Open CFoye-Creare opened 1 year ago
Some possible approaches include:
Also notable is the application of dimensionality reduction techniques before building surrogate models or approximations.
Since this issue, we have evolved our approach. We are now using the Law of the Unconscious Statistician and Change-of-Variable to solve this problem. See the following:
Our approach became:
This commit shows this using toy data: ab6618a51819ba216dbdba134572193edc762f79 . This commit shows using real data: 27140d217985e3437e22d65c2eaee723aa981959
Here are some figures: MSE vs Bin Size for calculating mean soil moisture.
And calculating variance:
Objective Develop an efficient method to compute the statistics s(c) for a given non-linear n-dimensional function f(x, y) with dependent variables x and y, such that F(f(s(x), s(y))) = s(c) while minimizing computational expense.
Background The non-linear n-dimensional function f(x, y) has dependent variables x and y, and is computationally expensive when directly calculating s(f(x, y)) to obtain s(c). Instead, we want to find an efficient approach to compute F(f(s(x), s(y))) to derive s(c) with reduced computational cost.
Input:
Output: Statistics on the function output, denoted s(c), such that F(s(x), s(y)) = s(c). For example, given two PDFs P(x) and P(y), we want to approximate F such that F(P(x), P(y)) = PDF(c)
Constraints: The proposed method should significantly reduce computational cost compared to directly calculating s(f(x, y)) to obtain s(c).
Evaluation Metrics: The efficiency of the proposed method will be evaluated based on the following criteria:
Deliverables