Hannah Ritchie https://www.sustainabilitybynumbers.com/p/iea-energy-scenarios How is it that an increase in final energy results in a decrease in primary energy?
I have to explain why use MC vs GA, here I go.
Imagine you’re given the total_allocated_emissions function with no context. Every time you run
it, you get a different result and you’ve no idea why. You have an idea of the inputs to the
function but don’t know which are the ones affecting the variation in the output.
Gaussian approach
Your going to assume that if you ran this function a million times (infinite really) and gathered the results, plotting the value output of the function vs the frequency of that value as the output would result in a Gaussian (Normal) distribution.
Assuming this, you say that you want the approximate the mean of this inevitable distribution. To do this you use something called the linearity of expectations. In our case, it says that if we use the mean of the random variables for each of our uncertain parameters, the output of the whole function will be the mean of the Gaussian (Normal) distribution we’re assuming it approaches.
MC approach
You assume nothing but start on your way to running the function a million times (20000) in your case. Here, we don’t assume that it’s Normal (but it normally is). You then take the resulting distribution and summary statistics of it.
Generally, this is the uncertainty hierarchy:
- sensitivity analysis: move one ucneratin parameter around and see it’s impact on our
total_allocated_emissions. - gaussian approximation: assume the output of
total_allocated_emissionsfollows a normal distribution and get its mean. - MC: assume nothing but hope to converge on some distribution that can be summarised.
Why use MC over Gaussian when it might be overkill?
The Gaussian has to make assumptions (like saying the function analysed is normal). Another assumption it makes is that all the uncertain parameters are independent of one another. This is more often than not a simplification of reality, especially if we were unceratinty about chemical composition (masses etc.) knowing the mass of triolein affects the value that trilinolein will take on. In the MC approach, we don’t make this assumption.