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

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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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27 views

simulating distributions with non-symmetrical confidence intervals in R

I have a software package that outputs estimates that have non-symmetrical confidence intervals. I am simulating these distributions for further Monte-Carlo estimates. In the below example I am trying ...
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17 views

Extreme value simulation @ Monte Carlo

Folks, 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 ...
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13 views

Monte carlo Finance Project [on hold]

Hi I have a project for my Master Course and I am trying to find topic for the Project Ideally I would like a finance oriented topic. My problem is that most of the literature is difficult to handle ...
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3answers
140 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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31 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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20 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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79 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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12 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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22 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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5 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 ...
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34 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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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 ...
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13 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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64 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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35 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
81 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 ...
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41 views

Importance Sampling to evaluate integral in R

I have asked the question here also. However, there might be something wrong with my theoretical understanding hence I'm asking here as it is more relevant. Kindly do not diss without looking first. ...
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1answer
78 views

How good is Monte Carlo Simulation when the variable distribution is unknown?

I am reading the book "how to measure everything", there is a chapter when the author encourages the usage of Monte Carlo simulation in simulating the future events in order to get a better ...
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2answers
213 views

Significance testing of cross-validated classification accuracy: shuffling vs. binomial test

I have a dataset with 2 classes and a certain way to build a binary classifier. I want to measure its performance and to test if it is significantly above the chance level. I measure its performance ...
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1answer
46 views

Reweighting importance-weighted samples in Bayesian bootstrap

Typically, in Bayesian bootstrap, you have samples {$x_1,...,x_n$} of a random variable $X$. Choose $\{p_1,...,p_n\}$ from a Dirichlet distribution, by sorting $\{0,1,u_1,...,u_{n-1}\}$ where $u_i$ ...
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43 views

Importance Sampling MC - a couple of questions regarding PDF

I implore the good people to quickly glance through this thread over at StackOverflow to get a better idea of my question if the following isn't clear. I have these integrals to evaluate using ...
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19 views

Randomization Testing help

I am scratching my head over this one...any help would be greatly appreciated. I want to know if the average travel time between Guell Park and the beach in Barcelona using the bus or the metro ...
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1answer
102 views

Monte Carlo simulation vs. machine learning algorithms: what is the difference in application?

I have been doing some research on different type of machine learning (ML) algorithms such as random forest/SVM etc. in order to model and best predict pharmaceutical needs of patients suffering from ...
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1answer
38 views

Data input uncertainty + Monte Carlo simulation + forecasting

Consider a variable $Y$ (e.g., temperature). Suppose that we were able to estimate this variable each year for the past $N$ years using some type of model. This means we have access to annual ...
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200 views

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 ...
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1answer
43 views

Reasons not to use fuzzy numbers instead of pds to represent uncertainty

Can someone explain why (if at all) it would be a bad idea to use fuzzy numbers to represent uncertainties in model parameters instead of probability distributions. I'll try to explain the motivation ...
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1answer
53 views

Plotting the coverage of the confidence interval as a function of sample size using Monte Carlo in R

I have a distribution $x\sim\text{exponential}(\lambda)$ and I know that $\hat{\lambda}=\bar{x}$ and Fisher's information to be $\lambda^{-2}$. Now, I need to use R ...
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28 views

Optimising test re-test reliability through randomly generating hypothetical repeated trials

I have had a look around the forum, and despite some similar questions on measurement error, no one appears to have asked this question specifically. I have developed a test where a small group of ...
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1answer
72 views

Delta function in monte carlo sampling

I am confused by the dirac delta function in the formulation of monte carlo sampling. http://www.cs.ubc.ca/~arnaud/doucet_johansen_tutorialPF.pdf, for instance, defines in section 3.1 page 8 the ...
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44 views

Conditionals for Gibbs sampling of relational clusters

I'm trying to implement a Gibbs sampler, but I'm having trouble to find some of the conditionals of this model. Model We have $A$ actors, $K$ classes or clusters, and a matrix $\phi$ that determines ...
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1answer
34 views

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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98 views

conditional sampling of bivariate normals

I would like to generate random samples from a bivariate normal distribution under a condition. First normal variable is $\varepsilon_1$ , and second normal is $\varepsilon_2$. The condition is ...
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1answer
50 views

Overlap Probability of Empirical Distributions

I have a load versus capacity problem, and I'm trying to determine the likelihood of failure. Here's a simple example of what I mean. I have load and capacity discrete pdfs that were determined ...
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66 views

When Monte Carlo simulation can't be used to simulate a statistical system?

