Computational Science Stack Exchange
Computational Science Stack Exchange

Questions tagged [monte-carlo]

Questions on Monte Carlo methods, methods that require the repeated generation of (pseudo-, quasi-)random numbers for computing their results.

138 questions
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Under what circumstances is Monte Carlo integration better than quasi-Monte Carlo?

A simple enough question: to do a multidimensional integral, given that one has decided that some sort of Monte Carlo method is appropriate, is there any advantage that a regular MC integration using pseudorandom numbers has over a quasi-Monte Carlo…
David Z
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8
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2 answers

Approximation of partial derivative of a function of stochastic variable

Let $X_t$ be an Ito process $$ dX_t=a(X_t,t)dt + b(X_t,t)dW_t $$ where $W_t$ is a Wiener process. A numerical approximations of the solution of this equations is proposed by Milstein: $$ X_T=X_t+a(X_t,t) \Delta t+ b(X_t,t)\Delta W_t+…
Fabio
8
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1 answer

Rebinning algorithm in VEGAS

I am trying to understand the rebinning algorithm of the VEGAS (original publication (preprint from LKlevin) and implementation notes) Monte Carlo integration. I will try to explain first what I think I understood and then pose my questions. For…
cschwan
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8
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1 answer

Choosing how many iterations to use in VEGAS

I'm using VEGAS integration, specifically the GSL implementation, for some QCD calculations, and I've been investigating the behavior of the algorithm for various numbers of iterations in an attempt to get more accurate results. The value produced…
David Z
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8
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1 answer

Quasi Monte Carlo in Matlab

I want to use Quasi Monte Carlo to try and improve the convergence of a simulation I am running. The random numbers are simply to produce the observation errors for a standard linear regression model, which is then estimated using a number of…
Bazman
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7
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3 answers

3d Ising model simulation - what critical exponents should I be looking for and how do I find them?

For the final project in my computational physics class, I've built and will be presenting results for monte carlo simulations of phase transition in the three dimensional ising model. Using the metropolis algorithm, I've been able to graph the…
Ami
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5
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Convergence rate of Monte-Carlo variance estimate

What is the convergence rate for Monte-Carlo variance estimate for a random variable $X \in {L^q}(\Omega ,R),2 < q < 4$?
learningmath
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3
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Separation of degrees of freedom in Monte Carlo simulation

My question is probably very simple and deals with separation of degrees of freedom in a Monte Carlo Brownian dynamics simulation. Dealing with a particle in an external potential, I want to simulate a Brownian motion in three spatial dimensions. Is…
bioEngineer
3
votes
1 answer

How to optimize sampling for global sensitivity analysis

What is a good way to sample parameters for performing global sensitivity analysis? Some methods are defined using integrals, some are use Monte Carlo. How do these compare?
Chris Rackauckas
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How can I compute autocorrelation values of end to end vector?

I obtained a list of $\overrightarrow{r}_{end-to-end}$ from a Monte Carlo simulation of polymer movement. # r_end-X r_end-Y r_end-Z -177.236 100.309 -130.930 -184.354 88.047 -117.760 -172.577 87.168 -117.745 -197.651 103.270…
user366312
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Vegas, Monte Carlo multi integration, QCD

To do some calculation on QCD on Lattice, I needed a Monte Carlo multi integration. I wrote a a C++ program according to what I understood from the paper “ Lepage (1978) “ A New Algorith For Adaptive Multidimensional Integration” SLAC_Pub_1839…
Matrix
2
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2 answers

Generating a random number based on a numerical distribution function

I have a probability distribution function that I don't have its analytical form (so I can't determine its CDF). How can I generate random numbers based on this distribution function? I'm looking for a way that is similar to that of using CDF.
Pourya Vakilipourtakalou
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1 answer

Use of Metropolis-Hasting algorithm for gathering statistics

I understand how MH work, I'm able to use it to simulate e.g. 2D Ising model. What I don't understand is what you actually take average of. When I run the simulation, it reaches equlibrium after some time: Now each new state is going to be the…
Tom83B
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DIST strings - Monte Carlo Simulation

I recently read something that talks about DIST distribution strings. It appears to be a way to take a long string of previously generated numbers and somehow compress them into a string that can then be used by others. I believe it's lossy. I'm…
Mitchell Kaplan
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1
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Variational Monte Carlo to calculate local energy of hydrogen like ions in python

I'm writing up a code to calculate the local energy for electrons in hydrogen like ions for a given wavefunction. My code is giving me weird results, which leads me to believe something is wrong. Firstly, am I going about accepting/rejecting moves…
istigatrice
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