# Questions tagged [monte-carlo]

Using (pseudo-)random numbers and the Law of Large Numbers to simulate the random behavior of a real system.

1,212 questions
Filter by
Sorted by
Tagged with
13 views

### Confidence interval for evaluating an integral via Monte-Carlo sampling

I am trying to evaluate the following integral using Monte-Carlo: $$\langle f \rangle = \int \mathrm{d}x~ \rho(x) f(x)$$ where $\rho(x)$ is a normalized positive function. The integration is ...
6 views

### Robustness analysis using Monte Carlo

Using a mathematical model, I have estimated some system parameters using Kalman filter. Now I have to verify whether the proposed system is robust against uncertainties. I have estimated data and ...
37 views

### Uncertainty/Standard Deviation of Monte Carlo methods

I am using a Monte Carlo method to estimate the expected value of the results of certain simulations. Consider this simplified case: $X, Y$ are independent random variables and $g(X,Y)$ is a nonlinear ...
7 views

### Computing significance using permutation test in nested cross-validated SVR model

I am running an SVR on multi-dimensional input data (X) to predict an outcome variable (Y). I am using a nested cross-validation approach, with the inner loop using a GridSearch CV to find the optimal ...
• 127
3 views

• 432
31 views

### No Variance in Monte Carlo Simulation

I wanted to do a Monte Carlo simulation for some of the electoral districts in my state in the upcoming US midterms. My methodology essentially was as follows: I have a list of populations and vote ...
• 123
62 views

### Metropolis - Hastings algorithm on a set of countable sequences

I want to simulate $\sigma$ from a measure $\pi(\sigma)$ through the Metropolis-Hastings algorithm, where $\sigma$ is a sequence of 0's and 1's on $S = \{0, 1\}^n$, the set of all sequences of 0's ...
• 119
1 vote
16 views

### Standard errors of Monte Carlo plus linear combination

I'm using Monte Carlo to estimate some quantity $V(x)$. To get an approximation of $V'(x)$ I would use the following $$V'(x)\approx\frac{V(x+h)-V(x-h)}{2h}$$ so I can simply evaluate it with two ...
• 211
14 views

### In stochastic maximum likelihood and contrastive divergence, why do we sample from model distribution for partition function?

I have been reading the "Deep Learning" book from Ian Goodfellow. In a topic on Restricted Boltzmann Machines and how to train them, techniques like Stochastic Maximum Likelihood and ...
• 121
110 views

### Monte-carlo simulation and extrapolation

I am reviewing some work and the proposed solution seems to me not to be reliable. But I fail to find any references or even consistently formulate why I think this approach does not work. Assume you ...
• 174
1 vote
33 views

### Sampling according to a product of a known density and a probability function

Given a known density $p(x)$, I'd like to generate samples according to $q(x) \propto p(x) f(x)$, where $f(x)$ is some probability function, $\forall x f(x) \in [0, 1]$, e.g., a sigmoid function. One ...
• 11
47 views

573 views

### Antithetic method for monte carlo when bounds of the integral are infinite

I wanted to apply Monte Carlo with antithetic variables to estimate $\int_{0}^{\infty} e^{-x} \,dx$ (equal to 1). I used this R code. ...
• 53
202 views

### Alternative to SimPy for continuous event simulation?

The python library, SimPy, is pretty explicit that it only handles discrete event simulation. Though it is theoretically possible to do continuous simulations with SimPy, it has no features that help ...
• 1,728
41 views

### Can you give an example of Metropolis and Metropolis-Hastings algorithm?

I have studied many books and tried to understand both the Metropolis and Metropolis-Hastings algorithm. Everywhere it is written in the context of the Ising model or Lenard-Jones Energy. I am having ...
• 1,528
54 views

### Monte Carlo and function minimization (simulated annealing)

I posted this question on math.stackexchange, but did not get an answer and a limited amount of views, so I removed the question there and post it here. Recently I was asking myself some basic ...
• 703
238 views

### Markov Chain Monte Carlo doesn't converge

I have a synthetic measurement model that looks like this, $$x(t) = e^{j u t \frac{4}{\lambda}},$$ $\lambda$ is a constant. $$z(t) = x(t) + n(t)$$ The quantity $j = \sqrt{-1}$, the imaginary unit. ...
• 111
53 views

### power analysis via Monte Carlo when effect size, means, and std unknown

Say you want to execute an experiment to see whether a treatment is better than a control and want to properly power your experiment. However, you have no beliefs a prior regarding the treatment's ...
• 1,728
In Hamiltonian Monte Carlo the proposal is accepted with probability:  \alpha\left(\mathbf{x}_n(0),\mathbf{x}_n(L\Delta t)\right) = \min\left(1, \frac{\exp\left[-H\left(\mathbf{x}_n(L\Delta t),\...