# 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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### 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 ...
707 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 ...
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, ...
344 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 ...
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 ...
455 views

### Regarding automatic differentiation, is source-code-transformation (STC) more efficient than operator-overloading (OO)?

We are working on a Bayesian model for a space-time process, and are using a No-U-Turn sampler (NUTS) that requires a model for the log-probability and it's gradient with respect to the model ...
1k 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 ...
858 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 ...
512 views

### Numerical method for equation solving that works on stochastically computed functions

There are many well known numerical methods for solving equations of the type $$f(x) = 0, \quad x \in \mathbb{R}^n,$$ e.g. bisection method, Newton's method, etc. In my application $f(x)$ is ...
842 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 ...
2k views

### Parallel Mersenne Twister for Monte Carlo

Recently, I came across a comment claiming that almost all researchers doing Monte Carlo methods are doing it wrong. It went on to elaborate that merely choosing different seeds for different ...
1k 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, ...
953 views

### Estimate information entropy through Monte Carlo sampling

I am looking for methods that allow estimating the information entropy of a distribution when the only practical ways of sampling from that distribution are Monte Carlo methods. My problem is not ...
792 views

### How to sample points in hyperbolic space?

Hyperbolic space in the PoincarĆ© upper half space model looks like ordinary $\Bbb R^n$ but with the notion of angle and distance distorted in a relatively simple way. In Euclidean space I can sample a ...
450 views

### Confusion about Quantum Monte Carlo

My question is about extracting observables from QMC methods, as described in this reference. I understand the formal derivation of various QMC methods like Path Integral Monte Carlo. However, at the ...
344 views

### suggestion for managing simulation runs?

This questions may be a bit off-topic in comp-sci. if it is needed please suggest where does it fit with. The question is regarding on how to manage all the simulation runs efficiently. let's say, ...
715 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,...
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 ...
168 views