Threshold Bootstrap Research Articles

수정된 임계값 부트스트랩을 적용한 자기상관형 이변량 데이터의 재추출 방법

시뮬레이션 출력분석 방법 중 가장 기본적이며 우수한 결과를 도출 가능한 방법은 독립반복 수행이다. 그러나 시스템이 복잡해질수록 독립 반복 시간 및 비용은 증가한다. 이러한 문제를 해결하기 위해 개발된 시뮬레 이션 출력분석방법 중 하나가 부트스트랩이다. 자기상관이 존재하는 출력 데이터 분석에 적용 가능한 대표적인 방 법으로는 이동블록 부트스트랩, 임계값 부트스트랩, 정상 부트스트랩 방법이 있다. 본 논문에서는 시스템 상태와 상태의 유지시간처럼 동시에 측정되어 이차원으로 표현되는 이변량 데이터에 대한 임계값 부트스트랩 적용 방법 을 제시한다. 특히, 두 변량의 데이터 내부에 각각 자기상관이 존재함은 물론 변량 간의 상관관계도 존재하는 경 우에 대해서 다룬다. 이 경우, 기존의 재추출 방법으로는 올바른 시스템 성능척도의 추론이 불가하다. 본 연구에서 는 이에 대한 해결책으로써 수정된 임계값 부트스트랩을 제시하며 실험을 통해 그 타당성을 검증하였다.

Bootstrap generated confidence interval for time averaged measure

In the simulation output analysis, there are some measures that should be calculated by time average concept such as the mean queue length. Especially, the confidence interval of those measures might be required for statistical analysis. In this situation, the traditional method that utilizes the central limit theorem (CLT) is inapplicable if the output data set has autocorrelation structure. The bootstrap is one of the most suitable methods which can reflect the autocorrelated phenomena in statistical analysis. Therefore, the confidence interval for a time averaged measure having autocorrelation structure can also be calculated by the bootstrap methods. This study introduces the method that constructs these confidence intervals applying the bootstraps. The bootstraps proposed are the threshold bootstrap (TB), the moving block bootstrap (MBB) and stationary bootstrap (SB). Finally, some numerical examples will be provided for verification.

추세 시계열 자료의 부트스트랩 적용

In the simulation output analysis, bootstrap method is an applicable resampling technique to insufficient data which are not significant statistically. The moving block bootstrap, the stationary bootstrap, and the threshold bootstrap are typical bootstrap methods to be used for autocorrelated time series data. They are nonparametric methods for stationary time series data, which correctly describe the original data. In the simulation output analysis, however, we may not use them because of the non-stationarity in the data set caused by the trend such as increasing or decreasing. In these cases, we can get rid of the trend by differencing the data, which guarantees the stationarity. We can get the bootstrapped data from the differenced stationary data. Taking a reverse transform to the bootstrapped data, finally, we get the pseudo-samples for the original data. In this paper, we introduce the applicability of bootstrap methods to the time series data having trend, and then verify it through the statistical analyses.

The Threshold Bootstrap Clustering: A New Approach to Find Families or Transmission Clusters within Molecular Quasispecies

BackgroundPhylogenetic methods produce hierarchies of molecular species, inferring knowledge about taxonomy and evolution. However, there is not yet a consensus methodology that provides a crisp partition of taxa, desirable when considering the problem of intra/inter-patient quasispecies classification or infection transmission event identification. We introduce the threshold bootstrap clustering (TBC), a new methodology for partitioning molecular sequences, that does not require a phylogenetic tree estimation.Methodology/Principal FindingsThe TBC is an incremental partition algorithm, inspired by the stochastic Chinese restaurant process, and takes advantage of resampling techniques and models of sequence evolution. TBC uses as input a multiple alignment of molecular sequences and its output is a crisp partition of the taxa into an automatically determined number of clusters. By varying initial conditions, the algorithm can produce different partitions. We describe a procedure that selects a prime partition among a set of candidate ones and calculates a measure of cluster reliability. TBC was successfully tested for the identification of type-1 human immunodeficiency and hepatitis C virus subtypes, and compared with previously established methodologies. It was also evaluated in the problem of HIV-1 intra-patient quasispecies clustering, and for transmission cluster identification, using a set of sequences from patients with known transmission event histories.ConclusionTBC has been shown to be effective for the subtyping of HIV and HCV, and for identifying intra-patient quasispecies. To some extent, the algorithm was able also to infer clusters corresponding to events of infection transmission. The computational complexity of TBC is quadratic in the number of taxa, lower than other established methods; in addition, TBC has been enhanced with a measure of cluster reliability. The TBC can be useful to characterise molecular quasipecies in a broad context.

