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

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Particle filter (sequential Monte Carlo) for a non-Gaussian hierarchical model

I have the following, which I am attempting to model with a particle filter. \begin{align*} y_{i,t}&\sim\mathrm{Poisson}\left(\lambda_{i,j,t}\right)\\ ...
6
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2answers
48 views

Seeking a continuous, parametric, bimodal sampling distribution for proportions

I am seeking a parametric probability model whose pdf has the following characteristics: (1) it is supported on a variate axis that is bounded between 0 and 1; (2) it is continuous; and (3) it is ...
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0answers
24 views

Demand Forecasting : Montecarlo Simulation

I am trying to build a demand forecasting model for human resource team. I have thought of using monte carlo simulation method to do it. Is it the right technique for it? Has anyone used it to ...
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1answer
42 views

Advantage of multiple simulations in old-fashioned Monte Carlo?

The spirit of this question comes from "Ordinary Monte Carlo", also known as "good old-fashioned Monte Carlo" Suppose I have a random variable $X$, with $$\mu := E[X]\\ \sigma^2:=Var[X] $$ Both are ...
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0answers
15 views

Simultaneous multiple perturbations in Markov chain Monte Carlo

I'm coding a McMC algorithm for geophysical applications. Using the Metropolis–Hastings scheme to accept/reject the proposed models is something that I thought I understood completely, but I don't. ...
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30 views

pairing algorithm in R

I have two sets of elements M and N, and a scalar-valued distance/similarity function between one element from M and one from N. The problem is to generate a set of pairs (one item from M and one ...
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14 views

Is Monte Carlo simulation more appropriate than parametric tests for constructing confidence intervals for weighted means?

A colleague suggested that Monte Carlo simulation should be preferred for constructing confidence intervals for weighted means calculated from a sample. How and why exactly might Monte Carlo perform ...
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1answer
10 views

Uncertainty analysis

Here is my situation. I am trying to predict the 'entire' distribution of the dependent variable, not just the mean( or conditional mean). Does it then make sense to seprateley predict quantiles of ...
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0answers
22 views

Question about Hybrid Monte Carlo

In a Hamiltonian system, the Hamiltonian is always preserved, but in HMC algorithm, new state is accepted by probability $\min(1,\frac{\exp(-H_{new})}{\exp(-H)})$, I think increase or decrease in ...
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1answer
43 views

Error Bars for Monte Carlo Experiment

Suppose we have a random variable $X$, where $\mathbb{E}(X)$ and $\text{Var}(X)$ are known. I have computed $N$ number of MC-type samples from the distribution of $X$. Let $\bar{x} = \frac{1}{N}\sum ...
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0answers
23 views

Distribution of number of values less than cutoff within symmetric Dirichlet

Assume have a symmetric Dirichlet distribution with $a_1= \dots =a_k = a$ $ (X_1, \ldots, X_K)\sim\operatorname{Dir}(a) $ I am trying to determine the distribution of the number of values less than ...
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21 views

Showing that the variance increases with the dimension of the random vector

This is actually related to a more complex question; but I want to re-ask it by trying to simplifying it as possible: 1- We have $n$ dimensional functions of the form $f_n:\mathbb{R}^{n} \mapsto ...
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1answer
21 views

Is it possible to randomly sample from single data set (Monte Carlo style) to create new data sets?

Background I understand Monte Carlo methods only superficially, but I understand you can repeatedly randomly sample, with or without replacement, from your data set to estimate population parameters ...
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14 views

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 ...
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0answers
28 views

Triangular distribution and simulation monte carlo

How can I do to incorporate Monte Carlo simulation on a triangular function. I'm trying to do this using JavaScript and found a very interesting bibliioteca http://jstat.github.io/distributions.html ...
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2answers
227 views

Misunderstanding of Monte Carlo Pi Estimation

I am fairly sure that I understand the how Monte Carlo integration works but I am not understanding the formulation of how it is used to estimate Pi. I am going by the procedure outlined in the 5th ...
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0answers
17 views

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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1answer
60 views

NP hard implementation optimisation using Monte Carlo method

I need to implement an algorithm ( or find an implementation) and optimise it using Monte Carlo method. This must be an NP hard such as the Travelling Salesman problem or the Knapsack problem. How can ...
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0answers
15 views

Tail probabilities and the GHK simulator

I am trying to use the GHK simulator to estimate the probabilities $F(\mathbf{x} > k\mathbf{a})$ that the values of a high dimensional ($n>1000$), correlated random vector $\mathbf{x}$ will ...
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1answer
47 views

10 minutes wind speed data to 1 second wind speed data

I have a wind speed data series .txt file (1 year long), in which in each register I have the following info: date; hour; 10 minute wind speed average; 10 minute max value; 10 minute sigma An ...
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1answer
53 views

NP-Hard optimisation problems that require approximate methods

What are some examples of NP-hard optimisation problem that requires approximate methods (such as Monte Carlo? I have done a lot of research but I can't find a suitable problem to implement apart from ...
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0answers
37 views

Combining unbiased estimators with unknown variance

Say we are given a sequence of independently (but not identically) distributed random variables $X_1,...,X_n$ which are known to be bounded, $X_t \in (a,b)$, and to have the same mean, $\mathbb{E}X_t ...
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39 views

Monte Carlo Optimisation

I have been doing a LOT of research about this but I can't figure out exactly how to do it. I need to find a problem that can be solved using Monte Carlo Optimisation (it is important that it is an ...
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95 views

How to mathematically prove that we are sampling from same distributions?

The content of this question is about rigorously proving something which is otherwise considered easily correct intuitively. Let's assume we have a multivariate distribution $g(x_1,x_2,...,x_n)$ over ...
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1answer
26 views
9
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126 views

Why use the parametric bootstrap?

