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

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'invalid file specification' when running Monte Carlo simulation [migrated]

I programmed the monte carlo simulation down below. The simulation itself works, but I do not seem able to summarize it. When I run my full program, the do file automatically ends after the monte ...
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9 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 ...
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13 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 ...
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1answer
50 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 ...
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21 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 ...
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1answer
30 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 ...
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1answer
49 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 ...
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1answer
23 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. ...
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35 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 ...
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35 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 ...
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39 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 ...
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11 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 ...
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1answer
50 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 ...
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1answer
38 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 ...
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1answer
468 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 ...
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1answer
65 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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39 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
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1answer
273 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 ...
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1answer
65 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 ...
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55 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 ...
2
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2answers
426 views

Metropolis-Hastings Algorithm within Gibbs Sampling

I have this $f$ function below. $$ f(x_1,x_2)\propto \left(\dfrac{x_1}{x_2}\right)\left(\dfrac{\alpha}{x_2}\right)^{x_1-1}exp\left\{-\left(\dfrac{\alpha}{x_2}\right)^{x_1} \right\}I_{R^+}(x) $$ where ...
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442 views

Is Markov chain based sampling the “best” for Monte Carlo sampling? Are there alternative schemes available?

Markov Chain Monte Carlo is a method based on Markov chains that allows us to obtain samples (in a Monte Carlo setting) from non-standard distributions from which we cannot draw samples directly. My ...
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29 views

Marginal distribution MLE or MCMC

I'm a bit confused about how to maximise the following likelihood: $\mathcal{L}(k, \lambda, p) \sim \mathrm{Binomial}(n, k, p)\mathrm{Poisson}(\lambda, n)$ i.e. my probability is relatd to a number ...
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2answers
189 views

What is this trick with adding 1 here?

I was looking at this page on Lillefors test's Monte Carlo implementation. I don't understand this sentence: There is random error in this calculation from the simulation. However, because of ...
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23 views

cumulative uncertainty with time series predictive model

So I have a time-series with a set of variables a, b, c... and another measured variable y. What I do is using the initial state of a,b,c and y (at t0), I predict what y "should" be at the next time ...
4
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1answer
181 views

Monte carlo simulation in R

I am trying to solve the following exercise but I actually have no clue on how to start doing this. I've found some code in my book that looks like it but it's a completely different exercise and I ...
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1answer
71 views

Information theory without normalization

I'd like to know if there is a way anyone knows of for doing information theory with unnormalized densities. Specifically, I hav two log likelihoods $\phi(x), \psi(x)$ and so I can write: $p(x) = ...
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14 views

What sort of data would be appropriate to analyze under an MCMC method?

MCMC methods describe stochastic sampling but I'm not entirely sure the contexts in real datasets one would wish to apply MCMC methods. What kind of data could I gain insight into with MCMC methods?
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24 views

Comparison of MCMC methods? [closed]

Where can I find a good comparison of Gibbs, Metropolis, and Hybrid MCMC in R or Python? I have thus far found this ...
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1answer
84 views

Error bars on log of big numbers

I am calculating a quantity of the following form: $\mu = \log( \frac{1}{n} \sum_{i=1}^{n} e^{\phi(X_i)} )$ via MC. $X_i$ are iid and I can sample them. I want to give error bars\ confidence ...
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1answer
43 views

Where should randomness come from in the Monte Carlo simulations?

Suppose that I want to check how good OLS works in some specific environment using Monte Carlo. I can simulate $Y=X\beta+\epsilon$. What should I do in Monte Carlo simulations, do I simulate the whole ...
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Are all simulation methods some form of Monte Carlo?

