Statistical Sampling Approach Research Articles

Constrained Hybrid Monte Carlo Sampling Made Simple for Chemical Reaction Simulations.

Most electrochemical reactions should be studied under a grand canonical ensemble condition with a constant potential and/or a constant pH value. Free energy profiles provide key insights into understanding the reaction mechanisms. However, many molecular dynamics (MD)-based theoretical studies for electrochemical reactions did not employ an exact grand canonical ensemble sampling scheme for the free energy calculations, partially due to the issues of discontinuous trajectories induced by the particle-number variations during MD simulations. An alternative statistical sampling approach, the Monte Carlo (MC) method, is naturally appropriate for the open-system simulations if we focus on the thermodynamic properties. An advanced MC scheme, the hybrid Monte Carlo (HMC) method, which can efficiently sample the configurations of a system with large degrees of freedom, however, has limitations in the constrained-sampling applications. In this work, we propose an adjusted constrained HMC method to compute free energy profiles using the thermodynamic integration (TI) method. The key idea of the method for handling the constraint in TI is to integrate the reaction coordinate and sample the rest degrees of freedom by two types of MC schemes, the HMC scheme and the Metropolis algorithm with unbiased trials (M(RT)2-UB). We test the proposed method on three different systems involving two kinds of reaction coordinates, which are the distance between two particles and the difference of particles' distances, and compare the results to those generated by the constrained M(RT)2-UB method serving as benchmarks. We show that our proposed method has the advantages of high sampling efficiency and convenience of implementation, and the accuracy is justified as well. In addition, we show in the third test system that the proposed constrained HMC method can be combined with the path integral method to consider the nuclear quantum effects, indicating a broader application scenario of the sampling method reported in this work.

Benchmarking laser scanning and terrestrial photogrammetry to extract forest inventory parameters in a complex temperate forest

National forest inventories (NFI) are important for the assessment of the state and development of forests. Traditional NFIs often rely on statistical sampling approaches as well as expert assessment which may suffer from observer bias and may lack robustness for time series analysis. Over the course of the last decade, close-range remote sensing techniques such as terrestrial and mobile laser scanning became ever more established for the assessment of three-dimensional (3D) forest structure. With the ongoing trend to make the systems smaller, easier to use and more efficient, the pathway is being opened for an operational inclusion of such devices within the framework of an NFI to support the traditional field assessment. Close-range remote sensing could potentially speed up field inventory work as well as increase the area in which certain parameters are assessed. Benchmarks are needed to evaluate the performance of different close-range remote sensing devices and approaches, both in terms of efficiency as well as accuracy. In this study we evaluate the performance of two terrestrial (TLS), one handheld mobile (PLS) and two drone based (UAVLS) laser scanning systems to detect trees and extract the diameter at breast height (DBH) in three plots with a steep gradient in tree and understorey vegetation density. As a novelty, we also tested the acquisition of 3D point-clouds using a low-cost action camera (GoPro) in conjunction with the Structure from Motion (SfM) technique and compared its performance with those of the more costly LiDAR devices. Among the many parameters evaluated in traditional NFIs, the focus of the performance evaluation of this study is set on the automatic tree detection and DBH extraction. The results showed that TLS delivers the highest tree detection rate (TDR) of up to 94.6% under leaf-off and up to 82% under leaf-on conditions and a relative RMSE (rRMSE) for the DBH extraction between 2.5 and 9%, depending on the undergrowth complexity. The tested PLS system (leaf-on) achieved a TDR of up to 80% with an rRMSE between 3.7 and 5.8%. The tested UAVLS systems showed lowest TDR of less than 77% under leaf-off and less than 37% under leaf-on conditions. The novel GoPro approach achieved a TDR of up to 53% under leaf-on conditions. The reduced TDR can be explained by the reduced area coverage due to the chosen circular acquisition path taken with the GoPro approach. The DBH extraction performance on the other hand is comparable to those of the LiDAR devices with an rRMSE between 2 and 9%. Further benchmarks are needed in order to fully assess the applicability of these systems in the framework of an NFI. Especially the robustness under varying forest conditions (seasonality) and over a broader range of forest types and canopy structure has to be evaluated.