The Interaction of Arsenazo III with Nd(III)—A Chemometric and Metrological Analysis

Interactions of Arsenazo III with Nd(III) in aqueous solutions (pH range 3 to 4) were studied using a spectrophotometric method. Some discrepancies are present in literature concerning the concentrations of the prevailing species and their composition. Threshold bootstrap computer-assisted target factor analysis (TB CAT) was applied to the evaluation of UV-VIS spectra of Arsenazo III in aqueous solutions containing varying amounts of neodymium(III) ions. The thus obtained experimental data are interpreted with consideration of the measurement uncertainties affecting this system. Within the limits of resolution of the experimental method, two complexes NdAazo and Nd(Aazo)2 were indicated in the studied pH range. The values of formation constants for log 10 β 11 fall in the range 4.9 to 6.3 and for log 10 β 12 fall between 10.5 and 12.1.

A systems approach for sizing a stand-alone residential PEMFC power system

Polymer electrolyte membrane fuel cells (PEMFCs) show great promise in portable, automotive, and stationary applications. They have reached the test and demonstration phase in automotive and power markets today. This paper is focused on a stand-alone residential PEMFC power system that provides the electricity needs of the house. A novel stochastic sizing methodology is developed that considers both fuel cell system dynamics and residential load dynamics in overall system sizing for the stand-alone residential fuel cell power system. Understanding the nature of demand side is critical in stand-alone system sizing. Thus, experimental measurements have been completed to capture the load side dynamics in detail. No such data is found in the current literature. The Threshold Bootstrap method is used to model the residential load demand and to produce many realistic load profiles. Matlab/Simulink is used to run system simulations to determine system sizes based on parameters defined through a designed experiment. Comparison between the proposed sizing method and a possible worst case scenario sizing is given. The new sizing methodology can be used together with sophisticated demand analysis programs to obtain customized sizing for each user as stand-alone power systems become more viable.

An application of the total measurement uncertainty budget concept to the thermodynamic data of uranyl (VI) complexation by sulfate

On the basis of UV–Vis absorption spectra from 33 aqueous solutions with a multivariate composition in uranium (VI), sulfate, and hydroxide, the evaluation of a complete measurement uncertainty budget of relevant physicochemical quantities describing the system is performed. The analysis was performed by threshold bootstrap computer-assisted target factor analysis and revealed the presence of the species UO 2 SO 4 and ( UO 2 ) 2 ( OH ) 2 2 + . The analytical procedure is scrutinized to identify and quantify relevant influence factors on the basis of cause-and-effect analysis. The complete measurement uncertainty budgets are obtained as empirical cumulative distribution functions, which show a marked non-Normality. Evidence is given that the apparent discrepant results reported in the literature, especially for formation constants of species ( UO 2 ) 2 ( OH ) 2 2 + , are not a result of faulty experimentation but of neglect of relevant uncertainty contributions. Thus, reliability has been considerably overestimated – making the results of different independent studies incompatible.

Spectroscopy, chemometrics and metrology—three aspects of lanthanide chemistry

Using spectroscopic data of the Nd(III)–nicotinic acid N-oxide (nic NO) system in methanol as example data, the requirements of the ISO Guide to the Expression of Uncertainty to the evaluation of spectroscopic data are demonstrated. The cause-and-effect diagram approach suggested by EURACHEM is shown and applied to the evaluation of single-component spectra and thermodynamic data of the Nd(III)-nic NO system using computer-intensive statistical methods like the threshold bootstrap in combination with target factor analysis (FA).

