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Title: Formulas for robust, parallel computation of arbitrary-order, arbitrary-variate, statistical moments with arbitrary weights and compounding.

Abstract

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and recall the first generalizations which we had obtained in [P$$\acute0$$8]. We then improve these arbitrary-order, numerically stable one-pass formulas to arbitrary-variate formulas which we further extend to arbitrary weights and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic.

Authors:
 [1];  [2];  [1];  [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. The Xiph.Org Foundation, Arlington, VA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States); The Xiph.Org Foundation, Arlington, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1504207
Report Number(s):
SAND-2015-0891
562631
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English

Citation Formats

Pebay, Philippe Pierre, Terriberry, Timothy, Kolla, Hemanth, and Bennett, Janine Camille. Formulas for robust, parallel computation of arbitrary-order, arbitrary-variate, statistical moments with arbitrary weights and compounding.. United States: N. p., 2015. Web. doi:10.2172/1504207.
Pebay, Philippe Pierre, Terriberry, Timothy, Kolla, Hemanth, & Bennett, Janine Camille. Formulas for robust, parallel computation of arbitrary-order, arbitrary-variate, statistical moments with arbitrary weights and compounding.. United States. doi:10.2172/1504207.
Pebay, Philippe Pierre, Terriberry, Timothy, Kolla, Hemanth, and Bennett, Janine Camille. Sun . "Formulas for robust, parallel computation of arbitrary-order, arbitrary-variate, statistical moments with arbitrary weights and compounding.". United States. doi:10.2172/1504207. https://www.osti.gov/servlets/purl/1504207.
@article{osti_1504207,
title = {Formulas for robust, parallel computation of arbitrary-order, arbitrary-variate, statistical moments with arbitrary weights and compounding.},
author = {Pebay, Philippe Pierre and Terriberry, Timothy and Kolla, Hemanth and Bennett, Janine Camille},
abstractNote = {Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and recall the first generalizations which we had obtained in [P$\acute0$8]. We then improve these arbitrary-order, numerically stable one-pass formulas to arbitrary-variate formulas which we further extend to arbitrary weights and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic.},
doi = {10.2172/1504207},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2015},
month = {2}
}