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Questions tagged [monte-carlo]

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

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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 ...
David Z's user avatar
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6 votes
0 answers
96 views

What is the best method to do a MC Integration of a multidimensional integral where the integration limits depend upon other variables?

What is the best method to do a Monte Carlo Integration of a multidimensional integral where the integration limits depend upon other variables? I am interested in getting a numerical value of a 5 ...
pollux33's user avatar
5 votes
0 answers
117 views

Probability approximation: monte carlo VS sde

I have a probability measure $\mu$ (say, in $\mathbb{R}^{d}$, with density) and I want to approximate it numerically. Today I noticed that my measure is ergotic for a certain Stochastic Differential ...
duccio's user avatar
  • 121
5 votes
0 answers
281 views

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's user avatar
4 votes
0 answers
96 views

Sample Average Approximation vs. Numerical Integration

To calculate the expected value of objective functions, we have two choices: Sample Average Approximation (SAA): $$ \frac{1}{N}\sum_{i=1}^N f(x,\xi^i). $$ Numerical Integration (e.g., Monte Carlo ...
Keith's user avatar
  • 41
4 votes
0 answers
136 views

How to stochastically estimate the trace of a matrix?

Specifically, the diagonal elements (can possibly both positive and negative) of the matrix can be computed efficiently but the total number is large ($\mathcal O(10^{18})$). My first thought about ...
Izzy Vang's user avatar
3 votes
0 answers
77 views

Hit-n-Run Monte Carlo on convex polytope

So, I'm currently trying to implement a MCMC to uniformly sampling hyper-points from the polytope defined as $\mathbb{K}=\{x\in\mathbb{R}^{n}\;\;\text{s.t.}\;\; A\,x=b \}$ in the specific case where, ...
Davide Papapicco's user avatar
3 votes
0 answers
90 views

Stochastic Collocation for time evolving ODE

For an Stochastic Differential Equation, e.g., $$ \frac{du}{dt} = \alpha*\sin(u*t) $$ where $\alpha$ is normally distributed with nonzero mean, I am trying to use a stochastic collocation approach ...
Raghu's user avatar
  • 31
2 votes
0 answers
66 views

How to implement a generic monte carlo algorithm for n-dimensional integration?

A very visual picture for Monte Carlo integration is the approximation of $\pi$, by sampling in a square which contains a quarter of the unit circle. We can extend this picture to 3 dimensions, by ...
infinitezero's user avatar
2 votes
0 answers
116 views

Random Orthogonal Matrix Generation

This post is inspired by N. Higham post "What is Random Orthogonal matrix?". In this post, N. Higham links to the two papers: G. W. Stewart, The efficient generation of random orthogonal matrices ...
Anton Menshov's user avatar
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2 votes
0 answers
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Monte Carlo domain not-so-dense

I already posted it on Physics SE, but maybe this is a better place: I have a 5D integral being calculated with a Monte Carlo uniform random sampling. The issue is that the region of integration is ...
LowFieldTheory's user avatar
2 votes
0 answers
814 views

Using C/C++ for Markov chain Monte Carlo (MCMC) methods

I'm working on optimizing the parameters of a mathematical model to fit experimental data, using an existing formula for the likelihood of observing the data given a set of parameter values. At the ...
Keith Fraser's user avatar
2 votes
0 answers
94 views

Tracking the speed of 2D oscillations on a lattice

I wrote a Monte Carlo simulation of the 2D Lotka-Volterra model on a discrete lattice (with periodic boundary conditions). A video that I produced (which images the system after some number of monte ...
Loonuh's user avatar
  • 253
1 vote
0 answers
81 views

Regarding the difference between Metropolis-Hastings and Wolff algorithm (synchronous vs asynchronous) applied to Ising Model?

I am trying to self-learn concepts at the intersection of physics and programming. When reading up on the Ising Model, I find that the typical programming tutorial (such as this one) covers the ...
user23358153's user avatar
1 vote
0 answers
46 views

Monte Carlo simulation of classical Heisenberg model doesn't represent Curie curve

I've created a JavaScript file to execute and log average energy and magnetization values of 2D lattice classical Heisenberg model. I run the simulation with parameters, ...
M. Çağlar TUFAN's user avatar
1 vote
0 answers
244 views

Monte Carlo simulation for the quantum oscillator in the path integral approach

The theory Consider a quantum harmonic oscillator described by the potential $V(q)=\frac{1}{2}m\omega^2 x^2$. In the path integral formulation, the partition function can be written as $$Z\propto\int ...
My Code is a Flying Circus's user avatar
1 vote
0 answers
42 views

Discretization formula for a system of two differential equations. "Solution to one of these is the initial condition of the other". In which sense?

