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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12
votes
3answers
1k views

Numeric integration of multi-dimensional integral with known boundaries

I have a (2-dimensional) improper integral $$I=\int_A \frac{W(x,y)}{F(x,y)}\,\mbox{d}x\mbox{d}y$$ where the domain of integration $A$ is smaller than $x=[-1,1]$, $y=[-1,1]$ but further restricted by ...
7
votes
2answers
2k views

Minimum image convention for triclinic unit cell

The minimum image convention (MIC), see for example a short note of W. Smith, is often used in molecular dynamics or monte carlo simulations of periodic systems with an orthorhombic unit cell. For ...
5
votes
2answers
1k views

Monte Carlo simulation of 3D X-Y model

I need to compute the helicity modulus as a function of temperature for a three-dimensional X-Y model (see N.K. Kultanov, Yu.E. Lozovik, "The critical behavior of the 3D X-Y model and its relation ...
13
votes
5answers
5k views

How can I approximate an improper integral?

I have a function $f(x,y,z)$ such that $\int_{R^3} f(x,y,z)dV$ is finite, and I want to approximate this integral. I'm familiar with quadrature rules and monte carlo approximations of integrals, ...
4
votes
1answer
69 views

How to use a web-embedded model in a computational workflow?

There is a model embedded in a web browser (Caprio 1998) that I would like to use in an MCMC algorithm. What is the best way to do this? I could implement the model in my favorite language but I ...
25
votes
4answers
8k views

How to add large exponential terms reliably without overflow errors?

A very common problem in Markov Chain Monte Carlo involves computing probabilities that are sum of large exponential terms, $ e^{a_1} + e^{a_2} + ... $ where the components of $a$ can range from ...
10
votes
3answers
2k views

Drawing samples from a finite mixture of normal distributions?

After some Bayesian update steps, I am left with a posterior distribution of the form of a mixture of normal distributions,$$\Pr(\theta| \text{data} ) = \sum_{i=1}^k w_i N(\mu_i, \sigma^2).$$ That is, ...
12
votes
1answer
859 views

Replacing Mathematica's QuasiMonteCarlo integration in C++

I have a Mathematica program which performs some integrals in 3 or 4 dimensions using the QuasiMonteCarlo method. The problem is, it takes an annoyingly long time ...
6
votes
3answers
2k views

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 ...
14
votes
3answers
713 views

PDEs in Many Dimensions

I know that most methods of finding approximate solutions to PDEs scale poorly with the number of dimensions, and that Monte Carlo is used for situations that call for ~100 dimensions. What are good ...
5
votes
0answers
258 views

Convergence rate of Monte-Carlo variance estimate

What is the convergence rate for Monte-Carlo variance estimate for a random variable $X \in {L^q}(\Omega ,R),2 < q < 4$?
2
votes
1answer
591 views

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 ...
7
votes
6answers
8k views

Python implementations of Gillespie's direct method

I'm looking for a decent implementation of Gillespie's Direct Method in Python, as if I code the algorithm myself I'm nigh positive I'll do it inefficiently. Anyone have a favorite?
9
votes
4answers
740 views

How do I know which low-discrepancy sequence to use?

Whenever one uses a quasi-Monte Carlo method for cubature or optimization, it seems that there's a wide variety of low-discrepancy sequences to choose from, associated with the names of van der Corput,...

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