Synthesis and spectroscopic characterisation of chosen heteropolyanions and their Ln(III) complexes containing tetrabutylammonium counter ion

Synthesis and spectroscopic characterisation of tetrabutylammonium salts of heteropolyanions (NBu 4HPAS) of Keggin’s (NBu 4) 5H 2PW 11O 39, (NBu 4) 6HPMo 2W 9O 39, (NBu 4) 6H 2SiMo 2W 9O 39, (NBu 4) 4H 3PMo 2W 9O 39, (NBu 4) 6HPMo 2W 9O 39, Dawson’s type (NBu 4) 9HP 2W 17O 61 and Preyssler heteropolyanion (NBu 4) 12[(Eu)P 5W 30O 110] are presented. Extraction procedure has been selected as the best method for synthesis of compositions containing an organic counter anion. Elemental and thermogravimetric analysis, spectrophotometric determination of W and Mo, and FTIR spectra have been applied for analysis of the compositions obtained. The complexation studies were carried out with the use of Nd(III) and Er(III) absorption spectra (in the range of their hypersensitive transitions) and Eu(III) luminescence lifetime measurements. Threshold bootstrap computer-assisted target factor analysis (TB CAT) has been applied to evaluate the Nd(III) and Er(III) spectra in DMF and DMSO solutions and to estimate conditional formation constants for Ln(III)(NBu 4HPAS) 2 sandwich species (Ln(III)Nd(III), Er(III)). Luminescence characterisation of the NBu 4EuHPAS compounds concerning their intensity, quantum yield and luminescence lifetime of Eu(III) ion in non-aqueous solutions and solid are discussed.

Threshold bootstrap target factor analysis study of neodymium with pyridine 2,4 dicarboxylic acid N-oxide—an investigation of traceability

Threshold bootstrap computer-assisted target factor analysis (TB CAT) has been applied to the evaluation of UV-Vis spectra of Nd(III) in aqueous solutions containing varying amounts of pyridine 2,4-dicarboxylic acid N-oxide (dipyr NO). Using the total uncertainty budget concept, probability distributions of the conditional formation constant(s) of the respective Nd(III) dipyr NO species have been evaluated. The experimental data are compatible with two different systems: a single Nd(III) dipyr NO species with log β11=2.8±0.11or, alternatively, a two species system with log β11=3.7±0.35and log β12=5.2±0.8. The results seem to favor the single species interpretation. However, a discussion of the influence of spectral correlation indicates that the situation should be considered with caution. The results are compared to a previous TB CAT study on Nd(III) picolinic acid N-oxide interaction illustrating the advantage of arguing in terms of probability density functions. The pyridine N-oxides with substituted carboxylic acids are structurally poorly investigated. Hence, this study calls for more structural information on rare earth pyridine N-oxide derivates.

Statistical analysis of the impact of spectral correlation on observed formation constants from UV-visible spectroscopic measurements.

Information retrieved from UV-visible spectroscopic data by application of a self-modelling factor analysis algorithm showed apparently systematically shifted thermodynamic properties for the same chemical system as a function of spectral slit widths. This empirical observation triggered a systematic investigation into the likely effects of residual and spectral correlation on the numerical results from quantitative spectroscopic investigations. If slit width was a nuisance factor it would reduce the comparability of information evaluated from spectroscopic data. The influence of spectral slit width was investigated by simulation, i.e. by generating and evaluating synthetic spectra with known properties. The simulations showed that increasing spectral correlation may introduce bias into factor analysis evaluations. By evaluation of the complete measurement uncertainty budget using threshold bootstrap target factor (TB CAT) analysis, the apparent shifts are insignificant relative to the total width of the quantity's measurement uncertainty. Increasing the slit widths causes some systematic effects, for example broadening of the registered spectral bands and reduction of spectral noise, because of higher light intensity passing to the detector. Hence, the observed systematic shifts in mean values might be caused by some latent correlation. As a general conclusion, slit width does not affect bias. However, the simulations show that spectral correlation and residual correlation may cause bias. Residual correlation can be taken into account by computer-intensive statistical methods, for example moving block or threshold bootstrap analysis. Spectral correlation is a property of the chemical system under study and cannot be manipulated. As a major result, evidence is given showing that stronger spectral correlation ( r<-0.7) causes non-negligible bias in the evaluated thermodynamic information from such a system.

