Larsson and Tomas Strömberg, Forced detection Monte Carlo algorithms for accelerated blood vessel image simulations, 2009, JOURNAL OF BIOPHOTONICS, (2), 3, 178-184.which has been published in final form at: http://dx.doi.org/10.1002/jbio.200810048Copyright: Wiley-Blackwell

We propose new control variates for variance reduction in estimation of mean values using the Metropolis–Hastings algorithm. Traditionally, states that are rejected in the Metropolis–Hastings algorithm are simply ignored, which intuitively seems to be a waste of information. We present a setting for construction of zero mean control variates for general target and proposal distributions and develop ideas for the standard Metropolis–Hastings and reversible jump algorithms. We give results for three simulation examples. We get best results for variates that are functions of the current state x and the proposal y, but we also consider variates that in addition are functions of the Metropolis–Hastings acceptance/rejection decision. The variance reduction achieved varies depending on the target distribution and proposal mechanisms used. In simulation experiments, we typically achieve relative variance reductions between 15% and 35%.

The Monte Carlo code DOSXYZnrc is a valuable instrument for calculating absorbed dose within a three-dimensional Cartesian geometry. DOSXYZnrc includes several variance reduction techniques used to increase the efficiency of the Monte Carlo calculation. One such technique is HOWFARLESS which is used to increase the efficiency of beam commissioning calculations in homogeneous phantoms. The authors present an enhanced version of HOWFARLESS which extends the application to include phantoms inhomogeneous in one dimension. When the enhanced HOWFARLESS was used, efficiency increases as high as 14 times were observed without any loss in dose accuracy. The efficiency gains of an enhanced HOWFARLESS simulation was found to be dependent on both slab geometry and slab density. As the number of two-dimensional voxel layers per slab increases, so does the efficiency gain. Also, as the mass density of a slab is decreased, the efficiency gains increase.

In many scientific studies, information that is not easily translated into covariates is ignored in the analysis. However, this type of information may significantly improve inference. In this research, we apply the idea of judgment post-stratification to utilize such information. Specifically, we consider experiments that are conducted under a completely randomized design. Sets of experimental units are formed, and the units in a set are ranked. Estimation is performed conditional on the sets and ranks. We propose a new estimator for a treatment contrast. We improve the new estimator by Rao-Blackwellization. Asymptotic distribution theory and corresponding inferential procedures for both estimators are developed. Simulation studies quantify the superiority of the new estimators and show their desirable properties for small and moderate sample sizes. The impact of the new techniques is illustrated with data from a clinical trial.

This paper presents a novel method that effectively combines both control variates and importance sampling in a sequential Monte Carlo context. The radiance estimates computed during the rendering process are cached in a 5D adaptive hierarchical structure that defines dynamic predicate functions for both variance reduction techniques and guarantees well-behaved PDFs, yielding continually increasing efficiencies thanks to a marginal computational overhead. While remaining unbiased, the technique is effective within a single pass as both estimation and caching are done online, exploiting the coherency in illumination while being independent of the actual scene rep- resentation. The method is relatively easy to implement and to tune via a single parameter, and we demonstrate its practical benefits with important gains in convergence rate and competitive results with state of the art techniques.