For large n (see below for how to determine what's large enough), it's safe to treat, by the central limit theorem, the distribution of the sample mean as normal (gaussian) but I'd like a procedure that gives a confidence interval for any n. The way to do that is to use a Student T distribution with n-1 degrees of freedom. So the quest...
I am working on a simulation system. I will soon have experimental data (histograms) for the real-world distribution of values for several simulation inputs. When the simulation runs, I would like to be able to produce random values that match the measured distribution. I'd prefer to do this without storing the original histograms...
What is an efficient way to generate a random contingency table? A contingency table is defined as a rectangular matrix such that the sum of each row is fixed, and the sum of each column is fixed, but the individual elements may be anything as long as the sum of each row and column is correct. Note that it's very easy to generate rando...
I have tried many algorithms for finding π using Monte Carlo. One of the solutions (in Python) is this: def calc_PI(): n_points = 1000000 hits = 0 for i in range(1, n_points): x, y = uniform(0.0, 1.0), uniform(0.0, 1.0) if (x**2 + y**2) <= 1.0: hits += 1 print "Calc2: PI result", 4.0 * floa...
My current task is to optimise a Monte Carlo Simulation that calculates Capital Adequacy figures by region for a set of Obligors. It is running about 10 x too slow for where it will need to be in production and number or daily runs required. Additionally the granularity of the result figures will need to be improved down to desk possib...
Hi all, Can I get your help on some Maths and possibly Excel? I have benchmarked my app increasing the number of iterations and number of obligors recording the time taken in seconds with the following result: 200 400 600 800 1000 1200 1400 1600 1800 2000 20000 15.627681 30.0968663 44.7592684 60.9037558 75.8267358 90.3718977...
So far I've been using the C# Mersenne Twister found here to generate random numbers: http://www.centerspace.net/resources.php I just discovered SFMT which is supposed to be twice as fast here: http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/SFMT/ Can anyone point me at a C# implementation of SFMT? My requirements are to generate an...
I have a set of numbers ~100, I wish to perform MC simulation on this set, the basic idea is I fully randomize the set, do some comparison/checks on the first ~20 values, store the result and repeat. Now the actual comparison/check algorithm is extremely fast it actually completes in about 50 CPU cycles. With this in mind, and in order...
Ocaml process can use just one core and in order to use multiple cores I have to run several processes. Are there any Ocaml frameworks to use to parallelize Monte Carlo simulations? ...
Whenever I run large scale monte carlo simulations in S-Plus, I always end up growing a beard while I wait for it to complete. What are the best tricks for running monte carlo simulations in R? Any good examples of running processes in a distributed fashion? ...
Could anybody explain to me why simulatedCase <- rbinom(100,1,0.5) simDf <- data.frame(CASE = simulatedCase) posterior_m0 <<- MCMClogit(CASE ~ 1, data = simDf, b0 = 0, B0 = 1) always results in a MCMC acceptance ratio of 0? Any explanation would be greatly appreciated! ...
I'm using monte carlo method to calculate pi and do a basic experience with parallel programming and openmp the problem is that when i use 1 thread, x iterations, always runs faster than n thread, x iterations. Can anyone tell me why? For example the code runs like this "a.out 1 1000000", where 1 is threads and 1000000 the iterations ...
I am thinking about getting one of these (PCI) to set up an internal entropy pool similar to this service who incidentally brought us fun captcha challenges. Prior to lightening my wallet, I'm hoping to gather feedback from people who may be using this device. As there is no possible 'correct' answer, I am making this CW and tagging it ...
Hello, I'm trying to make a randomizer that will use the Monte Carlo Hit or Miss Simulation. I have a Key-Value pair that represents the ID and the probability value: ID - Value 2 - 0.37 1 - 0.35 4 - 0.14 3 - 0.12 When you add all of those values, you will get a total of 1.0. You can imagine those values as the total area of a "sl...
Hi! I need a clarification with algorithm generating random values for my pet ray-tracer. I emit rays from one point. And I have the problem with distribution of these rays: I need the distribution to be uniform, but it isn't... The problem I face now is that the distribution being uniform initially is not uniform after my distortions...
Hi! Can anybody recommend a good introduction book on Monte Carlo algorithms in c++? Preferably with applications to physics, and even more preferably, the kind of physics being quantum mechanics. Thanks! ...
I've been given a free choice of final project for my software development course, I'm quite interested in attempting a distributed programming task, My initial thought was to create a simple photon scattering renderer but I don't think I'd get far past rendering platonic solids and metaballs. Any suggestions, or interesting areas I mig...
I need to run a MonteCarlo simulations in parallel on different machines. The code is in c++, but the program is set up and launched with a python script that set a lot of things, in particular the random seed. The function setseed thake a 4 bytes unsigned integer Using a simple import time setseed(int(time.time())) is not very good ...
I have a method, which uses random samples to approximate a calculation. This method is called millions of times, so its very important that the process of choosing the random numbers is efficient. I'm not sure how fast javas Random().nextInt really are, but my program does not seem to benefit as much as I would like it too. When cho...
I'm running some Monte Carlo simulations and making extensive use of the Excel function NORM.INV using Office Interrop. This functions takes three arguments (probability, average, standard deviation) and returns the inverse of the cumulative distribution. I'd like to move my code into a web app, but that will require installing Excel o...