Dear all, I am wondering whether there is an approved method to estimate the cost-benefit factor of statistical or even geostatistical models. That means to answer the question on how worth it is to put highly precise data into a model, f.i. to cover a proxy, in comparison to the enhancement of the model, e.g. better standard deviation and so forth.
Take this a as a poor example: If I have a model to predict the movement of one species from one ecosystem to another by correlating the length of the crossable boundary. How to evaluate the precision of the length needed to get a valuable model output. Would be a rough estimation be sufficient or is it necessary to determine the length up to the last millimeter.
Please get me right, I am not interested in this specific case but in the method to determine the effort that, at the end, can be described by statistical numbers.
Any hints or literature on that?
Thank you so much in advance,
Marc-O.
There is no benefit to increasing the precision of a variable if it does not lower the uncertainty. You can evaluate the effect of increasing accuracy/precision using the propagation of uncertainty formula. See attached.
If you need a reference see
https://www.researchgate.net/publication/227849139_On_the_Selection_of_Distributions_for_Stochastic_Variables
Article On the Selection of Distributions for Stochastic Variables
Dear Joseph,
Thank you very much for the literature. I am still working on it. However, I don't think that this will cover our problem since the independent variables we put into our regression model are somehow the result of a spatial analysis, or, in other words, hard to get. Maybe precision was, therefore, the wrong wording. Let me explain this with another example.
Imagine the correlation between local wind speed and tree volume that is, however given by cylinders (estimated high and classified diameter) that are approximating their volume. Sure, I can calculate a correlation. However, a geometrical representation of a tree composed of a simple cylinder, representing the stem and a sphere on top of this stem would approximate its volume quite better or, at least more trustful. Even better to have a cylindrical stem approximation and a refined canopy geometry. At a last step it would be the best to have the true geometry of every branch or even every leaf. Each step to get a better representation of the tree’s geometry but would cause ten times more effort. How do I define the point where this effort is not worthwhile to undertake? I thought about putting the best approximation I have into the regression model and then start checking against poorer approximation. However, I have no idea to evaluate or value the expected deterioration.
If I understand correctly, you have a two part problem that might be poorly connected. You are attempting to model a process and fit a regression. A series of measurements of say roughness length or canopy deposition under varying wind speeds can be used in a regression to obtain a relationship. Fitting a model to a regression is more difficult because regression will smooth the noise in the model with the possibility of missing details. Nevertheless, within the model you should be able to assess a degree of uncertainty for parts of the model. For example, is a tree canopy essentially a hard, smooth sphere, a rough sphere, or a circular filter.
Should you consider the model and regression separately?
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