Passive sampling in reproducing kernel Hilbert spaces using leverage scores

This paper deals with the selection of the training dataset in kernel-based methods for function reconstruction, with a focus on kernel ridge regression. A functional analysis is performed which, in the absence of noise, links the optimal sampling distribution to the one minimizing the difference between the kernel matrix and its low-rank Nyström approximation. From this standpoint, a statistical passive sampling approach is derived which uses the leverage scores of the columns of the kernel matrix to design a sampling distribution that minimizes an upper bound of the risk function. The proposed approach constitutes a passive method, able to select the optimal subset of training samples using only information provided by the input set and the kernel, but without needing to know the values of the function to be approximated. Furthermore, the proposed approach is backed up by numerical tests on real datasets.

The Early Steps of Molecule-to-Material Conversion in Chemical Vapor Deposition (CVD): A Case Study.

Transition metal complexes with β-diketonate and diamine ligands are valuable precursors for chemical vapor deposition (CVD) of metal oxide nanomaterials, but the metal-ligand bond dissociation mechanism on the growth surface is not yet clarified in detail. We address this question by density functional theory (DFT) and ab initio molecular dynamics (AIMD) in combination with the Blue Moon (BM) statistical sampling approach. AIMD simulations of the Zn β-diketonate-diamine complex Zn(hfa)2TMEDA (hfa = 1,1,1,5,5,5-hexafluoro-2,4-pentanedionate; TMEDA = N,N,N′,N′-tetramethylethylenediamine), an amenable precursor for the CVD of ZnO nanosystems, show that rolling diffusion of this precursor at 500 K on a hydroxylated silica slab leads to an octahedral-to-square pyramidal rearrangement of its molecular geometry. The free energy profile of the octahedral-to-square pyramidal conversion indicates that the process barrier (5.8 kcal/mol) is of the order of magnitude of the thermal energy at the operating temperature. The formation of hydrogen bonds with surface hydroxyl groups plays a key role in aiding the dissociation of a Zn-O bond. In the square-pyramidal complex, the Zn center has a free coordination position, which might promote the interaction with incoming reagents on the deposition surface. These results provide a valuable atomistic insight on the molecule-to-material conversion process which, in perspective, might help to tailor by design the first nucleation stages of the target ZnO-based nanostructures.

Considerations in characterizing real-world data relevance and quality for regulatory purposes: A commentary.

The 21st Century Cures Act of 2016 provided a framework to the US Food and Drug Administration (FDA) to rapidly move treatments to patients.1 The increased acceptability of real‐world data (RWD) sources allows for innovative ways to study products and has the potential to reduce trial costs. Published papers provide guidance regarding data quality issues, reproducibility, and validity assessment.2 Rapid evolvement of electronic health records (EHRs) encourages greater consideration of their use in research.1, 2, 3, 4, 5, 6 For years, the FDA has relied on epidemiological studies of postapproval product safety using RWD5, 6 (eg, administrative claims and EHR) and for device effectiveness studies4; however, regulatory use for evaluating drug effectiveness has been rare. As part of the Prescription Drug User Fee Act (PDUFA VI),3 use of RWD is being considered for potential contributions to evaluating effectiveness and safety of new indications for approved products and to satisfy postapproval study requirements. Recently, the Duke Margolis Center for Health Policy held workshops and issued two paper on this topic.5, 6 The first paper focused on defining RWD as data routinely collected pertinent to patient health status and/or delivery of care, and the use of RWD in regulatory and clinical contexts.5 The second white paper from the October 1, 2018, workshop focused on data relevancy and quality, including cleaning, transforming, and linking RWD to characterize RWD sources as “fit for regulatory purpose.”6 These papers offer a practical “commonsense” high‐level view of primary data and methods considerations for RWD use from a regulatory perspective, facilitating discussion around regulatory uses of RWD within the research community and industry. However, salient points are missing from the papers and the RWD discussions among FDA, researchers, and industry. Here, we provide a commentary on the data considerations discussed in the white papers and highlight pertinent considerations with respect to RWD in the context of whether data are relevant, representative, and robust. 1.1. Data relevance The recent white paper defines data relevance dimensions including representativeness of the population of interest, critical data field availability, accurate linking at the patient level with multiple data sources, and adequate sample size and follow‐up time to demonstrate expected treatment effects.6 Guidance from FDA on how to ensure RWD are fit for purpose and adequate to support regulatory decisions would be helpful on each dimension. Determining if RWD is fit for regulatory purpose is a “contextual exercise” where the specific research question, regulatory use, and data characteristics drive what meaningful conclusions can be drawn.6 Covariates may be critical for one research question but not another. Exposures and outcomes should be well defined when part of the research question but may not be critical for natural history studies. There is no “one‐size‐fits‐all” approach, and critical data components should be evaluated for each research question and regulatory use.7 A framework is needed to guide choice and evaluation of critical data elements for specific research questions for regulatory use. Representativeness of the population of interest is gauged in many ways. Recent FDA guidance on Patient Focused Drug Development suggests a statistical sampling approach be used to obtain patient experience data representative of the target population.8 However, most US real‐world databases use administrative claims or EHR for patients seeking medical attention. These RWD sources should be considered broadly representative of the population eligible for using most, if not all, new products and services. “Representativeness” should be assessed broadly in the context of likely product users with some diversity in geography, health status, and health care system as appropriate for the specific research question and regulatory context. While data linkage is likely to limit the eligible sample, it may be needed to increase the informative nature of RWD, especially with increasing evaluations to support precision medicine. Sample size should be derived based on anticipated treatment effects for studies of treatment effectiveness or safety, whether comparative or not, to ensure appropriate precision of estimates. For rare diseases, there should be flexibility given data sparseness worldwide, as indicated in the FDA guidance on rare disease.8 Additional guidance would be useful regarding how “accurate linking” should be assessed since linking 100% of patients with administrative claims and EHR is impractical. Would FDA accept limited linked data if it was supplemental to cruder variables in the full dataset? Would a subset of 60% be adequate? In the context of probabilistic linkage, what level of certainty would constitute adequate linkage? Salience of linkable individuals to the specific research question should be considered in this determination and pre‐specified sensitivity analyses should help assess robustness of results and conclusions.9, 10

