13,337 research outputs found
Sliced rotated sphere packing designs
Space-filling designs are popular choices for computer experiments. A sliced
design is a design that can be partitioned into several subdesigns. We propose
a new type of sliced space-filling design called sliced rotated sphere packing
designs. Their full designs and subdesigns are rotated sphere packing designs.
They are constructed by rescaling, rotating, translating and extracting the
points from a sliced lattice. We provide two fast algorithms to generate such
designs. Furthermore, we propose a strategy to use sliced rotated sphere
packing designs adaptively. Under this strategy, initial runs are uniformly
distributed in the design space, follow-up runs are added by incorporating
information gained from initial runs, and the combined design is space-filling
for any local region. Examples are given to illustrate its potential
application
Warranty Data Analysis: A Review
Warranty claims and supplementary data contain useful information about product quality and reliability. Analysing such data can therefore be of benefit to manufacturers in identifying early warnings of abnormalities in their products, providing useful information about failure modes to aid design modification, estimating product reliability for deciding on warranty policy and forecasting future warranty claims needed for preparing fiscal plans. In the last two decades, considerable research has been conducted in warranty data analysis (WDA) from several different perspectives. This article attempts to summarise and review the research and developments in WDA with emphasis on models, methods and applications. It concludes with a brief discussion on current practices and possible future trends in WDA
Predicted Residual Error Sum of Squares of Mixed Models: An Application for Genomic Prediction.
Genomic prediction is a statistical method to predict phenotypes of polygenic traits using high-throughput genomic data. Most diseases and behaviors in humans and animals are polygenic traits. The majority of agronomic traits in crops are also polygenic. Accurate prediction of these traits can help medical professionals diagnose acute diseases and breeders to increase food products, and therefore significantly contribute to human health and global food security. The best linear unbiased prediction (BLUP) is an important tool to analyze high-throughput genomic data for prediction. However, to judge the efficacy of the BLUP model with a particular set of predictors for a given trait, one has to provide an unbiased mechanism to evaluate the predictability. Cross-validation (CV) is an essential tool to achieve this goal, where a sample is partitioned into K parts of roughly equal size, one part is predicted using parameters estimated from the remaining K - 1 parts, and eventually every part is predicted using a sample excluding that part. Such a CV is called the K-fold CV. Unfortunately, CV presents a substantial increase in computational burden. We developed an alternative method, the HAT method, to replace CV. The new method corrects the estimated residual errors from the whole sample analysis using the leverage values of a hat matrix of the random effects to achieve the predicted residual errors. Properties of the HAT method were investigated using seven agronomic and 1000 metabolomic traits of an inbred rice population. Results showed that the HAT method is a very good approximation of the CV method. The method was also applied to 10 traits in 1495 hybrid rice with 1.6 million SNPs, and to human height of 6161 subjects with roughly 0.5 million SNPs of the Framingham heart study data. Predictabilities of the HAT and CV methods were all similar. The HAT method allows us to easily evaluate the predictabilities of genomic prediction for large numbers of traits in very large populations
Quantifying uncertainties on excursion sets under a Gaussian random field prior
We focus on the problem of estimating and quantifying uncertainties on the
excursion set of a function under a limited evaluation budget. We adopt a
Bayesian approach where the objective function is assumed to be a realization
of a Gaussian random field. In this setting, the posterior distribution on the
objective function gives rise to a posterior distribution on excursion sets.
Several approaches exist to summarize the distribution of such sets based on
random closed set theory. While the recently proposed Vorob'ev approach
exploits analytical formulae, further notions of variability require Monte
Carlo estimators relying on Gaussian random field conditional simulations. In
the present work we propose a method to choose Monte Carlo simulation points
and obtain quasi-realizations of the conditional field at fine designs through
affine predictors. The points are chosen optimally in the sense that they
minimize the posterior expected distance in measure between the excursion set
and its reconstruction. The proposed method reduces the computational costs due
to Monte Carlo simulations and enables the computation of quasi-realizations on
fine designs in large dimensions. We apply this reconstruction approach to
obtain realizations of an excursion set on a fine grid which allow us to give a
new measure of uncertainty based on the distance transform of the excursion
set. Finally we present a safety engineering test case where the simulation
method is employed to compute a Monte Carlo estimate of a contour line
Minimizing Negative Transfer of Knowledge in Multivariate Gaussian Processes: A Scalable and Regularized Approach
Recently there has been an increasing interest in the multivariate Gaussian
process (MGP) which extends the Gaussian process (GP) to deal with multiple
outputs. One approach to construct the MGP and account for non-trivial
commonalities amongst outputs employs a convolution process (CP). The CP is
based on the idea of sharing latent functions across several convolutions.
Despite the elegance of the CP construction, it provides new challenges that
need yet to be tackled. First, even with a moderate number of outputs, model
building is extremely prohibitive due to the huge increase in computational
demands and number of parameters to be estimated. Second, the negative transfer
of knowledge may occur when some outputs do not share commonalities. In this
paper we address these issues. We propose a regularized pairwise modeling
approach for the MGP established using CP. The key feature of our approach is
to distribute the estimation of the full multivariate model into a group of
bivariate GPs which are individually built. Interestingly pairwise modeling
turns out to possess unique characteristics, which allows us to tackle the
challenge of negative transfer through penalizing the latent function that
facilitates information sharing in each bivariate model. Predictions are then
made through combining predictions from the bivariate models within a Bayesian
framework. The proposed method has excellent scalability when the number of
outputs is large and minimizes the negative transfer of knowledge between
uncorrelated outputs. Statistical guarantees for the proposed method are
studied and its advantageous features are demonstrated through numerical
studies
A Time Truncated Moving Average Chart for the Weibull Distribution
A control chart of monitoring the number of failures is proposed with a moving average scheme, when the life of an item follows a Weibull distribution. A specified number of items are put on a time truncated life test and the number of failures is observed. The proposed control chart has been evaluated by the average run lengths (ARLs) under different parameter settings. The control constant and the test time multiplier are to be determined by considering the in-control ARL. It is observed that the proposed control chart is more efficient in detecting a shift in the process as compared with the existing time truncated control chart. ? 2013 IEEE.11Ysciescopu
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