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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Monte Carlo simulation from autocorrelated empirical distribution

So I'm trying to perform a Monte Carlo simulation an empirical distribution of log-return time series data. However, Ljung-Box test indicates that there is significant autocorrelation at multiple lags....
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Sequential monte carlo : A simple example

I am attempting to understand how to implement the sequential monte carlo algorithm using this article. Here are the steps that the author proposes: Example problem: Say I have a self moving robot ...
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47 views

Generate pseudodata by Monte Carlo

What does it mean for "Generate pseudodata by Monte Carlo"? For the text I was reading it says suppose that the real data $Z_n \sim N(\mu(\theta), \Sigma (\theta))$, then the pseudodata are generated ...
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39 views

How to do Monte Carlo with conditional input values?

Please apologise my likely ignorance of the correct terminology and notation. Any edits and suggestions to improve the question are very much appreciated. I want to perform a Monte Carlo simulation ...
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80 views

Monte Carlo Metropolis: Standard Error and Acceptance

In a time series data generated by Monte Carlo Metropolis algorithm, when is the standard error (correlation between two data points is assumed to be negligible) is higher - when the change in the ...
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31 views

Monte Carlo Sample input into OLS Regression

I am trying to find the best way to conduct a risk-based regression study. I have distribution data for both X and Y and used a monte-carlo sampling of the distributions to generate a data set. I then ...
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500 views

How to simulate data for generalized estimating equations (GEE) with logistic link function?

I am working with a pre/post test structure, measuring dichotomous outcomes. I am using GEE to estimate the coefficient for time (also a binary variable, 0 representing pre and 1 representing post), ...
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162 views

Standard Error in Auto correlated Data

I have time-series data generated via Metropolis algorithm - Monte Carlo simulations. Since these data must have some correlation between them, the formula of the standard error for IIDs variable must ...
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95 views

Monte Carlo / bootstrapping to generate a Kaplan Meier curve

I have 4 survival datasets from 4 different trials examining 2 different drug classes independently. I would like to model the likely survival curve resulting from a pooled selection of either drug ...
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60 views

Comparison of results of monte carlo simulations

I am doing monte carlo simulations. In the first run the experiment is repeated e.g. 10000 times. The result looks like x+/-y, y is the relative error. Next, I change a part of the experiment and run ...
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117 views

Unbiased sampling and subsampling

Suppose I have a distribution $\mathbb{F}$ with mean $M$. Also, assume we have a set of i.i.d samples of size $n$ denoted by $X=\{x_1, x_2,..., x_n\}$ from $\mathbb{F}$. As a result, all $x_1, ..., ...
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282 views

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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339 views

Is Monte Carlo Tree Search policy or value iteration (or something else)?

I am taking a Reinforcement Learning class and I didn’t understand how to combine the concepts of policy iteration/value iteration with Monte Carlo (and also TD/SARSA/Q-learning). In the table below, ...
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77 views

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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327 views

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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106 views

Applying MCMC Bayesian estimation to simple 2D problem

I'm having a conceptual problem applying Markov Chain Monte Carlo for Bayesian parameter estimation; I know how MCMC works in principle but it's applying it to this problem that troubles me. The ...
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24 views

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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121 views

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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85 views

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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100 views

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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45 views

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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92 views

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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62 views

Is there any particular converging pattern for Least Square Estimators and Maximum Likelihood Estimators when we increasing the sample size?

My questions is: Is there any particular converging pattern for Least Square Estimators and Maximum Likelihood Estimators of Weibull distribution when we increase the sample size? is there any ...
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598 views

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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28 views

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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215 views

How can bootstrap be used to establish confidence intervals for Theil regression parameters?

In References for methods for calculating the confidence interval for Theil-Sen Estimator, we note that Wilcox (1998, 2009?) proposed the use of bootstrap as a method for finding confidence intervals ...
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64 views

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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86 views

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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442 views

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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1k views

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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46 views

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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466 views

Sobol variance based decomposition

I have 6 input variables, each of which is normally distributed. Can I use Sobol variance-based sensitivity analysis? I have read some articles where they said that input variables must have uniform ...
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203 views

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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57 views

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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174 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 ...
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35 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 ...
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106 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 ...
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117 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 ...
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68 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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102 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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1k 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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26 views

Uncertainty analysis

Here is my situation. I am trying to predict the 'entire' distribution of the dependent variable, not just the mean( or conditional mean). Does it then make sense to seprateley predict quantiles of ...
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292 views

Box-Muller algorithm and Monte Carlo Integration

Can someone help me out here? Using Box-Muller would generate N(0,1) however X ~ N(-1, 4). How do I transform the variables to the distribution of X? And would the pseudocode include the usage of the ...
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291 views

Understanding a double peaked distribution

I am running a Monte Carlo Simulation and am sampling randomly from about 65 Normal Distributions, each with a different $\mu$ and $\sigma$. I end up with the Mixture Distribution graph shown below ...
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107 views

Error Bars in a Monte Carlo Coin Experiment

An excel program runs a Monte Carlo coin experiment. 10,000 coins are tossed 1000 times, with the number of times ...
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938 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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