Uncertainty quantification for radio interferometric imaging: II. MAP estimation

Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Statistical sampling approaches to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC) sampling, can in principle recover the full posterior distribution of the image, from which uncertainties can then be quantified. However, for massive data sizes, like those anticipated from the Square Kilometre Array (SKA), it will be difficult if not impossible to apply any MCMC technique due to its inherent computational cost. We formulate Bayesian inference problems with sparsity-promoting priors (motivated by compressive sensing), for which we recover maximum a posteriori (MAP) point estimators of radio interferometric images by convex optimisation. Exploiting recent developments in the theory of probability concentration, we quantify uncertainties by post-processing the recovered MAP estimate. Three strategies to quantify uncertainties are developed: (i) highest posterior density credible regions; (ii) local credible intervals (cf. error bars) for individual pixels and superpixels; and (iii) hypothesis testing of image structure. These forms of uncertainty quantification provide rich information for analysing radio interferometric observations in a statistically robust manner. Our MAP-based methods are approximately $10^5$ times faster computationally than state-of-the-art MCMC methods and, in addition, support highly distributed and parallelised algorithmic structures. For the first time, our MAP-based techniques provide a means of quantifying uncertainties for radio interferometric imaging for realistic data volumes and practical use, and scale to the emerging big-data era of radio astronomy.

Uncertainty quantification for radio interferometric imaging – I. Proximal MCMC methods

Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Since radio interferometric imaging requires solving a high-dimensional, ill-posed inverse problem, uncertainty quantification is difficult but also critical to the accurate scientific interpretation of radio observations. Statistical sampling approaches to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC) sampling, can in principle recover the full posterior distribution of the image, from which uncertainties can then be quantified. However, traditional high-dimensional sampling methods are generally limited to smooth (e.g. Gaussian) priors and cannot be used with sparsity-promoting priors. Sparse priors, motivated by the theory of compressive sensing, have been shown to be highly effective for radio interferometric imaging. In this article proximal MCMC methods are developed for radio interferometric imaging, leveraging proximal calculus to support non-differential priors, such as sparse priors, in a Bayesian framework. Furthermore, three strategies to quantify uncertainties using the recovered posterior distribution are developed: (i) local (pixel-wise) credible intervals to provide error bars for each individual pixel; (ii) highest posterior density credible regions; and (iii) hypothesis testing of image structure. These forms of uncertainty quantification provide rich information for analysing radio interferometric observations in a statistically robust manner.

