# 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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### Confusion on three “types” of Markov Chain Monte Carlo for the same inference

This is a long question but I would be very grateful if someone can help or provide some reference! And I believe this is a common confusion among beginners of MCMC. Background Given a directed ...
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### Monte Carlo simulation for fitting distributions (Weibull and log-normal)

I am working on a computer project which needs statistical analysis and I am not much of a statistic person. I have a Bluetooth (BT) detector device which detects passing Bluetooth devices (i.e one ...
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### Indirect solution for maximum entropy through sampling?

Is there a way to sample from a finite set $\{A,B,C,D\}$ such that the limiting empirical proportions converges to the maximum entropy solution of their probabilities consistent with known constraints?...
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### MCMC for Maximum Entropy?

Is there a way to sample from a discrete probability distribution, whose distribution itself is the solution to a Maximum Entropy problem with known linear constraints, without needing to solve for ...
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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 ...
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### Do Monte Carlo perturbations capture all the uncertainty in prediction?

I have a model $M$ that I use to predict a value $y = M(\vec x)$. I have known one-$\sigma$ error bars on each input $x_i \in \vec x$. I want to know the one-$\sigma$ error bar on my prediction $y$. ...
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### Uniform convergence of Monte Carlo approximation

Usually Monte Carlo method is used to compute integration. For example, let $g(x,\theta)$ be a continuous function about $x$ and $\theta$, $f(x \mid \theta)$ is a continuous pdf with parameter $\theta$...
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### How to show that the variance of Sequential Importance Sampling estimates increase with the dimension?

I am trying to understand the Particle Filter and the motivation to use it over the regular Sequential Importance Sampling. As far as I understand until now: 1- We try to estimate the expectation of ...
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### Effect of each parameter on a Monte Carlo Simulation

I was wondering what is the best way to determine the effect of each random parameter on the result obtained from a Monte Carlo Simulation. I realise I have asked a similar question here, but this ...
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### Selecting uncorrelated samples from a set of bulk data that contains correlated and dependent samples

i have a set of data that is generated by expensive computational model evaluations, on a total data set of 10000 samples in 40 dimensions. This sample data set is composed of different data sets, ...
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### Relation between statistical randomness, uniform distribution and independence

In Monte Carlo simulation, we often consider how well a sequence of generated points are. If I am correct, one aspect is statistical randomness: A numeric sequence is said to be statistically ...
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### Practical problems with difficult posteriors

I'm looking for difficult Bayesian inference problems to test out different Monte Carlo sampling methods. I've mostly been looking at Hamiltonian Monte Carlo based algorithms and in particular, I've ...