Credible intervals for nanoparticle characteristics

Richard Charnigo, Mathieu Francoeur, Patrick Kenkel, M. Pinar Mengüç, Benjamin Hall, Cidambi Srinivasan

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Solving the inverse problem of nanoparticle characterization has the potential to advance science and benefit society. While considerable progress has been made within a framework based on the scattering of surface plasmon-polaritons, an aspect not heretofore considered is the quantification of uncertainty in the estimation of a nanoparticle characteristic. Therefore, the present article offers a technique by which an investigator may augment an estimate of a nanoparticle characteristic with a companion "credible interval". Analogous to the familiar confidence interval but arising from within the Bayesian statistical paradigm, a credible interval allows the investigator to make a statement such as "the nanoparticle diameter lies between 36 and 48. nm with 95% probability" instead of merely "the nanoparticle diameter is estimated to be 42 nm". Our technique may even be applied outside of the surface plasmon-polariton scattering framework, as long as the investigator specifies his/her prior beliefs about the nanoparticle characteristic and indicates which potential outcomes are likely or unlikely in whatever experiment he/she designs to estimate the nanoparticle characteristic. Two numerical studies illustrate the implementation and performance of our technique in constructing ranges of likely values for nanoparticle diameters and agglomeration levels, respectively.

Original languageEnglish
Pages (from-to)182-193
Number of pages12
JournalJournal of Quantitative Spectroscopy and Radiative Transfer
Issue number2
StatePublished - Jan 2012

Bibliographical note

Funding Information:
This material is based upon work supported by the National Science Foundation under Grant no. DMS-0706857 . Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We thank two anonymous reviewers for constructive suggestions that improved this work.


  • Bayesian
  • Compound estimation
  • Confidence interval
  • Inverse problem
  • Scattering
  • Sufficient statistic
  • Surface plasmon-polariton

ASJC Scopus subject areas

  • Radiation
  • Atomic and Molecular Physics, and Optics
  • Spectroscopy


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