Is there a simulation method that is not Monte Carlo? All simulation methods involve substituting random numbers into the function to find a range of values for the function. So are all simulation ...
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1answer
37 views

Sampling Order Statistics for Numerical Integration

This may be a stupid question. I want to do Monte Carlo integration over a region $$ {\int}_{D_{1} \geq D_{2} \geq ... \geq D_{m} \geq 0} g(d_1,\ldots,d_m) f(d_1) f(d_2) \cdots f(d_m) ...
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135 views

Simulation of Monte Carlo test

Using R, I am trying to simulate how the power of a Monte Carlo two-sample test for central tendency changes with sample size. However, my simulation results does not show power increasing with sample ...
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111 views

Combine several different sets of Linear Square Monte Carlo (LSMC) or Model Average

I am doing a project similar to LSMC (Linear Square Monte Carlo) for prediction. A Monte Carlo simulation engine is used to produce results, and a linear model is built on the same inputs and ...
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52 views

Monte-Carlo Simulations with multiple random variables

I have the following observation model : $y_i=x_i+a_i$, where $a_i$ is a Gaussian random variable whose mean is function of a uniform random variable $b_i$. I have designed, $\hat{x}_i$, an estimator ...
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1answer
53 views

What to do when rejecting a proposed point in MCMC?

I'm writing a simple Metropolis-Hastings MCMC algorithm. Every time a move gets accepted, the point is added to a list of accepted points. I wonder what exactly I should do when a proposed move has ...
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1answer
40 views

On approximating the MSE of an estimator

I'm trying to approximate the MSE of an estimator through simulation, in particular estimators of the form $$ \hat{\theta} = \sum_{i=1}^N w_i X_i $$ Where $X = \{X_1,...,X_N\}$ are i.i.d. samples ...
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1answer
43 views

Does Accept - Reject Algorithm Monte Carlo help fit a distribution to the data?

As far as I understand the Accept - Rejection Algorithm is used to help us simulate hard to simulate densities or unknown densities by first simulating an easy density and then accepting or rejecting ...
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22 views

Simulation of CI of amount of values in different intervals by adding noise to original data

I am having a hard time trying to solve this problem, so maybe some of you guys can sort it out. I have a large data set containing a value describing the thermal comfort in buildings called PMV. The ...
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334 views

How to interpret the results of bootstrapping and Monte Carlo simulation utilised to test lasso logistic regression results?

My situation: sample size: 116 binary outcome (32 events) number predictors: 42 (both continuous and categorical) predictors did not come from the top of my head; their choice was based on the ...
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1answer
46 views

Big Data Regression Coefficient Estimation

I am working on a very large data set (n = 6.5 million) and I am trying to come up with a simple linear regression between two variables. I am working in R and using a monte carlo style simulation to ...
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17 views

Need help with importance sampling over HUGE sample space

My underlying problem is fairly simple, but the sheer size is what is causing issues. I would like to use importance sampling, but am unsure about its implementation. Problem statement: We have $N$ ...
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35 views

Monte Carlo test for spatio-temporal randomness

I have a collection of discrete spatio-temporal observations $d(x,y,z,t)$ on the surface of a sphere. The data is sparse and is in the order of ~100 points, but there is a bimodal clustering of these ...
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30 views

How many models I need?

I am doing an estimation using a bunch of sparse data. Suppose that I have a 100x100 grid and 20 data is available on this 2D grid. One solution is to use a determiastic method and estimate the other ...
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36 views

Selection of failed fitting results in MC Simuation

I recorded a set of experimental rates $r = r(c,T,P)$ at 2 values of $c$ and >15 values of $T$. $r(c,T,P)$ obeys the following functional form: $$ r(c,T,P) = ...
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1answer
38 views

Run Many Small or a Few Big Simulations to Estimate the Mean?

I was just running some simulations on tossing a coin given certain conditions, to test out some ideas I had. I was trying to find the ratio $\frac{\mathtt{successful\ tosses}}{\mathtt{total\ ...
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2answers
120 views

Normal Distribution with random mean and standard deviation

When trying to code this in R, I'm getting very confused about what to do. Apologies if my terminology is incorrect but I would be grateful for any advice. The Problem: I have been given two normal ...
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3answers
234 views

Simulation involving conditioning on sum of random variables

I was reading this question, and thought about simulating the required quantity. The problem is as follows: If $A$ and $B$ are iid standard normal, what is $E(A^2|A+B)$? So I want to simulate ...
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30 views

Testing if points on a line are over/under dispersed

I have a series of about 1000 points on a chromosome and I want to know if they are clumped, over-dispersed, or neither. The chromosome can be viewed as a 1-dimensional. I've looked over some ...