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Title: Multivariate Quadrature Rules for Correlated Random Variables.


Abstract not provided.

Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
Report Number(s):
DOE Contract Number:
Resource Type:
Resource Relation:
Conference: Proposed for presentation at the SIAM Conference on Computational Science and Engineering. held February 27 - March 3, 2017 in Atlanta, GA.
Country of Publication:
United States

Citation Formats

Jakeman, John Davis. Multivariate Quadrature Rules for Correlated Random Variables.. United States: N. p., 2017. Web.
Jakeman, John Davis. Multivariate Quadrature Rules for Correlated Random Variables.. United States.
Jakeman, John Davis. Wed . "Multivariate Quadrature Rules for Correlated Random Variables.". United States. doi:.
title = {Multivariate Quadrature Rules for Correlated Random Variables.},
author = {Jakeman, John Davis},
abstractNote = {Abstract not provided.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}

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  • A {ital q}-vector of responses, y, is related to a {ital p}-vector of explanatory variables, x, through a causal linear model. In analytical chemistry, y and x might represent the spectrum and associated set of constituent concentrations of a multicomponent sample which are related through Beer`s law. The model parameters are estimated during a calibration process in which both x and y are available for a number of observations (samples/specimens) which are collectively referred to as the calibration set. For new observations, the fitted calibration model is then used as the basis for predicting the unknown values of the newmore » x`s (concentrations) form the associated new y`s (spectra) in the prediction set. This prediction procedure can be viewed as parameter estimation in an errors-in-variables (EIV) framework. In addition to providing a basis for simultaneous inference about the new x`s, consideration of the EIV framework yields a number of insights relating to the design and execution of calibration studies. A particularly interesting result is that predictions of the new x`s for individual samples can be improved by using seemingly unrelated information contained in the y`s from the other members of the prediction set. Furthermore, motivated by this EIV analysis, this result can be extended beyond the causal modeling context to a broader range of applications of multivariate calibration which involve the use of principal components regression.« less