Cloud Cover Assessment for Operational Crop Monitoring Systems in Tropical Areas

The potential of optical remote sensing data to identify, map and monitor croplands is well recognized. However, clouds strongly limit the usefulness of optical imagery for these applications. This paper aims at assessing cloud cover conditions over four states in the tropical and sub-tropical Center-South region of Brazil to guide the development of an appropriate agricultural monitoring system based on Landsat-like imagery. Cloudiness was assessed during overlapping four months periods to match the typical length of crop cycles in the study area. The percentage of clear sky occurrence was computed from the 1 km resolution MODIS Cloud Mask product (MOD35) considering 14 years of data between July 2000 and June 2014. Results showed high seasonality of cloud occurrence within the crop year with strong variations across the study area. The maximum seasonality was observed for the two states in the northern part of the study area (i.e., the ones closer to the Equator line), which also presented the lowest averaged values (15%) of clear sky occurrence during the main (summer) cropping period (November to February). In these locations, optical data faces severe constraints for mapping summer crops. On the other hand, relatively favorable conditions were found in the southern part of the study region. In the South, clear sky values of around 45% were found and no significant clear sky seasonality was observed. Results underpin the challenges to implement an operational crop monitoring system based solely on optical remote sensing imagery in tropical and sub-tropical regions, in particular if short-cycle crops have to be monitored during the cloudy summer months. To cope with cloudiness issues, we recommend the use of new systems with higher repetition rates such as Sentinel-2. For local studies, Unmanned Aircraft Vehicles (UAVs) might be used to augment the observing capability. Multi-sensor approaches combining optical and microwave data can be another option. In cases where wall-to-wall maps are not mandatory, statistical sampling approaches might also be a suitable alternative for obtaining useful crop area information.

Understanding Anharmonicity in fcc Materials: From its Origin to ab initio Strategies beyond the Quasiharmonic Approximation.

We derive the Gibbs energy including the anharmonic contribution due to phonon-phonon interactions for an extensive set of unary fcc metals (Al, Ag, Au, Cu, Ir, Ni, Pb, Pd, Pt, Rh) by combining density-functional-theory (DFT) calculations with efficient statistical sampling approaches. We show that the anharmonicity of the macroscopic system can be traced back to the anharmonicity in local pairwise interactions. Using this insight, we derive and benchmark a highly efficient approach which allows the computation of anharmonic contributions using a few T=0 K DFT calculations only.

Statistical sampling approaches for soil monitoring

SummaryThis paper describes three statistical sampling approaches for regional soil monitoring, a design‐based, a model‐based and a hybrid approach. In the model‐based approach a space‐time model is exploited to predict global statistical parameters of interest such as the space‐time mean. In the hybrid approach this model is a time‐series model of the spatial means. In the design‐based approach no model is used: estimates are model‐free. Full design‐based inference requires that both sampling locations and times are selected by probability sampling, whereas the hybrid approach requires probability sampling of locations only. In a case study on soil eutrophication and acidification, a rotational panel design was implemented with probability sampling of locations and non‐probability sampling of times. The hybrid and model‐based predictions of the space‐time means and trend of the mean for pH and ammonium at three depths in the soil profile were very similar. For pH the standard errors of the space‐time means were about equal, but for ammonium the full model‐based predictor was more precise than the hybrid predictor. For soil monitoring I advocate the selection of sampling locations by probability sampling so that the statistical inference approach is flexible. Selecting locations by a self‐weighting probability sampling design ensures that the model‐based predictor is not affected by selection bias.

SU‐E‐J‐62: Estimating Plausible Treatment Course Dose Distributions by Accounting for Registration Uncertainty and Organ Motion

Purpose:Dose accumulation following deformable image registration (DIR) is challenging. In this study, we used a statistical sampling approach, which takes into account both DIR uncertainties and patient‐specific organ motion, to study the distribution of possible true dose distributions.Methods:The study included ten patients (six CT scans/patient) treated with radiotherapy for prostate cancer. For each patient, the planned dose was re‐calculated on the repeated geometries, following rigid registration based on fiducial markers. The dose re‐calculated on the first CT served as our snapshot dose distribution (D1) and the average of the first five repeat scans as our treatment course reference dose distribution (Dref). Patient‐specific motion and DIR‐uncertainties, at each voxel in CT1, were assessed using a previously developed DIR performance measure, the distance discordance metric (DDM). To sample the distribution of possible true, predicted dose distributions (Dpred), we resampled D1 by perturbing the location of each voxel with the corresponding DDM. The three dose distribution approaches are compared for the rectum and the bladder.Results:The bladder generalized equivalent uniform dose (gEUD) from the averaged Dpred was closer to the gEUDref than to the gEUD1 (difference: 0.6 vs. 1.0 Gy). For both structures, the gEUDpred was higher than the gEUDref, and significantly higher (p≤0.05) for the rectum (average: 50.8 Gy vs. 48.0 Gy).Conclusion:We have shown that the bladder gEUD values resulting from our DIR‐uncertainty inclusive dose sampling approach, Dpred, were closer to the gEUD from Dref than the gEUD values from D1. For the rectum, gEUDpred overestimated gEUDref. Theoretically however, gEUDpred values, sampled from DDM uncertainties are more representative of dose uncertainties.

