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

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2
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17 views

G-test vs Pearson's chi-squared test

I'm testing independence in an $N \times M$ contingency table, I don't know which of the G-test or Pearson's chi-squared test is the best ? The sample size is in the hundreds but there are some low ...
1
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0answers
9 views

convergence of MSE (mean square error) using Sequential monte carlo

I am using sequential monte carlo method for a regression problem with bayesian estimation . I am trying to find a measure to confirm that my distribution has converged to the actual posterior ...
1
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0answers
18 views

understanding and reporting results from monte-carlo simulation

I apologize upfront if the the question is vague. Basically I have results from monte carlo simulation and I'm trying to understand how to present the results and importantly the "why" part of the ...
3
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1answer
91 views

What is this random number generation algorithm and why does it work (or does it)?

Found the following (Monte Carlo) RNG algorithm in a certain article. Let $f(x),f:\mathbb{R}^n \rightarrow \mathbb{R}$ be the function from which the samples are desired. Draw a random point $x \in ...
0
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0answers
13 views

Determining distribution type in Python?

What is the best way to determine what type of distribution data has in Python? I am looking at daily data and I want to be able to run some scenarios and Monte Carlo. I was using np.random.normal to ...
0
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0answers
37 views

Average of Monte-Carlo estimates: Increasing observations vs. iterations

In the context of Monte Carlo simulations, I would like to understand better the difference between increasing the number of iterations vs. the number of observations. As an example, please consider ...
2
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1answer
26 views

Can Metropolis be considered as evolutionary algorithm?

If we compare simple 1+1 evolutionary algorithm (e.g. Droste, Jansen, and Wegener, 2002) 1+1 evolutionary algorithm Set $p_m := 1/n$. Choose randomly an initial bit string $x \in ...
1
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1answer
21 views

Gibbs sampling for inferring the parameters of a GMM

I came across the following in Kevin Murphy's "a probabilistic perspective on machine learning". I am struggling to understand the derivation of the conditional probability for $z_i$. I tried ...
1
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2answers
42 views

Number of samples needed in Monte Carlo simulation: how good is this approximation?

In Risk Theory Beard, Pentikanen and Pesonen (1969) mention a method of assessing number of samples needed for Monte Carlo simulation as $$ \sigma = \sqrt{\frac{p(1-p)}{s}} \leq \frac{1}{2} \sqrt{ ...
0
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0answers
17 views

Detecting Gibbs Sampler convergence with Raftery and Lewis Diagnostic

Hi! I'm trying to understand and implement the Raftery and Lewis Diagnostic for detecting the number of iterations required for a gibbs sampler but cant seem to understand the formula. ...
0
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1answer
17 views

Multivariate Box Muller

i am reading "machine learning - a probabilistic perspective" by Kevin Murphy - who states the following in the chapter on monte carlo inference. i understand that cov[y] = $\Sigma$, but i do not see ...
0
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1answer
32 views

How do I split a normal distributed sample into groups of percentiles but with an additional random noise component for uncertainty?

I have a sample of students that I want to divide into smaller groups based on a their IQ but with a certain random noise component - how can I do that? I need to cluster the best, the average and ...
1
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0answers
22 views

Sampling correlated categorical variables

I am looking for a way to sample correlated categorical (non-binary) variables, and in particular I am interested in the category counts: I have a set of $n$ correlated categorical random variables ...
0
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1answer
18 views

Rationale for MCEM

From what I've read, the main advantage of the EM algorithm is that the expectation step can be expressed in closed form giving a deterministic answer and thus 0 variance. What's the rationale then ...
0
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0answers
13 views

Evaluation of the semi-closed Heston pricing formula for call options

I'd like to know, how the integral part of the semi-closed Heston pricing formula for call options can be simulated for a given set of model parameters. Monte Carlo simulations shoud work for this ...
0
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0answers
17 views

Standard Error of dependent variable

I am estimating a regression where a variable depends on several lags of another variable, which represents some kind of shock. I have the mean and standard error of each of these lags, but I need to ...
0
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0answers
12 views

Using Monte Carlo to calculate lagged effect of shock in multivariate regression

I'm new to Stack Exchange. I am working on my master's Thesis (finance) and I have one question that I would like to share. I am reading Romer & Romer (2004), where they estimate the following ...
0
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0answers
15 views

Explanation of mcstoc from empircal distribution in mc2d

I'm using the mc2d package to simulate from a cost distribution. I have lots of data so rather than fit a weibull or some such, I want to just estimate from the empirical. Below I show you the data ...
0
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1answer
60 views

Getting Expected Value from Monte Carlo Simulation

There are two independent uniform continuous random variables $X$ and $Y$ (such that $0 \leq X \leq 10$, $0 \leq Y \leq 10$). The function $f$ is the difference between the two random variables ...
2
votes
1answer
33 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
44 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
votes
1answer
58 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
80 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
68 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
32 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
10 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
53 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
votes
1answer
86 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
votes
1answer
32 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
42 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
77 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 ...
5
votes
2answers
321 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
56 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
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2answers
105 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
60 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 ...
0
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0answers
19 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
27 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 ...
2
votes
2answers
51 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
54 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
34 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
votes
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
41 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) ...
1
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0answers
24 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
86 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
123 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
156 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
116 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
158 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 ...