The main thing that caught my attention was that random variables are often assumed to be independent. I am not sure if it is already included, but if one wants to allow for adding, multiplying, taking mixtures etc of random variables that are not independent, one way to do it is via copulas. For sampling based methods, working with copulas is a way of incorporating a moderate variety of possible dependence structures with little additional computational cost.
The basic idea is to take a given dependence structure of some tractable multivariate random variable (e.g., one where we can produce samples quickly, like a multivariate Gaussian) and transfer its dependence structure to the individual one-dimensional distributions one likes to add, multiply, etc.
My background is more in engineering than probability, so have been educating myself on probability and probability related software for this. I’ve looked into copulas a small amount but wasn’t sure how tractable they would be. I’ll investigate further.
The main thing that caught my attention was that random variables are often assumed to be independent. I am not sure if it is already included, but if one wants to allow for adding, multiplying, taking mixtures etc of random variables that are not independent, one way to do it is via copulas. For sampling based methods, working with copulas is a way of incorporating a moderate variety of possible dependence structures with little additional computational cost.
The basic idea is to take a given dependence structure of some tractable multivariate random variable (e.g., one where we can produce samples quickly, like a multivariate Gaussian) and transfer its dependence structure to the individual one-dimensional distributions one likes to add, multiply, etc.
Thanks for the suggestion.
My background is more in engineering than probability, so have been educating myself on probability and probability related software for this. I’ve looked into copulas a small amount but wasn’t sure how tractable they would be. I’ll investigate further.