Advanced search
Publication Cover
Inverse Problems in Science and Engineering Volume 12, 2004 - Issue 3
Submit an article Journal homepage
302
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Backward specification of prior in bayesian inference as an inverse problem

Andrei V. Gribok Department of Nuclear Engineering, 315 Pasqua Engineering Building, The University of Tennessee, Knoxville, TN 37996-2300, USA
,
Aleksey M. Urmanov Department of Nuclear Engineering, 315 Pasqua Engineering Building, The University of Tennessee, Knoxville, TN 37996-2300, USA
,
J. Wesley Hines Department of Nuclear Engineering, 315 Pasqua Engineering Building, The University of Tennessee, Knoxville, TN 37996-2300, USA
&
Robert E. Uhrig Department of Nuclear Engineering, 315 Pasqua Engineering Building, The University of Tennessee, Knoxville, TN 37996-2300, USA
Pages 263-278 | Received 11 Jan 2002, Accepted 15 Mar 2003, Published online: 13 Oct 2011

Figures & data

FIGURE 1 Predictive distribution π(z).

FIGURE 1 Predictive distribution π(z).

FIGURE 2 Prior distribution on parameter θ.

FIGURE 2 Prior distribution on parameter θ.

FIGURE 3 OLS solution.

FIGURE 3 OLS solution.

FIGURE 4 Regularized solution.

FIGURE 4 Regularized solution.

FIGURE 5 Marginal distribution.

FIGURE 5 Marginal distribution.

FIGURE 6 Ordinary least squares solution.

FIGURE 6 Ordinary least squares solution.

FIGURE 7 Regularized solution.

FIGURE 7 Regularized solution.

FIGURE 8 Marginal probability density function.

FIGURE 8 Marginal probability density function.

FIGURE 9 OLS solution.

FIGURE 9 OLS solution.

FIGURE 10 Regularized solution.

FIGURE 10 Regularized solution.

FIGURE 11 Empirical marginal distribution.

FIGURE 11 Empirical marginal distribution.

FIGURE 12 OLS solution.

FIGURE 12 OLS solution.

FIGURE 13 Regularized solution.

FIGURE 13 Regularized solution.

FIGURE 14 Conjugate prior distribution.

FIGURE 14 Conjugate prior distribution.

FIGURE 15 Empirical predictive distribution.

FIGURE 15 Empirical predictive distribution.

FIGURE 16 Prior distribution on the probability of tumor obtained through the solution of integral equation.

FIGURE 16 Prior distribution on the probability of tumor obtained through the solution of integral equation.

FIGURE 17 Two posterior distributions obtained using two different priors.

FIGURE 17 Two posterior distributions obtained using two different priors.

Table

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.