I am currently trying to get my head around some things concerning parametric bootstrap. Most things are probably trivial but i still think i may have missed something. Suppose i want to get ...
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0answers
28 views

Box-Muller algorithm and Monte Carlo Integration

Can someone help me out here? Using Box-Muller would generate N(0,1) however X ~ N(-1, 4). How do I transform the variables to the distribution of X? And would the pseudocode include the usage of ...
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0answers
23 views

Integration via importance sampling - expectation and variance

I need to calculate $$\int_A f(x) \; dx$$ via Monte Carlo Importance Sampling and, for simulations purposes, I need to calculate the variance and mean of my estimator. In importance sampling ...
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1answer
33 views

Importance Sampling Simulation

I need to calculate an integral using importance sampling method and, for the stopping criteria of the simulation, it is given an relative error. I've found that the relative error is defined by the ...
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1answer
66 views

Monte Carlo Simulation…?

I just have 2 questions: (1) If we can obtain samples from the posterior distribution, is there any need to try to compute posterior expectations and intervals analytically...? (2) Also, I know ...
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3answers
158 views

Monte Carlo integration aim for maximum variance

I have a question about Monte Carlo integration. As I understand it the method takes a region S of known volume V which contains the region T specified in the definite integral. $T \in S$. Then ...
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0answers
30 views

Monte Carlo Based A-Priori Power Calculation for Logistic Regression

I have been wanting to get a Monte Carlo based power calculation working for Logistic Regression cases for a little bit. I have put together a workflow with some assisstnace and I wanted to ask the ...
6
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1answer
141 views

Required number of simulations for Monte Carlo analysis

My question is about the required number of simulations for Monte Carlo analysis method. As far as I see the required number of simulations for any allowed percentage error $E$ (e.g., 5) is $$ n = ...
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0answers
37 views

Use of Monte Carlo vs predictive modeling?

I am building a scoring model for rating an individual on trustworthiness. The parameters of the model are not fixed and I have no historical data to test. So to test the validity of the parameters ...
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0answers
39 views

Monte Carlo method

I need to write a report on what is Monte Carlo method suitable for and for what it is not suitable for, however, I can't find a lot of material regarding this information. What is it suitable for ...
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2answers
43 views

Monte Carlo Integration Interval Probability

Use MC integration to estimate the probability that X * exp(X) < 2.5, assuming that X ~ Gamma(1.2,3.7) ...
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1answer
56 views

Extreme value simulation with Monte Carlo

I would like to seek your help with some questions to simulating extreme values. For example, I have written the following R code to generate QQplots for a normally distributed data, varying the size ...
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3answers
158 views

Monte Carlo integration help needed

I'm trying to simulate these two integrals using Monte Carlo simulation: $$ \int_{-\infty}^\infty \exp(-x^2) dx, \quad \mbox{and } \int_{-\infty}^\infty \exp(-|x|) dx . $$ When I use ...
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0answers
47 views

Proving that Markov Chain Monte Carlo converges

I actually asked the same question in http://math.stackexchange.com/ as well at http://math.stackexchange.com/questions/753105/proving-that-markov-chain-monte-carlo-converges but since the question is ...
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0answers
25 views

Sample variance and error using Monte Carlo

Asked to compute estimator for the following function, $\theta = \int_0^\infty e^{-x^2}$ which can be solved by transforming the limits to 0 to 1 and solving the following expectation using Monte ...
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0answers
97 views

Monte Carlo integration

I am calculating a simple integral $\int^1_{-2} \exp{x^2}(x+1)dx $ with Monte Carlo method using a linear density function $p_\xi (x) = \frac{4}{9} + \frac{2}{9} x $. Let say I have a a sample which ...
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0answers
17 views

Subsampling two datasets so that the new sets have similar joint prob. distribution

I want to subsample two equivalent (in terms of features/columns) data sets in a way that the new subsampled data sets have the same joint probability distribution. To explain it better on an example: ...
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0answers
31 views

Method of Composition to sample from a t density

I got stuck with this, I will appreciate a lot any help. I need to make an R program in order to run this algorithm (in the photo below), with simulated data. The question is to use the method of ...
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0answers
10 views

Using low-discrepancy sequence for bernoulli trials in MC sim

I need to generate binomial distribution random numbers for my Carlo simulation (I need Bernoulli trials for a parameter). Thus far, I've used R "rbinom" function for that. However, as I understand, I ...
2
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0answers
45 views

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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0answers
56 views

Understanding the effect of each parameter in a Monte Carlo Simulation [duplicate]

I am running a Monte Carlo simulation where I sample from Normal Distributions associated with parameters E11, E22, and GIC to get the plot in red which can be seen in the figure below. The figure ...
2
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0answers
20 views

Does quasi-random number generator have a period?

I read somewhere, maybe incorrectly, that the Niederreiter quasi-random generator in MKL is 32 bit, and hence as a period of 2^32. This is pretty low, is this correct? This made me wonder if ...
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0answers
69 views

Determining the confidence interval of Monte Carlo data

I want to determine the confidence interval for my set of data. I have obtained the data by sampling from several Normal Distributions and running a Monte Carlo Simulation. I was wondering how I could ...
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0answers
44 views

Understanding a double peaked distribution

I am running a Monte Carlo Simulation and am sampling randomly from about 65 Normal Distributions, each with a different $\mu$ and $\sigma$. I end up with the Mixture Distribution graph shown below ...
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1answer
121 views

How does the proof of Rejection Sampling make sense?

I am taking a course on Monte Carlo methods and we learned the Rejection Sampling (or Accept-Reject Sampling) method in the last lecture. There are a lot of resources on the web which shows the proof ...