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

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2
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1answer
29 views

Which distribution is correct in modeling conversion rate in a Monte Carlo

I am building a model for a Monte Carlo simulation that estimates the number of sales made for a door-to-door salesman. Looking at his historic success by city, it seems he converts about 80% +/- 20% ...
0
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0answers
20 views

What's the difference between Monte Carlo simulation and sensitivity analysis? [on hold]

What's the difference between the two? In what situations would you choose one over the other? What do they each output?
0
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0answers
42 views

How to use variation in MLEs to construct a new PDF?

My simulation has 8 uncertainties and 1 output quantity of interest: Satellite mass. Each uncertainty is characterized by a Gaussian distribution. For a large number $N$; I feed these $8 \times N$ ...
2
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1answer
45 views

Simulating random variables given partial distributions and correlation

After Monte Carlo simulations I obtained approximated distributions for X and Y. Now I want to add some form of correlation between them. To simulate random variables from a distribution the idea is ...
0
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0answers
62 views

Simple Monte Carlo for task estimation

I want to simulate using Monte Carlo how confident I can be about my task estimates. So I think I can simulate and draw a curve. (e.g) So if 30% of the time my tasks can be completed within my ...
2
votes
1answer
63 views

Computation of expected values

I have a $N$-dimensional (normal) random vector $\mathbf{X}$, where $N$ is large, and a function $f : \mathbb{R}^N \to \mathbb{R}$. My goal is to compute $\operatorname{E}[f(X)]$ or at least ...
0
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0answers
26 views

Markov Modeling, My repair is constant and not memoryless

I want to calculate a markov model, but there is a problem; my repairing transition is not memoryless and it's constant for every time that it will happen.(Markov model consider all of transitions are ...
0
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0answers
9 views

“Best” sequence of halton in more dimensions?

I want to use the Halton sequence for a monte carlo simulation with more dimensions (3 dimensions). Because I know that some combinations of base value of the Halton sequence gives a non-random ...
1
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1answer
35 views

How can a 95% confidence interval not overlap with my trendline forecast?

I used holt winters in excel to forecast 12 moths ahead based on 40 months of historic data. Then I ran a monte carlo simulation to create 1000 scenarios and computed upper and lower bounds to create ...
2
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1answer
85 views

MCEM algorithm in normal distribution

Consider $z_1,\ldots,z_n$ as a sample of observations of $Z$ and $y_1,\ldots,y_n$ the missing data, where $Z\sim N(\mu,\sigma^2+1)$ and $Y\sim N(0,1)$. i)Find the expression of ...
0
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1answer
28 views

Particle Filter Inefficiency

As I understand it, Particle Filters are a Monte Carlo method to narrow down a search space and find a posterior through a survival-of-the-fittest type method. The particular application of Particle ...
1
vote
1answer
32 views

SEM - sample size and power

Muthén & Muthén offer a MPLUS based syntax for calculating sample size and power on SEM, using a Monte Carlo simulation. https://www.statmodel.com/download/FinalSEMsingle.pdf Is there any ...
1
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0answers
63 views

Simulate from a dynamic mixture of distributions, honoring the tail

This question is a follow-up to this other question, brilliantly answered by Xi'an. I have a dynamic mixture of Weibull and GPD distributions (with a CDF Cauchy mixing function). The mixture is ...
4
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2answers
276 views

Simulate from a dynamic mixture of distributions

I need to sample from the following mixture of two distributions: $h_{\vec{\beta}}(r)=c(\vec{\beta})[(1-w_{m,\tau}(r))f_{\vec{\beta_{0}}}(r)+w_{m,\tau}(r)g_{\epsilon,\sigma}(r)]$ where ...
0
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0answers
23 views

How does R calculate prediction intervals in the forecast package?

I have a large dataset with different factors that I want to forecast to the future. These forecasts I will then later on use as inputs for a Monte Carlo simulation. My idea would be to use arima ...
2
votes
2answers
103 views

Nontrivially simulated distributions

I'm learning Monte-Carlo approach in sampling. There I faced with ways of how to draw samples from given distribution. But can you give me an example of a distribution which can not be trivially ...
-1
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1answer
43 views

Interpretation of Monte Carlo results - R

I have a question regarding the interpretation of Monte Carlo results. I am applying the Monte Carlo simulations to an estimate process about development team size. The input distribution of the ...
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0answers
11 views

Monte Carlo mc2d package, levels of uncertainty

I have the following question regarding the mc2d package for Monte Carlo simulations. Given a mc node, i.e. a mc object. How can we get the uncertainty for the values of the distribution? For ...
1
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0answers
20 views

Monte-Carlo simulation of repeated-measures ANOVA

I want to conduct a Monte-Carlo simulation of a repeated-measures ANOVA. The random numbers used for the simulation need to have specified mean values, standard deviations and correlations between the ...
1
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2answers
41 views

averaging after n trials of monte carlo simulation or not? which is better statistically?

related to my job I want to code a realistic monte carlo simulation for availability, reliability and related sensitivity analysis. Scenario will be complex and there will be many parameters. What I ...
0
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0answers
7 views

Deriving conditional distributions for a normally distributed change point problem

So, considering the change point problem of $y_i \left\{ \begin{array}{ll} y_i \tilde{~} N(u_1, \sigma) & i=1,..,t \\ y_i \tilde{~} N(u_2,\sigma) & i= t+1,...,n \\ \end{array} ...
5
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0answers
47 views

Metropolis-Hastings integration - why isn't my strategy working?

Assume I have a function $g(x)$ that I want to integrate $$ \int_{-\infty}^\infty g(x) dx.$$ Of course assuming $g(x)$ goes to zero at the endpoints, no blowups, nice function. One way that I've been ...
1
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0answers
27 views

Monte-Carlo Weather Simulation

I have a trained model that predicts some interesting things (like energy usage) based on the weather (temperature, humidity, etc.). I would like to run a monte carlo on the model and get a ...
2
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0answers
24 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
29 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 ...
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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) ...
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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
66 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
115 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
150 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
votes
4answers
115 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 ...
0
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2answers
107 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 ...
4
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1answer
49 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
18 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
31 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 ...
2
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0answers
40 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
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1answer
27 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 ...
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0answers
12 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
59 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
135 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
51 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
50 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
47 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
27 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 ...
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0answers
44 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 ...
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0answers
23 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
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1answer
51 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
35 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
50 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 ...