# Tagged Questions

Questions on Monte Carlo methods, methods that require the repeated generation of (pseudo-, quasi-)random numbers for computing their results.

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### Monte Carlo Search Tree iterations

I have had this example in my exam last week and I can not figure out how to solve it. I have watched lots of tutorials on Monte Carlo Search Tree but I can't still understand this algorithm properly. ...
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### How to compute integrals using any probability law with Monte Carlo?

I am intrested in providing an estimation of : $\iint C(x,y)dP_X(x)dP_Y(y)$ I am able to generate random numbers from the distribution of $P_Y$ and $P_X$. Therefore I generate a big number (n=10 000)...
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### Approximating Minkowski Sum of 3 dimensional Convex Polytopes by Sampling

Let $P_1,P_2...P_r$ be a set of convex polytopes with $n_r$ vertices in 3 dimensions. These polytopes basically represent uncertainties of '$r$' number of 3d-points respectively in space. The global ...
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### Importance sampling example

I have a question regarding importance sampling. During a lecture we were told that importance sampling is simply a shift to another PDF to improve point sampling. I=\int_{a}^{b}dx\ f(...
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### Monte Carlo method for solving integrals [closed]

My professor gives us an intro to how to evaluate integration using Monte Carlo method. But I tried to search about it and never find the algorithm he used. Any help how can I find an explanation ...
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### Loss probability and VaR

I would like to estimate Value-at-Risk analytically and through delta-gamma aproximation. I don't know if my idea is ok, but i would like to build a portfolio of European option. Suppose that in this ...
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### Estimator of expectation value for standard normal distribution

In the case of a standard normal distribution, I just read that a good estimator for E[f(x)] is $\frac{1}{M}\sum_{i=1}^M f(X_i)$ (where each $X_i$ is standard normally distributed and independent). ...
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### Limiting Distribution of a Gibbs Distribution

I know that the Gibbs distribution at a particular state, x, is given by $\frac{e^{-\beta E_i}}{\sum_j e^{-\beta E_j}}$ with $\beta = \frac{1}{T}$, but I do not understand what a limiting distribution ...
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### Quasi-Monte Carlo with Conditional Distributions

I want to estimate $E(f(X))$ using quasi-Monte Carlo where $X = (X_1,\ldots,X_n)$ is a random vector and $$X_i\sim f(\cdot; \theta), \quad \text{independent},$$ where $\theta \in \mathbb{R}$ is some ...
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### References on probability theory, stochastic processes, Monte Carlo and convex optimisation, with similar writing style to Terence Tao

I learned a lot from prof Tao's notes and books because unlike many authors, he seems to prefer writing more words, explanations and intuitions rather than just mathematical formulae. His approach is ...