Statistical Uncertainty Estimates Research Articles

Statistical Uncertainty Estimation Using Random Forests and Its Application to Drought Forecast

Drought is part of natural climate variability and ranks the first natural disaster in the world. Drought forecasting plays an important role in mitigating impacts on agriculture and water resources. In this study, a drought forecast model based on the random forest method is proposed to predict the time series of monthly standardized precipitation index (SPI). We demonstrate model application by four stations in the Haihe river basin, China. The random‐forest‐ (RF‐) based forecast model has consistently shown better predictive skills than the ARIMA model for both long and short drought forecasting. The confidence intervals derived from the proposed model generally have good coverage, but still tend to be conservative to predict some extreme drought events.

Hybrid and Parallel Domain-Decomposition Methods Development to Enable Monte Carlo for Reactor Analyses

** This paper describes code and methods development at the Oak Ridge National Laboratory focused on enabling high-fidelity, large-scale reactor analyses with Monte Carlo (MC). Current state-of-the-art tools and methods used to perform “real” commercial reactor analyses have several undesirable features, the most significant of which is the non-rigorous spatial decomposition scheme. Monte Carlo methods, which allow detailed and accurate modeling of the full geometry and are considered the “gold standard” for radiation transport solutions, are playing an ever-increasing role in correcting and/or verifying the deterministic, multi-level spatial decomposition methodology in current practice. However, the prohibitive computational requirements associated with obtaining fully converged, system-wide solutions restrict the role of MC to benchmarking deterministic results at a limited number of state-points for a limited number of relevant quantities. The goal of this research is to change this paradigm by enabling direct use of MC for full-core reactor analyses. The most significant of the many technical challenges that must be overcome are the slow, non-uniform convergence of system-wide MC estimates and the memory requirements associated with detailed solutions throughout a reactor (problems involving hundreds of millions of different material and tally regions due to fuel irradiation, temperature distributions, and the needs associated with multi-physics code coupling). To address these challenges, our research has focused on the development and implementation of (1) a novel hybrid deterministic/MC method for determining high-precision fluxes throughout the problem space in k-eigenvalue problems and (2) an efficient MC domain-decomposition (DD) algorithm that partitions the problem phase space onto multiple processors for massively parallel systems, with statistical uncertainty estimation. The hybrid method development is based on an extension of the FW-CADIS method, which attempts to achieve uniform statistical uncertainty throughout a designated problem space. The MC DD development is being implemented in conjunction with the Denovo deterministic radiation transport package to have direct access to the 3-D, massively parallel discrete-ordinates solver (to support the hybrid method) and the associated parallel routines and structure. This paper describes the hybrid method, its implementation, and initial testing results for a realistic 2-D quarter core pressurized-water reactor model and also describes the MC DD algorithm and its implementation.

Geomagnetic field for 0–3 ka: 2. A new series of time‐varying global models

Steadily increasing numbers of archeomagnetic and paleomagnetic data for the Holocene have allowed development of temporally continuous global spherical harmonic models of the geomagnetic field extending present and historical global descriptions of magnetic field evolution. The current work uses various subsets of improved data compilations, details of which are given in a companion paper by Donadini et al. (2009), and minor modifications of standard modeling strategies (using temporally and spatially regularized inversion of the data and cubic spline parameterizations for temporal variations) to produce five models with enhanced spatial and temporal resolution for 0–3 ka. Spurious end effects present in earlier models are eliminated by enforcing large‐scale agreement with the gufm1 historical model for 1650–1990 A.D. and by extending the model range to accommodate data older than 3 ka. Age errors are not considered as a contribution to data uncertainties but are included along with data uncertainties in an investigation of statistical uncertainty estimates for the models using parametric bootstrap resampling techniques. We find common features but also significant differences among the various models, indicating intrinsic uncertainties in global models based on the currently available Holocene data. Model CALS3k.3 based on all available archeomagnetic and sediment data, without a priori quality selection, currently constitutes the best global representation of the past field. The new models have slightly higher dipole moments than our previous models. Virtual axial dipole moments (VADMs) calculated directly from the data are in good agreement with all corresponding model predictions of VADMs. These are always higher than the spherical harmonic dipole moment, indicating the limitations of using VADMs as a measure of geomagnetic dipole moments.

Determining Optimal Population Monitoring for Rare Butterflies

Determining population viability of rare insects depends on precise, unbiased estimates of population size and other demographic parameters. We used data on the endangered St. Francis' satyr butterfly (Neonympha mitchellii francisci) to evaluate 2 approaches (mark-recapture and transect counts) for population analysis of rare butterflies. Mark-recapture analysis provided by far the greatest amount of demographic information, including estimates (and standard errors) of population size, detection, survival, and recruitment probabilities. Mark-recapture analysis can also be used to estimate dispersal and temporal variation in rates, although we did not do this here. Models of seasonal flight phenologies derived from transect counts (Insect Count Analyzer) provided an index of population size and estimates of survival and statistical uncertainty. Pollard-Yates population indices derived from transect counts did not provide estimates of demographic parameters. This index may be highly biased if detection and survival probabilities vary spatially and temporally. In terms of statistical performance, mark-recapture and Pollard-Yates indices were least variable. Mark-recapture estimates were less likely to fail than Insect Count Analyzer, but mark-recapture estimates became less precise as sampling intensity decreased. In general, count-based approaches are less costly and less likely to cause harm to rare insects than mark-recapture. The optimal monitoring approach must reconcile these trade-offs. Thus, mark-recapture should be favored when demographic estimates are needed, when financial resources enable frequent sampling, and when marking does not harm the insect populations. The optimal sampling strategy may use 2 sampling methods together in 1 overall sampling plan: limited mark-recapture sampling to estimate survival and detection probabilities and frequent but less expensive transect counts.

