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

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35 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
16 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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5 views

montecarlo study using Stata [migrated]

I regressed y one simulated variables as follows: ...
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0answers
30 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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0answers
28 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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0answers
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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9 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
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1answer
39 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
34 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
460 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
53 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
33 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 ...
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1answer
214 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
58 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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0answers
46 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 ...
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2answers
395 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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428 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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28 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
180 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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22 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
151 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 ...
2
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1answer
68 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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21 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
78 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
34 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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112 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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100 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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48 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
50 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
34 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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0answers
21 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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267 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
43 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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34 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
36 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
112 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
223 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 ...
2
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0answers
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 ...
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20 views

significant differences between time series - Monte Carlo simulation

I would like to test if there are significant differences between 3 time series. First, I thought to run a simple chi square test, then a Monte Carlo simulation. Comparing the two methods: P-values ...
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0answers
14 views

Restricted Boltzman Machine Non-Hidden Layer Approach

An RBM is defined by the joint probability distribution $$p({\bf x},{\bf h})=\exp(-E({\bf x},{\bf h}))/Z$$ where $$E({\bf x},{\bf h})=-{\bf h}^TW{\bf x} - {\bf c}^T{\bf x} - {\bf b}^T{\bf h}$$ ...
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230 views

Forward Filtering Backwards Sampling (FFBS) and Look-Ahead Bias

Assumptions / Context: Let's assume that I have data that can be modeled as a dynamic linear model. To estimate the parameters (e.g., covariance matrix of the state/system equation), I use a Gibbs ...
2
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1answer
36 views

Refining Monte Carlo predictions using observed measurements

I'm trying to build a monte-carlo simulation that can revise it's distribution of outcomes of a project based on observed measurements after the project has started. I have a few questions about the ...
2
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42 views

Monte Carlo simulation of investment account

I'm trying to estimate performance of an investment account over 20 years. The question is, have I set up the Monte Carlo simulation correctly? I've used Excel. I've assumed 8% average return and 13% ...