Consider the following stochastic differential equation \begin{equation} dy=\left(A-\left(A+B\right)y\right)dt+C\sqrt{y\left(1-y\right)}dW\tag{1} \end{equation} where $A$, $B$ and $C$ are parameters ...
Strictly_increasing's user avatar
1 vote
0 answers
67 views

Is there a software package for Quantum Monte Carlo estimation of the exchange correlation functional?

Quantum Monte Carlo (QMC) calculations historically have been used to parameterise the exchange-correlation functionals for Density Functional Theory (DFT). For example, this article explains a way to ...
Okarin's user avatar
  • 191
1 vote
0 answers
85 views

Metropolis algorithm and thermal sine-Gordon model

I try to simulate thermal version of 1D $(x, t)$ sine-Gordon field model. I am interested in finding thermal static solution that minimizes functional of energy $E$: $$E = \int dx \left( \frac{1}{2} \...
newt's user avatar
  • 159
1 vote
0 answers
200 views

Maxwellian distribution of velocities with Shake algorithm present

I am writing a code to perform hybrid monte carlo molecular dynamics. To do this, I need to have a code to initialize the velocities of all particles according to a maxwell distribution. The code is ...
user3225087's user avatar
1 vote
0 answers
196 views

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. ...
istigatrice's user avatar
1 vote
0 answers
101 views

Monte Carlo sampling of particle system for velocity dependent potential

When sampling configurations of point particles in statistical mechanics by means of (Markov chain) Monte Carlo, we may work with a potential that only depends on the positions of the particles, and ...
doetoe's user avatar
  • 593
0 votes
0 answers
23 views

Monte-Carlo metropolis algorithm for Ising model

I am using the Monte-Carlo metropolis algorithm to simulate the Ising model. Since the convergence is slow near $T_c$, I am looking for a method to speed up the problem. What I did was instead of ...
Michael's user avatar
  • 61
0 votes
0 answers
72 views

How can I compute the longest relaxation time?

Cross-posted on Stats.SE and on MMSE. In the case of Monte Carlo simulations: Autocorrelation Time ($\tau_{\text{int}}$): A measure of how many steps are needed for the correlations in the chain to ...
user366312's user avatar
0 votes
0 answers
127 views

what is the proper way to update the XY model for a Metropolis MC simulation

I am trying to do a 2D simulation of the classical XY model in order to observe vortexes in the system. I am not really interested at the moment in calculating variables such as Magnetization because ...
Mephistopheles Faust's user avatar
0 votes
0 answers
61 views

Absence of discontinuity in Specific Heat in liquid-gas transition (Based on the Ising Model)

I'm trying to do a model for the transition liquid-gas based on the Ising model and the metropolis algorithm, instead of using values of spins, I'm saying that a cell is occupied by a particle or not. ...
madcreatorfr's user avatar
0 votes
0 answers
159 views

Numerical integration library interfacing with eigen

I am looking for a numerical integration library like this one. The examples look very appealing but I see that all test functions use very barebones C arrays. Do you have any recommendations of ...
KeynesCoeFen's user avatar
0 votes
0 answers
79 views

How to perform a monte carlo simulation on a honeycomb lattice with first, second and third nearest neighbor interactions?

I want to perform monte carlo simulation on a honeycomb lattice. Can someone please help me on how to define a matrix for these interactions and how many terms there will be while sampling the ...
Shashank's user avatar
0 votes
0 answers
67 views

Comparison of computational complexities of MD versus MC simulations

In my humble understanding MD simulations of systems with short-range(like LJ interactions) and long-range(electrostatic) has a computational complexity $O(N . log(N))$. What will be the computational ...
dexterdev's user avatar
0 votes
0 answers
91 views

Why is perfect sampling not used in large-scale lattice model simulations?

The statistical physics literature is replete with papers describing simulations of lattice models, such as the Ising model. Typically, these are done through Monte Carlo methods, such as the ...
alligator's user avatar
  • 105
0 votes
0 answers
139 views

Error in Monte Carlo integration

I am looking for a concise description to help me understand the error for Monte Carlo Integration using Uniform Sampling and Importance Sampling For Importance Sampling I have that the error is just ...
Student146's user avatar