Validation of Geant4-Based Radioactive Decay Simulation

Radioactive decays are of concern in a wide variety of applications using Monte-Carlo simulations. In order to properly estimate the quality of such simulations, knowledge of the accuracy of the decay simulation is required. We present a validation of the original Geant4 Radioactive Decay Module, which uses a per-decay sampling approach, and of an extended package for Geant4-based simulation of radioactive decays, which, in addition to being able to use a refactored per-decay sampling, is capable of using a statistical sampling approach. The validation is based on measurements of calibration isotope sources using a high purity Germanium (HPGe) detector; no calibration of the simulation is performed. For the considered validation experiment equivalent simulation accuracy can be achieved with per-decay and statistical sampling.

A statistical sampling approach for measurement of fracture toughness parameters in a 4330 steel by 3-D femtosecond laser-based tomography

A new approach using statistically random material volume sampling has been developed to model the variability of fracture toughnesses in steels. A recently developed femtosecond laser-based serial sectioning (FSLSS) technique was utilized to collect 3-D datasets showing the distribution of titanium nitride (TiN) phases in a 4330 high strength steel. Random volumes were sampled from widely spaced regions within the bulk steel specimen. Plastic zone sized volumes were sampled from the 3-D reconstructions to produce statistically representative volume elements containing TiN particles. Fracture toughness was calculated for 48 different plastic zone sized volumes using two different toughness models. Weibull analysis was performed to relate the modeled fracture toughness to the probability of occurrence. Variability in the fracture toughness gave a Weibull modulus of m=1.4–1.5, similar to the variability measured in 22 bulk sample specimens analyzed by Ruggieri et al. for a similar steel.

Sampling of illicit drugs for quantitative analysis. Part I: Heterogeneity study of illicit drugs in Europe

Sampling of illicit drugs for qualitative and quantitative analysis would normally be considered as routine and comparable tasks in forensic drugs laboratories and previously similar statistical sampling approaches have been applied. However, we believe that two different sampling approaches, based on two different theoretical and statistical backgrounds are more appropriate. Furthermore the application of the qualitative sampling approach can be impractical for quantitative sampling as it could generate many analytical samples from a single seizure. In some countries the purity of the illicit drug in a seizure may affect the criminal sentence and therefore, reliable results for quantitative analysis are crucial.It was decided to investigate a new approach, which although incorporating some statistics also took account of our background knowledge about the composition of the drugs we were analysing. The ultimate goal was to produce recommendations for a practical sampling plan for quantitative analysis. It was found that the two key factors which had a significant effect on obtaining a representative analytical sample from a bulk seizure were the heterogeneity of the drug powder and the particle sizes of its components. This article concentrates on drug heterogeneity. Particle size effects will be addressed in part II of this study.A sampling plan was devised for a range of drug seizure types and asked ENFSI member laboratories to use it when analysing real drug seizures to provide heterogeneity data for the most common illicit drugs (heroin, cocaine, amphetamine, MDMA and cannabis (herbal and resin)). It was found that for routine quantitative drugs analysis, the sampling problems caused by heterogeneity can be solved by using an incremental sampling protocol. Furthermore, the number of increments that need to be taken for a particular drug is dependent on the relative standard deviation (RSD) required by an individual laboratory and the analytical method that they employ. A 1g increment size was found to be suitable for powdered drugs and cannabis resin. However, 1g increments were not suitable for herbal cannabis, because of particle size issues. Sampling of herbal cannabis will be addressed in Part II of this study. Recommendations for a sampling plan, based on the heterogeneity and particle size of specific drugs seizures in casework will be discussed in Part III of this study.

Evaluating the effect of disturbed ensemble distributions on SCFG based statistical sampling of RNA secondary structures.

