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

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2
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20 views

Monte Carlo choice of sample size

If I have $U_1,U_2,... \sim i.i.d~~ \text{Uniform}(0,1)$, and $f(x) = \sqrt{1-x^2}$. Then, by the Strong Law of Large Numbers: $$ P \left( \bigg{\lvert} \frac{1}{n}\sum_{k=1}^nf(U_k)-\int_0^1f(x)dx ...
0
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0answers
19 views

Deriving errors for fitted parameters using Monte Carlo

I have the following data: One 2D image, each of its pixels is a measurement. I will call this "data map". One 2D image, each of its pixels is the error (1 sigma) of the above measurements. I will ...
1
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0answers
17 views

hypothesis testing with uncertainty in variables

This is one of those questions that are easier to be explained with an example. Suppose we have the following data (made in R) ...
1
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0answers
21 views

How to call extreme samples in a Monte Carlo simulation for hypothesis testing?

For many hypothesis tests, Monte Carlo methods are used to estimate the empirical $p$-value which is defined as $$p=\#{(T_{sample} > T_{observed})}/N.$$ Is there a name for the samples with ...
0
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0answers
35 views

Bounding the bias of standard deviation estimate for stratified sampling (MC)

I cannot find an answer to this issue: in Monte Carlo runs, if one uses stratified sampling then the unknown bias of the variance estimator ( $\bar{\sigma}^2=\frac{1}{N}\sum{(y_i-\bar\mu_y)}$ where ...
2
votes
2answers
107 views

Double integral, monte carlo estimation

Suppose I have pairs of random variables where $X_i$~$U[0,1]$ and $Y_i$~$U[0,1]$ and I want to estimate it $$\theta=\int_{0.5}^{1}\int_0^{0.5}e^{xy}xydxdy$$ but $\theta$ needs to have variance less ...
2
votes
2answers
129 views

R random vector generator

Create an R function generating ordered pairs x,y sampled from the two dimensional distribution whose pdf is of the form $f(x,y)=cxy$, where $0<x,y<1$, and $c$ is a constant to be ...
2
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4answers
114 views

Monte Carlo integration with imposed variance

Implement an estimator using Monte Carlo integration $$\theta=\int_0^1e^{-x^2}(1-x)dx$$ Estimate $\theta$ with variance lower than $0.0001$ and write the variance of estimator depending on ...
-1
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0answers
29 views

How this Monte-Carlo method called(name) optimization of functions with multiple parameters [duplicate]

I have a description of a Monte Carlo method and don't know if it is a sequential monte -carlo, dynamic monte-carlo? What should I be looking for? Do you know similar methods? This is optimization ...
0
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2answers
77 views

Monte carlo optimisation (find maximum of function with multiple parameters)

UPDATE 4 UPDATE I JUST NEED TO know name of method(because there are hundreds of mmc methods) I have a description of a Monte Carlo method and don't know if it is a sequential monte -carlo, dynamic ...
1
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0answers
36 views

Analyzing output in MCMC

I am using emcee to do inference on some data. I am trying to fit my data to a line of equation $ y = mx + b $. ...
0
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0answers
17 views

Possible Monte Carlo usage for defining t?

I have the following question. As a part of a research, I am trying to determine based on repository contribution factors which users can be classified as core developers, that is, developers that ...
1
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0answers
29 views

Monte Carlo (variance reduction)

Suppose we are to estimate $$ I = \int_0^1e^xdx $$ Suppose $Y$ random variable of density $f(x)=x+1, \ \ x \in [0,1]$. $$ Z = \frac{e^Y}{1+Y} $$ We know that $E(Z)=I$. The question is : How ...
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0answers
10 views

Monte-Carlo: R script not returning anything [migrated]

My R script is mcnorm.R <- function(M,N) { library("mvtnorm", lib.loc="~/R/win-library/3.2") R <- as.matrix(read.csv("Data.csv", header=FALSE)) mu <- colMeans(R) ...
2
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0answers
35 views

Are Latin hypercube samples uncorrelated

I understand the basics to Latin hypercube sampling, such as implemented by the algorithm LHSA mentioned in the book Design and Modeling for Computer Experiments. But I'd like to make sure: 1, n ...
3
votes
1answer
26 views

Variance Reduction calculate

If $\phi(x)=\frac{e^x-1}{e-1}I_{[0,1]}(x)$, use the variance reduction techniques: Importance Sampling, Antithetic Variables, Control Variates.Compare the methods and check which provides the greatest ...
1
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0answers
8 views