My question is simple. Which are the general conditions for which a Monte Carlo simulation can be used to represent a statistical system? Or conversely, which are the statistical system that cannot be ...
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62 views

Hamiltonian Monte Carlo: why is reparameterizing needed?

In the Stan user's manual (Version 2.0.1, page 157), it says A hierarchical model such as the above will suffer from the same kind of inefficiencies... [for a Hamiltonian Monte Carlo method] ...
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1answer
72 views

Accept-reject algorithm for Beta(1,$\beta$)

Consider the pdf $$f(x)= \begin{cases} \beta x^{\beta -1 }\quad 0<x<1 \\ 0\quad \text{elsewhere} \end{cases} $$ for $\beta >1 $ Use the accept-reject algorithm to generate an observation ...
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Adjusted-size in a Monte Carlo bootstrap simulation

For my thesis I computed various rejection frequencies based on p-values using various statistics based on the Wild Restricted Efficient bootstrap scheme of Davidson & Mackinnon (2010) by ...
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1answer
62 views

Distribution of logically constrained parameters in Monte Carlo simulation

Papers like Briggs et al. 2002 say that logical constraints on inputs such as probability parameters exclude the the Normal distribution from consideration due to its unboundedness. In this example, ...
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48 views

CLT in a Monte Carlo simulation, small sample

A CLT says that asymptotically the sampling distribution of the sampling mean converges to the Normal. I would like to run a Monte Carlo simulation using information on one of the model's variables ...
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38 views

determining probability of spatial pattern metric greater than some instance

Let's say I have a grid of cells from a satellite image that take on the value of 0 or 1, with 1 being forest. There are many spatial pattern metrics that measure things about this pattern such as ...
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1answer
72 views

Rate of convergence for SLLN

I am interested in writing a non-asymptotic rate of convergence for SLLN as a function of number of samples. From the literature I've read so far, CLT provides an asymptotic convergence rate of ...
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127 views

What method is simulating pvalues from re sampling from the data

A while back I asked a question about correlating times between time stamps and received a response from Peter Ellis that said I could calculate mean distances between codes... This already will ...
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1answer
114 views

MCMC on a bounded parameter space?

I am trying to apply MCMC on a problem, but my priors(in my case they are $\alpha\in[0,1],\beta\in[0,1]$)) are restricted to an area? Can I use normal MCMC and ignore the samples that fall outside of ...
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3answers
85 views

MCMC for an explicitly uncomputable prior?

I am trying to sample from a posterior distribution and I only have an explicit formula for likelihood but I can sample from the prior distribution. How can I sample from the posterior distribution ...
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52 views

MCMC sampling from a function with a conditional distribution as Dirac delta function

Suppose the following distribution $p(x,y)$, $p:[0,1]^2 \to [0,+\infty]$ and: $p(x,y) = \left\{ \begin{array}{ll} 0 & \mbox{if } y>0 \\ +\infty & \mbox{if } y = 0 \end{array} ...
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15 views

Sum of the samples as the normalising factor in MCMC?

Suppose using an specific sampling method I have generated a sample but I now want the normalising factor to be able to calculate the probabilities. Can I consider the sum of the values as their ...
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27 views

Approximately sampling $(X, Y)$ when sampling $X$ is easy

Suppose I am interested in sampling many pairs $(\mathbf X, Y)$ from some distribution $f(\mathbf x, y)$ where $\mathbf x \in \mathbb R^p$, $p$ large ; I am interested in both exact and approximate ...
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45 views

Resampling from Monte Carlo simulation runs

Say I run a Monte Carlo simulation to generate a regression model of a simulation space. All variable parameters in the original sample have been selected at random from a uniform distribution. Is it ...
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179 views

Generating causally dependent random variables

I'm trying to generate sets of causally connected random variables and started off doing this with a monte carlo approach. The baseline is a 2-dimensional measured histogram from which I draw random ...