# Questions tagged [monte-carlo]

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

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### Rule of thumb for number of bootstrap samples

I wonder if someone knows any general rules of thumb regarding the number of bootstrap samples one should use, based on characteristics of the data (number of observations, etc.) and/or the variables ...
22k views

### What is the difference between Metropolis-Hastings, Gibbs, Importance, and Rejection sampling?

I have been trying to learn MCMC methods and have come across Metropolis-Hastings, Gibbs, Importance, and Rejection sampling. While some of these differences are obvious, i.e., how Gibbs is a special ...
18k views

### Approximate $e$ using Monte Carlo Simulation

I've been looking at Monte Carlo simulation recently, and have been using it to approximate constants such as $\pi$ (circle inside a rectangle, proportionate area). However, I'm unable to think of a ...
38k views

### K-fold vs. Monte Carlo cross-validation

I am trying to learn various cross validation methods, primarily with intention to apply to supervised multivariate analysis techniques. Two I have come across are K-fold and Monte Carlo cross-...
16k views

### Can somebody explain to me NUTS in english?

My understanding of the algorithm is the following: No U-Turn Sampler (NUTS) is a Hamiltonian Monte Carlo Method. This means that it is not a Markov Chain method and thus, this algorithm avoids the ...
9k views

### How to determine significant principal components using bootstrapping or Monte Carlo approach?

I am interested in determining the number of significant patterns coming out of a Principal Component Analysis (PCA) or Empirical Orthogonal Function (EOF) Analysis. I am particularly interested in ...
8k views

### Are all simulation methods some form of Monte Carlo?

Is there a simulation method that is not Monte Carlo? All simulation methods involve substituting random numbers into the function to find a range of values for the function. So are all simulation ...
10k views

### Generating random numbers manually

How can I manually generate a random number from a given distribution, as for instance, 10 realisations from the standard normal distribution?
2k views

### What are examples of statistical experiments that allow the calculation of the golden ratio?

There are some very simple experiences that can be done by a kid at home, whose result allows one to statistically approach famous numbers such as $\pi$ or $e$. An example where $\pi$ shows up is ...
4k views

### Why use Monte Carlo method instead of a simple grid?

when integrating a function or in complex simulations, I have seen the Monte Carlo method is widely used. I'm asking myself why one doesn't generate a grid of points to integrate a function instead of ...
32k views

### Would a Random Forest with multiple outputs be possible/practical?

Random Forests (RFs) is a competitive data modeling/mining method. An RF model has one output -- the output/prediction variable. The naive approach to modeling multiple outputs with RFs would be to ...
14k views

### What is importance sampling?

I'm trying to learn reinforcement learning and this topic is really confusing to me. I have taken an introduction to statistics, but I just couldn't understand this topic intuitively.
6k views

### Why is the term "Monte Carlo simulation" used instead of "Random simulation"? [duplicate]

I always read/hear "Monte Carlo" simulations. I have done "Monte Carlo" simulations before to calculate the odds in certain gambling games as part of my job and it was nothing more than basically ...
7k views

### Can Machine Learning or Deep Learning algorithms be utilised to "improve" the sampling process of a MCMC technique?

Based on the little knowledge that I have on MCMC (Markov chain Monte Carlo) methods, I understand that sampling is a crucial part of the aforementioned technique. The most commonly used sampling ...
8k views

### What are some techniques for sampling two correlated random variables?

What are some techniques for sampling two correlated random variables: if their probability distributions are parameterized (e.g., log-normal) if they have non-parametric distributions. The data are ...
20k views

### When are Monte Carlo methods preferred over temporal difference ones?

I've been doing a lot of research about Reinforcement Learning lately. I followed Sutton & Barto's Reinforcement Learning: An Introduction for most of this. I know what Markov Decision Processes ...
461 views

### How can we simulate from a geometric mixture?

If $f_1,\ldots,f_k$ are known densities from which I can simulate, i.e., for which an algorithm is available. and if the product $$\prod_{i=1}^k f_i(x)^{\alpha_i}\qquad \alpha_1,\ldots,\alpha_k>0$$ ...