Power of a case control test as a function of P(X=1) & P(Y=1)

For our course in statistics we had to build a simulation which would give insight in the power of a case-control study vs that of a cohort study, both trying to discover an association between 2 ...
3
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1answer
54 views

Control Variates, Monte Carlo integration

Exercise: Calculate $P(N>2.5)$ where $N$~$N(0,1)$ through simple monte carlo integration, and then use control variables to reduce the variance of my estimator. I did ...
4
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1answer
122 views

Variance reduction technique in Monte Carlo integration

I have some trouble understanding the variance reduction method called "Antithetic variables": Suppose that the integrand is $g(x)=x^2$ and the reference density $f(x)=e^{-x}I_{[0,\infty]}$ is ...
0
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1answer
37 views

Proof of Marsaglia polar method

I studied Polar method and I can use it very well to simulate to Standard Normal Variable. But I can't figure it out that how it works! So is there any proof/theorem to learn reasoning behind Polar ...
3
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2answers
45 views

Strategy for geometric die guessing game

The first day of statistics class, we played a betting game to visualize the basics of probability distributions. It worked like this: The teacher begins by rolling a die repeatedly until the number ...
2
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1answer
41 views

How to run Chisq independence test using monte carlo method

I've been investigating exact tests and during that I find monte carlo method very useful. I can write my own code for randomization and permutation tests but I cannot figure out how R function ...
2
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0answers
22 views

After Monte Carlo simulations, should I do multiple test correction?

I performed Monte Carol simulation to assess the significance of a certain motif in genome DNA. I also carried out hundred different motifs using the same procedure. So I got a bunch of p-values for ...
1
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0answers
42 views

Combining variance reduction techniques

I'm looking for some reference on the combination of various variance reduction techniques, in particular a best linear unbiased estimator. The only reference I have is McLeish - Monte Carlo ...
0
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0answers
29 views

Bayesian Monte Carlo modeling and selecting priors [duplicate]

Could anyone recommend some not-too-mathy introductory texts to Bayesian regression and Monte Carlo modeling? I am neither a statistician nor an econometrician. The frequentist perspective makes ...
1
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0answers
20 views

Monte Carlo integration and reweighting

I have to find the expectation of a particular function, $f(x)$ with respect to a gamma distribution $Ga(a_k,b_k)$. However, at each iteration $k$, the gamma parameters $a_k,b_k$ change. Suppose ...
2
votes
1answer
49 views

Monte-Carlo integration

Calculate $\int_1^2 cx^2e^xdx$ where c is constant $f(x)=ce^x, x\in[1,2]$ $\phi(x)=x^2 $ i)Using Monte-Carlo integration ii) Using antagonistic variables I do not know how to do this, as in the ...
1
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1answer
33 views

Predicting value over time

I'm trying to predict the value of a variable after a specified number of days. I'm assuming it will change each day by a normally distributed random amount. For example, today the value is 10. Over ...
0
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0answers
44 views

How do I sample from a black-box model of a probability distribution?

I have a function 'P(x)' where we query for any 'x' it gives a probability value. This function 'P' does not have a closed form and the evaluation is costly. Now 'x' is a set of vectors(matrix whose ...
3
votes
1answer
46 views

Gibbs Sampler - Sample mean convergence

To simulate from the posterior distribution $p(\theta|Y)$ where $\theta = (\mu,\lambda_1,\lambda_2)$, I run a Gibbs sampler to draw approximately random values from $p(\theta|Y)$. This Gibbs sampler ...
0
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0answers
19 views

Using the terms significance, probability or likelihood, in connection with estimators

Imagine a number of variates $x_i$, and a number of processes $P_k$ which depend on these variables, in an unknown way (ie no clear cut formulas to work with). Now consider the scenario where you ...
0
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0answers
23 views

Algorithm calculating the autocorrelation time

I am in the middle of the analysis of a large set of Monte-Carlo data and you may know that calculating the autocorrelation of the Chain is a good part of the error estimation. I am doing this error ...
0
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0answers
17 views

Better approach to determining parameter error bars than my Monte Carlo approach?

I have a certain astrophysical phenomenon currently described by a few different models. For a given model I can expect a certain number of particles passing by earth as a function of time. From this ...
0
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1answer
75 views

Gibbs Sampler Running Wild

So, I'm setting up a Gibbs Sampler using a multivariate normal model with a Jeffreys prior (working through the Hoff book on my own). There's also missing data to be imputed. I've checked my posterior ...
0
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0answers
33 views

Montecarlo analysis: how many iterations I need?

