# 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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### In sports modelling, are hot simulations better or cold simulations?

I'm thinking here largely of the context in which someone has an Elo rating model for a particular sport. To calculate things such as how often the team makes the Finals series, or wins the ...
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### Expected value of softmax transformation of Gaussian random vector

Let $\mathbf w_1,\mathbf w_2,\ldots,\mathbf w_n \in \mathbb R^p$ and $\mathbf v \in \mathbb R^n$ be fixed vectors, and $\mathbf x \sim \mathcal N_p(\boldsymbol{\mu}, \mathbf{\Sigma})$ be an $p$-...
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### Monte carlo method and Convergence in Distribution

Monte Carlo method, from what I could gather, allows one to obtain observations/draws from a possibly unknown statistical distribution. Let's say $T(X)\sim F$, where $T$ is a statistic, $X$ is a ...
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439 views

### Importance sampling: what is this bias?

I am experiencing what seems to be a bias in importance sampling, which, given that it's an unbiased procedure, should not be there. Consider linear regression $$y = X\beta+\epsilon$$ where there ...
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### Error bars for sum of Monte Carlo integrations

I want to calculate a quantity $I$ which is the sum of integrals $I_k$, $$I = \sum_k I_k\;,\quad I_k = \int_{\Omega} f_k(x)\,\textrm d x\;,$$ Every integral $I_k$ is evaluated independently by a ...
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### sampling from a posterior derived from hierarchical Bayesian using HMC

I have a complex pdf based on hierarchical Bayesian formalism where x depends on the priors w'and w'', and I consider hyper-prior for the latter's as w=Php(zeta,beta) where Php stands for the hyper ...
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### Is there a survey that explores all the available Markov chain Monte Carlo methods?

I am interested in exploring the efficacy of various Monte Carlo methods. I am aware of the Metropolis acceptance criterion, Hamiltonian Markov chains, Gibbs sampling, importance sampling, slice ...
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### How to explain simply that the set of runs for Non Intrusive Polynomial Chaos cannot be used as a Monte Carlo sample

I had quite an annoying problem at work, a few days ago. I was doing a forward Uncertainty Quantification analysis using Non Intrusive Polynomial Chaos (NISP) (see for example here). Basically, you ...