Redshifts of Emission-Line Objects in the Hubble Ultra Deep Field

We present redshifts for 115 emission line objects in the Hubble Ultra Deep Field (HUDF) identified through the GRism ACS Program for Extragalactic Science (GRAPES) project using the slitless grism spectroscopy mode of the ACS Camera on the Hubble Space Telescope (HST). The sample was selected by an emission line search on all extracted 1-dimensional GRAPES spectra. We identify the emission lines using line wavelength ratios where multiple lines are detected in the grism wavelength range (5800A < lambda < 9600A), and using photometric redshift information where multiple lines are unavailable. We then derive redshifts using the identified lines. Our redshifts are accurate to delta(z) = 0.009, based on both statistical uncertainty estimates and comparison with published ground-based spectra. Over 40% of our sample is fainter than typical magnitude limits for ground-based spectroscopy (with i_{AB}>25 mag). Such emission lines would likely remain undiscovered without our deep survey. The emission line objects fall into 3 categories: 1) Most are low to moderate redshift galaxies (0 < z < 2), including many actively star forming galaxies with strong HII regions; 2) 9 are high redshift (4 < z < 7) Lyman-alpha emitters; and 3) at least 3 are candidate AGNs.

Temperature Weighted Histogram Analysis Method, Replica Exchange, and Transition Paths

We analyzed the data from a replica exchange molecular dynamics simulation using the weighted histogram analysis method to combine data from all of the temperature replicas (T-WHAM) to obtain the room-temperature potential of mean force of the G-peptide (the C-terminal beta-hairpin of the B1 domain of protein G) in regions of conformational space not sampled at room temperature. We were able to determine the potential of mean force in the transition region between a minor alpha-helical population and the major beta-hairpin population and identify a possible transition path between them along which the peptide retains a significant amount of secondary structure. This observation provides new insights into a possible mechanism of formation of beta-sheet secondary structures in proteins. We developed a novel Bayesian statistical uncertainty estimation method for any quantity derived from WHAM and used it to validate the calculated potential of mean force. The feasibility of estimating regions of the potential of mean force with unfavorable free energy at room temperature by T-WHAM analysis of replica exchange simulations was further tested on a system that can be solved analytically and presented some of the same challenges found in more complex chemical systems.

Nonlinearity Corrections and Statistical Uncertainties Associated with Near‐Infrared Arrays

ABSTRACTWe derive general equations for nonlinearity corrections and statistical uncertainty (variance) estimates for data acquired with near‐infrared detectors employing correlated double sampling, multiple correlated double sampling (Fowler sampling), and uniformly spaced continuous readout techniques. We compare our equation for the variance on each pixel associated with Fowler sampling with data taken with the array installed in the near‐infrared cross‐dispersed spectrograph (SpeX) at the NASA Infrared Telescope Facility and find that it provides an accurate representation of the empirical results. This comparison also reveals that the read noise associated with a single readout of the SpeX array increases with the number of nondestructive reads, nr, as n0.16r. This implies that the effective read noise of a stored image decreases as n-0.34r, shallower than the expected rate of n-0.5r. The cause of this read noise behavior is uncertain but it may be due to heating of the array as a result of the multiple readouts. Such behavior may be generic to arrays that employ correlated or multiple correlated double sampling readouts.

Implementation of a Monte Carlo based inverse planning model for clinical IMRT with MCNP code

Inaccurate dose calculations and limitations of optimization algorithms in inverse planning introduce systematic and convergence errors to treatment plans. This work was to implement a Monte Carlo based inverse planning model for clinical IMRT aiming to minimize the aforementioned errors. The strategy was to precalculate the dose matrices of beamlets in a Monte Carlo based method followed by the optimization of beamlet intensities. The MCNP 4B (Monte Carlo N‐Particle version 4B) code was modified to implement selective particle transport and dose tallying in voxels and efficient estimation of statistical uncertainties. The resulting performance gain was over eleven thousand times. Due to concurrent calculation of multiple beamlets of individual ports, hundreds of beamlets in an IMRT plan could be calculated within a practical length of time. A finite‐sized point source model provided a simple and accurate modeling of treatment beams. The dose matrix calculations were validated through measurements in phantoms. Agreements were better than 1.5% or 0.2 cm. The beamlet intensities were optimized using a parallel platform based optimization algorithm that was capable of escape from local minima and preventing premature convergence. The Monte Carlo based inverse planning model was applied to clinical cases. The feasibility and capability of Monte Carlo based inverse planning for clinical IMRT was demonstrated. Systematic errors in treatment plans of a commercial inverse planning system were assessed in comparison with the Monte Carlo based calculations. Discrepancies in tumor doses and critical structure doses were up to 12% and 17%, respectively. The clinical importance of Monte Carlo based inverse planning for IMRT was demonstrated.

