# Questions tagged [monte-carlo]

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

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### Is this an appropriate use of bootstrapping? variability in a fleet's fuel economy

I have a data set consisting of the make and models of a diverse fleet of vehicles (e.g. 100 Honda Civics, 200 Ford F150s, 10 Tesla Model 3s). My goal is to estimate the average fuel economy of the ...
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### Monte Carlo and random walk

Can a Monte Carlo-Simulation be considered as a kind of ensembles of random walks?
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### sampling from an unknown bivariate distribution

I want to generate samples from a bivariate distribution whose joint PDF doesn't resemble any known distribution.  I have two events A and B where B depends on A. I have empirical observations of ...
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### Behavior of kernel density estimation

Consider the random variable $X=YZ$, where $Y\sim\text{Normal}(0,1)$ and $Z\sim\text{log-Normal}(0,1)$ are independent. I wanted to assess the accuracy of kernel density estimates for the density ...
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### Is two group comparison test combinig rarefaction and permutation usefull and correct?

I wish to know if the analytical procedure using R environment described below is statistically coherent to enable interpretations and conclusions. I looking for evaluations and opinions about the ...
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### Monte Carlo simulation percentile convergence

Suppose I have a normal distribution random variable $X$ with mean $\mu$ and variance $\sigma^2$. I can easily calculate the 99.7 percentile, which $\approx\mu+3\sigma$. In the Monte Carlo simulation ...
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### type I error using montecarlo method in R

i want to calculate the type i error rate and power for the correlation test for bivariate normal data using Monte Carlo simulation. But i am getting unexpected values for the type I error and for ...
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### Help finding central limit theorem approximations - Normal Distribution Equation

I was given f(x)=|x| as a probability distribution. I've summed the results of a Monte Carlo with N terms and plotted a thousand of these sums in a normalized histogram. Now I need to compare this ...
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### How to find the power of a permutation test?

I am new to the permutation test and has found some online resources to learn how to conduct the permutation test. But I have yet to find a good explanation of how to find the power of a permutation ...
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### Gibbs sampler from from $p(x) = C g(x)$ with $C$ unknown and discrete elements in $X$

By using the Hasting-Metropolis method, is there a way to draw samples from a distribution of this form: $$p(\textbf{x}) = C g(\textbf{x})$$ For $x$ being two dimensional and discrete. The reason that ...
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### Sample a probability distribution with an evolutionary algorithm?

I've been doing some initial level reading on Markov chain Monte Carlo (MCMC). For what I can tell given a probability distribution $P(x_1, x_2, ..., x_N)$ (dependent on $N$ parameters), MCMC ...
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### Pi using Monte Carlo on Circular Crown (an Annulus)

I am a computer science student and I am currently studying (for fun if you could say that) during my college break, I was implementing a simple program to calculate pi using the Monte Carlo method by ...
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### How can I find the probability distribution function from the observed data to use in a Monte Carlo Simulation?

In exploring a data set, I think I've found an interesting instance where using a Monte Carlo method to plot a simulated group of points could yield somewhat accurate results. The plotted data looks ...
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### How do I handle first-stage estimation error in a two-stage simulation?

I have a variable $v \sim N(0, 1)$ (i.e., mu=0, sigma=1). Every day I estimate $v$'s interquartile range (IQR). Instead of using the empirical IQR, I estimate $v$'s mu and sigma from 24 hourly ...
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### Method for Sampling High Dimensionality Simulation (similar to Latin Hypercube Sampling)

I need to calculate the expected outputs (Yj) from a large non-linear simulation model (Mj) which takes 2^N possible input strings (Bi), each with known probability fi (simple binomial). N is ...
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### Simulating Monte Carlo p-values (t-distribution)

Suppose we are interested in testing the null hypothesis that the mean of a normal population is 10 against the alternative that it is greater than 10. A random sample of size 20 from this population ...
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### What is the point in using Monte Carlo methods to measure statistical estimators?

Let's say I have a dataset that is 100 elements long, $X = \{x_0...x_{100}\}$ and I do 1,000 Monte Carlo realizations of the data, $X_j, 0\leq j \leq1000$, sampling 10 points each time. If I then ...
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### Poker Equity Calulator

I am writing a tool that calculates the chance of winning a poker hand. Without going into the rules each player has 2 hole cards and there are 5 shared cards on the board. From 2 cards in the ...
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### Efficiently sampling from Markov Chain with low-probability transitions

I need to sample a large number of paths from a Markov Chain with known state transition matrix $T$, where some of the state transitions are low probability (~0.01%). For example, I might have a large ...
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### Monte Carlo Simulations: Can I Use Real Data as Universe?

In Monte Carlo simulations, it is a commonly used procedure to generate synthetic data based on a large survey (e.g. a microcensus) first. These synthetic data is then used as universe/population for ...
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### uncertainties from Monte Carlo simulation and error propagation are different

Inspired by this post Is Monte Carlo uncertainty estimation equivalent to analytical error propagation?, I try to check it myself using a simple function f=A/B, where A is 10 with uncertainty 1 and B ...
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### Likelihood that a given outcome was generated by a Markov model

I am new to the concept of Markov Models and Markov Chain Monte Carlo simulations. I would like to take a piece of data and determine the likelihood that it was generated by a known MCMC model/...
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### improving accuracy for sample skewness and kurtosis under Student's t distribution with low degrees of freedom

There is no skewness in Student's t distribution. Given the degrees of freedom, the kurtosis estimator is given by $\frac{6}{\nu - 4}$. However, when sampling form a t-distribution with low degrees of ...
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### How to report a convergence on a random walk on Markov Chain Monte Carlo

In our psychology experiment we have found Markov Chain transition probabilities to be a good way to analyse data, and the convergence of two Markov Chains on a random walk (we used 10,000 walks) to ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...