Application of cause-and-effect diagrams to the interpretation of UV-Vis spectroscopic data.

The application of cause-and-effect diagrams to the evaluation of thermodynamic data from UV-Vis absorption spectroscopic analysis is demonstrated. The contributions of measurement uncertainty identified from a cause-and-effect diagram are implemented into a Monte Carlo procedure based on the threshold bootstrap computer-assisted target factor analysis (TB CAT). This algorithm aims at an improvement of data comparability and accounts for non-normality, spectral, residual and parameter correlation as well as random noise in target factor analysis. The ISO Type-B measurement uncertainties are included into the process by normally distributed random numbers with specified mean values and dispersions. The TB CAT procedure is illustrated by a flow diagram and a case study of Nd(III) complexation by picolinic acid N-oxide (pic NO) in aqueous solution. Using 12 experimental spectra as input data, the single component spectra and the formation constant 1g betaML of the Nd(pic NO)2+ species are obtained together with the respective probability density distributions. The role of the cause-and-effects approach on the further development of chemical thermodynamics is discussed.

Simulation output analysis using the threshold bootstrap

The threshold bootstrap extends the bootstrap method of inference to autocorrelated data series, such as the outputs of discrete event simulations. The method works by resampling random chunks that are some multiple of a cycle. A cycle consists of alternating high and low runs that are created when the time series wanders back and forth across a threshold. Monte Carlo simulations show that the threshold bootstrap performs well in estimating the standard error of the sample mean and constructing confidence intervals with appropriate coverage and compact half-widths. We establish the asymptotic unbiasedness and consistency of threshold bootstrap estimates in the case of the sample mean. Comparison with the method of batch means and the moving blocks bootstrap shows that the threshold bootstrap is an attractive alternative for simulation output analysis.

Chemometric and statistical analysis of polyoxometalate interaction with lanthanide(III) ions

Application of CAT (computer-assisted target factor analysis) for quality assessment and quality control in spectroscopy is demonstrated. As a working example, interaction of polyoxometalates (POM) with neodymium in aqueous solutions is followed by UV–Vis spectroscopy. CAT is combined with Monte Carlo and resampling techniques (i.e. threshold bootstrap methods) in order to capture the complete distribution of suitable interpretations of the systems under study. Decisions during the evaluation process are based on statistical criteria conditional on the empirical distributions obtained from CAT. Single component spectra of the Nd–POM solution species are extracted and species concentrations in the experimental samples are obtained together with their respective confidence limits.

The threshold bootstrap and threshold jackknife

We propose two new resampling schemes for weakly dependent time series: the threshold bootstrap (TB) and the threshold jackknife (TJ). The TB works by resampling random length chunks which are some multiple of a cycle. A cycle consists of alternating high and low runs that are created when the time series wanders back and forth across a threshold. Similarly, TJ replicates are created by sequentially deleting chunks. Monte Carlo simulations show that, for various ARMA models, the TB performs better than the moving blocks bootstrap and stationary bootstrap with respect to the mean squared error of the standard error estimate of the sample mean, when each resampling scheme uses its optimal chunk/block size. The TB and stationary bootstrap are comparable when approximating the sampling distribution of the sample mean, while the moving blocks bootstrap has relatively poor performance. The TB is simpler than the matched-block bootstrap, though less accurate for short AR(1) series. Simulations also show that the TB and TJ have similar performance when estimating the standard error of the sample mean.