Estimation of statistical uncertainties in quantitative phase analysis using the Rietveld method and the whole-powder-pattern decomposition method

Formulae for estimating statistical uncertainties in quantitative phase analysis using the Rietveld method and the whole-powder-pattern decomposition method have been derived. The relative magnitude of statistical uncertainty for a derived weight fraction of a component in a mixture is given by σ(Wm)/Wm= (1/Wm− 1)1/2F(D\textstyle\sum_{i = 1}^NYoi)−1/2, whereWmis the weight fraction of themth component,Fis the goodness-of-fit index,D(≤1) is a factor depending on the degree of peak overlap, and ∑Yoiis the total sum of profile intensities in the 2θ range used for whole-powder-pattern fitting. If the step width Δ2θ in step scanning is halved, ∑Yoiis almost doubled; on the other hand, ∑Yoiis proportional to the fixed counting timeT. Therefore, σ(Wm)/Wm∝ (Δ2θ/T)1/2. Extension of the 2θ range for whole-powder-pattern fitting towards the high-angle region is not effective for improving the precision of the derived weight fractions if the profile intensities in that region are weak. The formulae provide guidelines for optimizing experimental parameters in order to obtain a required precision.

Statistical uncertainty in the analysis of structure functions in turbulence.

This Rapid Communication is about a procedure for the statistical uncertainty estimation of velocity structure functions measured in turbulent flows. The proposed method is based on the determination of the number of statistically independent samples calculated by the correlation function of the velocity increments and it is applied to experimental data obtained by hot wire measurements in a turbulent jet flow.

Combined Benedetti-Pichler/Stange–Poole sampling equation for two-component particulate mixtures

General equations for the estimation of statistical uncertainty in the sampling of mixtures of two types of particles were developed that take into account variability in particle size and composition. Different expressions were obtained for situations where the component of interest is present in bulk or trace amounts. The general equation for a bulk component was verified experimentally by sampling KCl–NaCl and KCl–sucrose mixtures with various particle sizes and compositions with a spinning riffler and determining the relative standard deviation of the percentage of Cl or KCl under conditions where the analytical uncertainty was small.

CNR/Istituto di Metrologia "G Colonnetti", Torino, Italy and National Physical Laboratory, Teddington, UK International Euroconference: Advanced Mathematical Tools in Metrology

27-30 September 1995, Lady Margaret Hall, Oxford, UKFirst announcementThe conference is the first in a Euroconference Series on the theme of advanced mathematical tools in metrology. Its aims are to present and promote recent and current applications of mathematical modelling and analysis. statistics, numerical methods and software to metrology/measurement science.Emphasis will be placed on the benefits that mathematical tools can bring to problems facing researchers and practitioners of metrology. Tutorial sessions in key areas of mathematics will support the applications talks.A previous meeting on the subject, in Torino in September 1993, led to improved communication between several organizations and acted as a catalyst for developing a number of international collaborations.Metrologists will benefit from formal and informal opportunities to discuss problems. Mathematicianswill gain from an increased awareness of a range of metrological disciplines and the identification of common areas for mathematical application. Important themes will be realistic statistical uncertainty estimation and quality management systems.Support for a number of young European researchers is available.Call for papersThere are opportunities for a limited number of unsolicited papers. s of at most 300 words should be submitted to the address below by 14 April 1995 by e-mail, fax, or conventional mail. LaTeX source is encouraged. Indicate your full name, organization, address, telephone and fax numbers and e-mail address.It is intended that the proceedings will be published.Further details are available from the following address. Professor Maurice G Cox, Chairman, International Organizing Committee, 1995 Euroconference on Advanced Mathematical Tools in Metrology, Division of Information Technology and Computing, National Physical Laboratory, Teddington, Middlesex TW11 0LW, UK. Tel: +44 (0)181 943 6096 (direct), +44 (0)181 943 7002 (office). Fax: +44 (0)181 977 7091. e-mail: mgc@ditc.npl.co.uk

Estimation of systematic and statistical uncertainties in reactor physics measurements by the partition technique

We propose a novel method to estimate simultaneously the systematic and statistical uncertainties of any parameter in reactor physics measurements which are correlated due to the process of measurement and due to many systematic components of measurement using the partition technique.

Statistical and systematical errors in RBS depth profiling of implanted atoms

Simple expressions for estimation of statistical uncertainties in depth-profile parameters determined using standard RBS technique are derived. Possible sources of systematic uncertainties are also discussed along with some simple procedures for their elimination. For the simple case of RBS depth profiling of heavy atoms implanted into light matrices at low implantation energies statistical uncertainties as low as < 1% ( R p), < 5% ( ΔR p), < 20% (profile skewness) and < 10% (profile kurtosis) may be achieved providing the measuring statistics is sufficiently high.