I am working on a Montecarlo analysis. I have a transfer function from R^m-->R (i.e. m inputs to one single output), whose I do not know deterministically the m inputs. So I generate N random values ...
2
votes
1answer
51 views

Simulated chi-square distribution doesn't match theoretical

Can someone explain why the distribution of Chi-square values I'm getting (using Pearson goodness-of-fit test) doesn't match the expected Chi-sqaure distribution? The test seems in this case to be ...
0
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1answer
53 views

Bootstrap and MonteCarlo Method

I am trying to make sense of the bootstrap method. I am studying on Rice, "mathematical statistics and data analysis" Here it is its explanation of the bootstrap method: Imagine for the moment ...
2
votes
1answer
26 views

Adjusting Monte Carlo estimates to generate correct even moments - improving on antitthetic draws

If I want to generate a matrix 10,000 (row) samples of 3 uniform (uncorrelated) variables it is trivial to use antithetic draws to ensure the odd moments such as the mean equal their "true" value. ...
0
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0answers
37 views

Bootstrap resampling for constructing hypothesis test

I need to use bootstrap resampling to test the significant difference between two datasets (data1 & data2). I have already used bootstrap resampling to estimate the confidence interval of the mean ...
1
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0answers
41 views

Confidence intervals for sample mean when estimated standard deviation is 0

I ran a Monte Carlo simulation to determine a confidence interval for the population mean based on N trials. The underlying distribution of results is not normal (the values are discrete -- 0, .5 or ...
0
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0answers
47 views

Can you perform bootstrap resampling from a sampling distribution?

The quick and to-the-point question I have is: Can you perform bootstrap resampling on a sampling distribution, using the sampling distribution as if it were an original sample of observations? What ...
0
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0answers
14 views

Do the number of entries per bin of a histogram obtained out of a try and reject sampling of a pdf follow a Poisson distribution?

Imagine we have this pdf $\frac{3}{8}(1+x^2)+0.017x$ defined in $x\in[-1,1]$. Imagine we make a try and reject sampling and get many values of $x$. Imagine that with this variables we make a ...
2
votes
1answer
71 views

Get distribution for aggregate loss using Monte Carlo

I am given two data sets containing dates and losses (in some currency). Given a distribution for the amount of losses and an (a,b,0) distribution for frequency of losses, how can I use Monte Carlo ...
0
votes
1answer
41 views

bivariate normal distribution probability

We have two genes X and Y. Let $(X,Y)\sim N(\mu_x=9,\mu_y=10,\sigma^2_x=3,\sigma^2_y=5,\rho\sigma_x\sigma_y=2)$. To find $P(X+0.5<Y)$ the probability that the sample mean for the second gene ...
8
votes
1answer
476 views

Does Monte Carlo == apply a random process?

I never had a formal statistics course but due to my line of research I'm constantly coming across articles which apply several statistical concepts. Often I'll see a description of a Monte Carlo ...
3
votes
1answer
105 views

Estimating quantiles by simulation

I'm a bit confused about how I would go about estimating quantiles by simulation. Say I have some statistical model $f(x,\theta)$. I can estimate the parameter $\theta$ and am able to generate random ...
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0answers
41 views

How can I sample multivariate binary variables such that sum of them follows a gamma distribution?

Edit: Since the original question was confusing as whuber pointed out, let me rephrase the question with a Poisson distribution instead of a gamma distribution. The energy term of a Poisson ...
4
votes
1answer
455 views

How to create a toy survival (time to event) data with right censoring

I wish to create a toy survival (time to event) data which is right censored and follows some distribution with proportional hazards and constant baseline hazard. I created the data as follows, but I ...
3
votes
1answer
78 views

Residual based bootstrap autoregressive series in MATLAB

I have defined the model as follows. Let $$y_1 = 0$$ and $$ y_i = \alpha + \beta y_{i-1} + \epsilon_i $$ for $i_2\ldots i_T$, where $\alpha$ and $\beta$ are the estimated coefficients and ...
0
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0answers
62 views

MonteCarlo simulations to test light curve variability

I have an average orbital light curve for a source, that is, binned count rate vs orbital phase, where the count rate are averaged over a number of orbit. I want to run MonteCarlo simulations to find ...