Questions on Monte Carlo methods, methods that require the repeated generation of (pseudo-, quasi-)random numbers for computing their results.
1
vote
1answer
36 views
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 ...
2
votes
2answers
136 views
Monte Carlo approximation of PI
I'm trying to understand how to compute the value of Pi by means of the Monte Carlo simulation.
I have a circle inside a square where the sides of the square are tangent to the circle. As data I have ...
8
votes
4answers
159 views
Parallel (GPU) algorithms for asynchronous cellular automata
I have a collection of computational models that could be described as asynchronous cellular automata. These models resemble the Ising model, but are slightly more complicated. It seems as if such ...
4
votes
3answers
127 views
nuclear reaction fluid modelling
I'm pretty ignorant regarding the dark arts of numerical codes and modelling, but i'm interested in trying to pursue it for a particular pet project. It regards modelling of nuclear reactions like ...
4
votes
0answers
23 views
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:
$$
...
4
votes
1answer
117 views
index representation of the diamond lattice
For a kinetic Monte Carlo simulation of solids that crystallize in the diamond lattice structure, I need some efficient representation of the diamond lattice as integer(s), to store it in some ...
4
votes
0answers
100 views
Rebinning algorithm in VEGAS
I am trying to understand the rebinning algorithm of the VEGAS (original publication and implementation notes) Monte Carlo integration. I will try to explain first what I think I understood and then ...
2
votes
1answer
68 views
Randomly choose among N alternatives
I understand how to generate a random sequence of binary variables where 1 occurs with probability p and ...
7
votes
2answers
155 views
Maximizing unknown noisy function
I'm interested in maximizing a function $f(\mathbf \theta)$, where $\theta \in \mathbb R^p$.
The problem is that I don't know the analytic form of the function, or of its derivatives. The only thing ...
8
votes
2answers
125 views
Under what circumstances is Monte Carlo integration better than quasi-Monte Carlo?
A simple enough question: to do a multidimensional integral, given that one has decided that some sort of Monte Carlo method is appropriate, is there any advantage that a regular MC integration using ...
8
votes
3answers
327 views
Numeric integration of multi-dimensional integral with known boundaries
I have a (2-dimensional) improper integral
$$I=\int_A \frac{W(x,y)}{F(x,y)}\,\mbox{d}x\mbox{d}y$$
where the domain of integration $A$ is smaller than $x=[-1,1]$, $y=[-1,1]$ but further restricted by ...
4
votes
1answer
141 views
Minimum image convention for triclinic unit cell
The minimum image convention (MIC), see for example a short note of W. Smith, is often used in molecular dynamics or monte carlo simulations of periodic systems with an orthorhombic unit cell. For ...
5
votes
2answers
215 views
Monte Carlo simulation of 3D X-Y model
I need to compute the helicity modulus as a function of temperature for a three-dimensional X-Y model (see N.K. Kultanov, Yu.E. Lozovik, "The critical behavior of the 3D X-Y model and its relation ...
11
votes
5answers
438 views
How can I approximate an improper integral?
I have a function $f(x,y,z)$ such that
$\int_{R^3} f(x,y,z)dV$
is finite, and I want to approximate this integral.
I'm familiar with quadrature rules and monte carlo approximations of integrals, ...
4
votes
1answer
58 views
How to use a web-embedded model in a computational workflow?
There is a model embedded in a web browser (Caprio 1998) that I would like to use in an MCMC algorithm. What is the best way to do this?
I could implement the model in my favorite language but I ...
13
votes
3answers
720 views
How to add large exponential terms reliably without overflow errors?
A very common problem in Markov Chain Monte Carlo involves computing probabilities that are sum of large exponential terms,
$ e^{a_1} + e^{a_2} + ... $
where the components of $a$ can range from ...
8
votes
3answers
587 views
Drawing samples from a finite mixture of normal distributions?
After some Bayesian update steps, I am left with a posterior distribution of the form of a mixture of normal distributions,$$\Pr(\theta| \text{data} ) = \sum_{i=1}^k w_i N(\mu_i, \sigma^2).$$ That is, ...
7
votes
0answers
301 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 ...
3
votes
1answer
299 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 ...
11
votes
3answers
430 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 ...
4
votes
0answers
162 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
249 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 ...
5
votes
3answers
624 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?
5
votes
4answers
180 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 ...