BackgroundOver the past years, statistical and Bayesian approaches have become increasingly appreciated to address the long-standing problem of computational RNA structure prediction. Recently, a novel probabilistic method for the prediction of RNA secondary structures from a single sequence has been studied which is based on generating statistically representative and reproducible samples of the entire ensemble of feasible structures for a particular input sequence. This method samples the possible foldings from a distribution implied by a sophisticated (traditional or length-dependent) stochastic context-free grammar (SCFG) that mirrors the standard thermodynamic model applied in modern physics-based prediction algorithms. Specifically, that grammar represents an exact probabilistic counterpart to the energy model underlying the Sfold software, which employs a sampling extension of the partition function (PF) approach to produce statistically representative subsets of the Boltzmann-weighted ensemble. Although both sampling approaches have the same worst-case time and space complexities, it has been indicated that they differ in performance (both with respect to prediction accuracy and quality of generated samples), where neither of these two competing approaches generally outperforms the other.ResultsIn this work, we will consider the SCFG based approach in order to perform an analysis on how the quality of generated sample sets and the corresponding prediction accuracy changes when different degrees of disturbances are incorporated into the needed sampling probabilities. This is motivated by the fact that if the results prove to be resistant to large errors on the distinct sampling probabilities (compared to the exact ones), then it will be an indication that these probabilities do not need to be computed exactly, but it may be sufficient and more efficient to approximate them. Thus, it might then be possible to decrease the worst-case time requirements of such an SCFG based sampling method without significant accuracy losses. If, on the other hand, the quality of sampled structures can be observed to strongly react to slight disturbances, there is little hope for improving the complexity by heuristic procedures. We hence provide a reliable test for the hypothesis that a heuristic method could be implemented to improve the time scaling of RNA secondary structure prediction in the worst-case – without sacrificing much of the accuracy of the results.ConclusionsOur experiments indicate that absolute errors generally lead to the generation of useless sample sets, whereas relative errors seem to have only small negative impact on both the predictive accuracy and the overall quality of resulting structure samples. Based on these observations, we present some useful ideas for developing a time-reduced sampling method guaranteeing an acceptable predictive accuracy. We also discuss some inherent drawbacks that arise in the context of approximation. The key results of this paper are crucial for the design of an efficient and competitive heuristic prediction method based on the increasingly accepted and attractive statistical sampling approach. This has indeed been indicated by the construction of prototype algorithms.

An Optimization-Based Sampling Scheme for Phylogenetic Trees

Much modern work in phylogenetics depends on statistical sampling approaches to phylogeny construction to estimate probability distributions of possible trees for any given input data set. Our theoretical understanding of sampling approaches to phylogenetics remains far less developed than that for optimization approaches, however, particularly with regard to the number of sampling steps needed to produce accurate samples of tree partition functions. Despite the many advantages in principle of being able to sample trees from sophisticated probabilistic models, we have little theoretical basis for concluding that the prevailing sampling approaches do in fact yield accurate samples from those models within realistic numbers of steps. We propose a novel approach to phylogenetic sampling intended to be both efficient in practice and more amenable to theoretical analysis than the prevailing methods. The method depends on replacing the standard tree rearrangement moves with an alternative Markov model in which one solves a theoretically hard but practically tractable optimization problem on each step of sampling. The resulting method can be applied to a broad range of standard probability models, yielding practical algorithms for efficient sampling and rigorous proofs of accurate sampling for heated versions of some important special cases. We demonstrate the efficiency and versatility of the method by an analysis of uncertainty in tree inference over varying input sizes. In addition to providing a new practical method for phylogenetic sampling, the technique is likely to prove applicable to many similar problems involving sampling over combinatorial objects weighted by a likelihood model.

