From d8fcb1484317a9f7aebb37e25fe95306b14da54e Mon Sep 17 00:00:00 2001 From: wtrainor Date: Wed, 6 Nov 2024 14:41:11 -0800 Subject: [PATCH] Posterior explanation --- paper/paper.md | 7 +++---- 1 file changed, 3 insertions(+), 4 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index acf0840..81d3dcd 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -94,15 +94,14 @@ The demo problem allows users to build intuition on how $V_{prior}$ and $V_{perf This figure provides a visual example of the empirical likelihood (bars) of the electrical conductivity assosciated with positive sites (green) and negative sites (red): -![Likelihoods of Electrical Conductivity of Lower Crust for INGENIOUS area.\label{fig:Likelihood_CondLowCrust}][width=0.7](Likelihood_CondLowCrust.png) - -\includegraphics[width=0.7\textwidth,height=\textheight]{Likelihood_CondLowCrust.png} +![Likelihoods of Electrical Conductivity of Lower Crust for INGENIOUS area.\label{fig:Likelihood_CondLowCrust}](Likelihood_CondLowCrust.png) The continuous lines in \autoref{fig:Likelihood_CondLowCrust.png} are the fitted kde likelihoods of the optimal bandwidth given the grid search for accuracy in Naïve Bayes. The likelihood scaled to a prior probability of success ($Pr(\Theta = positive$)=0.2) ![Prior-Scaled Likelihoods of Electrical Conductivity of Lower Crust for INGENIOUS area.\label{fig:Scaled20Likelihood_CondLowCrust}](Scaled20Likelihood_CondLowCrust.png){width=50%} The posterior plot of $Pr(\Theta = positive$)=0.2 are shown below -![Posterior of Electrical Conductivity of Lower Crust for INGENIOUS area.\label{fig:Posterior_Prior20}](Posterior_Prior20.png){ width=0.5} +![Posterior of Electrical Conductivity of Lower Crust for INGENIOUS area.\label{fig:Posterior_Prior20}](Posterior_Prior20.png) +This plot shows, given any of the conductivity bin values are observed, how likely are you in a positive (green) versus negative (red) hidden geothermal resource. In general, electrical conductivities of lower crust less than 4.5 (S-m) are more likely to be a negative geothermal site, whereas greater than 4.75 S-m the calibrated dataset show $Pr(\Theta = positive)$= 100%. # Acknowledgements We acknowledge contributions from Sierra Rosado during the genesis of this project and from Nicole Taverna for providing feedback.