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As a package this seems perfectly reasonable, but I'm skeptical of the use of Monte Carlo being a technical buzzword rather than a choice made because it was th

As a package this seems perfectly reasonable, but I'm skeptical of the use of Monte Carlo being a technical buzzword rather than a choice made because it was the appropriate tool for the task. I wasn't able to find any technical details in the "How it works" section, but if you assume the distribution of time to complete a task is uniform on the interval [worst case, best case], then at any time point the underlying distribution seems to be a composition of sums and minima of uniform distributions. These are available in closed form. I see in another comment the distributions are assumed to be log-normal -- that's fine too, there are good approximation to these. On the website it says thousands of trajectories are generated. It seems likely that one can straightforwardly compute the result that the Monte Carlo approach would give in the limit of infinitely many generated trajectories.

diiq 5y ago
I promise, this is the result of real constraints! Monte carlo is used because of the limitations of analysis when using log-normal distributions. Normal distributions can be summed algebraically; log normal distributions cannot. https://blog.vistimo.com/post/169546687605/estimation-math https://blog.vistimo.com/post/169546687605/estimation-math Note that Monte-carlo is not used prominently anywhere on the site, just here because I thought HN would find that part of the implementation interesting.
- asdf_snar 5y ago
  It is true that there is no closed form expressions for the sum of two independent log normal distributions. However, like I said, good approximations exist. Moreover, if you were to ask me to compute some expectation E[f(X)] where X is the sum of independent one-dimensional log-normals, it seems simplest to convolve the densities and simply compute the expectation by trapezoidal integration.
  - diiq 5y ago
    Fair enough! There's more than one way to skin a cat. This way was easier for me, and has additional benefits as described.
    - asdf_snar 5y ago
      I think I misled myself into thinking your selling point was the technology (Monte Carlo), whereas as you say there is little about that on the website. And your comments below are right: building the tool around MC affords you a lot of flexibility without having to be increasingly clever. The only thing I would worry about then are events which have low probability but potentially very high "weight" in whatever measure of risk you are using. Sometimes the weight can be so large that your MC estimates seem to converging, and then the addition of a single trajectory completely blows up your variance. These are related to the "black swan" events people sometimes talk about. I don't think this is a problem in your model. Thanks again for ansnwering.

diiq 5y ago

I promise, this is the result of real constraints! Monte carlo is used because of the limitations of analysis when using log-normal distributions. Normal distributions can be summed algebraically; log normal distributions cannot. https://blog.vistimo.com/post/169546687605/estimation-math https://blog.vistimo.com/post/169546687605/estimation-math Note that Monte-carlo is not used prominently anywhere on the site, just here because I thought HN would find that part of the implementation interesting.

asdf_snar 5y ago
It is true that there is no closed form expressions for the sum of two independent log normal distributions. However, like I said, good approximations exist. Moreover, if you were to ask me to compute some expectation E[f(X)] where X is the sum of independent one-dimensional log-normals, it seems simplest to convolve the densities and simply compute the expectation by trapezoidal integration.
- diiq 5y ago
  Fair enough! There's more than one way to skin a cat. This way was easier for me, and has additional benefits as described.
  - asdf_snar 5y ago
    I think I misled myself into thinking your selling point was the technology (Monte Carlo), whereas as you say there is little about that on the website. And your comments below are right: building the tool around MC affords you a lot of flexibility without having to be increasingly clever. The only thing I would worry about then are events which have low probability but potentially very high "weight" in whatever measure of risk you are using. Sometimes the weight can be so large that your MC estimates seem to converging, and then the addition of a single trajectory completely blows up your variance. These are related to the "black swan" events people sometimes talk about. I don't think this is a problem in your model. Thanks again for ansnwering.