Data driven surrogate-based optimization in the problem solving environment WBCSim

Large scale, multidisciplinary, engineering designs are always difficult due to the complexity and dimensionality of these problems. Direct coupling between the analysis codes and the optimization routines can be prohibitively time consuming due to the complexity of the underlying simulation codes. One way of tackling this problem is by constructing computationally cheap(er) approximations of the expensive simulations that mimic the behavior of the simulation model as closely as possible. This paper presents a data driven, surrogate-based optimization algorithm that uses a trust region-based sequential approximate optimization (SAO) framework and a statistical sampling approach based on design of experiment (DOE) arrays. The algorithm is implemented using techniques from two packages—SURFPACK and SHEPPACK that provide a collection of approximation algorithms to build the surrogates and three different DOE techniques—full factorial (FF), Latin hypercube sampling, and central composite design—are used to train the surrogates. The results are compared with the optimization results obtained by directly coupling an optimizer with the simulation code. The biggest concern in using the SAO framework based on statistical sampling is the generation of the required database. As the number of design variables grows, the computational cost of generating the required database grows rapidly. A data driven approach is proposed to tackle this situation, where the trick is to run the expensive simulation if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations are performed. Results show that the proposed methodology dramatically reduces the total number of calls to the expensive simulation runs during the optimization process.

INFOCARB: A regional scale forest carbon inventory (Provincia Autonoma di Trento, Southern Italian Alps)

The aim of this inventory (acronym: INFOCARB) was to measure the organic carbon stored in the forest ecosystems of the Trento region (Provincia Autonoma di Trento, Northern Italy) in both above- and belowground pools, according to the Kyoto protocol and IPCC requirements. A total of 150 forest sampling points were selected on the entire regional area (6206 km 2) with a statistical sampling approach, based on the timber volume as a proxy variable for a stratified sampling. Each sampling point was located with a GPS receiver and a 600 m 2 circular plot was delimited around each point. Inside the plots, the biomass of trees, shrubs and herbaceous vegetation was measured, while litter was collected in systematically placed subplots. Topsoil (down to 30 cm depth) was sampled with the excavation method on three systematically located pits, to determine the organic carbon content, the bulk density and the volume occupied by stones and roots. The inventory estimated the regional total carbon content of the forests as 71.9 ± 5.2 Tg C, with an average carbon density of 207.01 ± 14.5 Mg C ha −1. The aboveground biomass and the soil had a similar carbon content, 43.2% and 44.6% of the total ecosystem carbon, respectively, whereas the root systems and the litter accounted for 9.6% and 2.6%, respectively. Due to the high inter-site variability, only weak statistical relationships were found between the soil carbon content and main ecosystem and climatic variables. However, when dividing the plots into different species-dominated forests, the beech sites differed significantly from the conifer sites in the carbon stock and the C/N ratio in the soil organic layers.

Evaluation of photovoltaic modules based on sampling inspection using smoothed empirical quantiles

AbstractAn important issue for end users and distributors of photovoltaic (PV) modules is the inspection of the power output specification of a shipment. The question is whether or not the modules satisfy the specifications given in the data sheet, namely the nominal power output under standard test conditions† relative to the power output tolerance. Since collecting control measurements of all modules is usually unrealistic, decisions have to be based on random samples. In many cases, one has access to flash data tables of final output power measurements (flash data) from the producer. We propose to rely on the statistical acceptance sampling approach as an objective decision framework, which takes into account both the end users and producers risk of a false decision. A practical solution to the problem is discussed which has been recently found by the authors. The solution consists of estimates of the required optimal sample size and the associated critical value where the estimation uses the information contained in the additional flash data. We propose and examine an improved solution which yields even more reliable estimated sampling plans as substantiated by a Monte Carlo study. This is achieved by employing advanced statistical estimation techniques. Copyright © 2009 John Wiley & Sons, Ltd.

Software for generating liability distributions for pedigrees conditional on their observed disease states and covariates

For many multifactorial diseases, aetiology is poorly understood. A major research aim is the identification of disease predictors (environmental, biological, and genetic markers). In order to achieve this, a two-stage approach is proposed. The initial or synthesis stage combines observed pedigree data with previous genetic epidemiological research findings, to produce estimates of pedigree members' disease risk and predictions of their disease liability. A further analysis stage uses the latter as inputs to look for associations with potential disease markers. The incorporation of previous research findings into an analysis should lead to power gains. It also allows separate predictions for environmental and genetic liabilities to be generated. This should increase power for detecting disease predictors that are environmental or genetic in nature. Finally, the approach brings pragmatic benefits in terms of data reduction and synthesis, improving comprehensibility, and facilitating the use of existing statistical genetics tools. In this article we present a statistical model and Gibbs sampling approach to generate liability predictions for multifactorial disease for the synthesis stage. We have implemented the approach in a software program. We apply this program to a specimen disease pedigree, and discuss the results produced, comparing its results with those generated under a more naïve model. We also detail simulation studies that validate the software's operation.