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-   -   Problem 4.4 - computation time/variance (http://book.caltech.edu/bookforum/showthread.php?t=4861)

stnvntngrn 11-13-2018 03:24 AM

Problem 4.4 - computation time/variance
1 Attachment(s)
I am implementing the framework of problem 4.4, and am wondering how nice I should expect the results to be.

The analogue of figure 4.3(a) that I generate, apart from resolution as per the parameters given in the problem, does not look nearly as nice as the actual figure 4.3(a) -- while the figures are qualitatively the same, mine has significant "noise".

Initially my implementation took 200 experiments at each data point, as a compromise between precision and computation time, but I just let it run over night at with 5000 experiments (took a bit over three hours in the end), and still get noticeable noise, cf. attached image.

As such, I would like to know how many experiments were used to generate figure 4.3(a) in the book. Moreover, if this is not significantly higher than my 5000, do you have any guesses how I could manage to have generated incorrect noise but otherwise seemingly correct data? Finally, if your implementation of 4.3(a) involves some significant clever tricks compared to problem 4.4, or involves a very large number of experiments/very long computation time for an exercise in a book, maybe it would be nice to indicate this in the problem.

htlin 11-18-2018 08:14 PM

Re: Problem 4.4 - computation time/variance
Thanks for asking. The current figure is generated with 1000000 experiments per point to generate high-quality figures for printing. Usually we don't think readers/students need to run so many experiments to understand the concepts, though.

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