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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multi-dim monte carlo integration -- some complicated integration
I want to integrate
$$I= \int^1_0 \int^1_0 \frac{g(x,y)}{\int^1_0 h(x,y)\,dx} \,dx\,dy. $$
For now, I sampled $n \times n$ simulation samples from $unif[0,1]$ and estimate
$$\hat{I} = n^{-2}\sum_{j}...
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Using a single sample sequence for estimates of several integrals whose integrands have disjoint support
Let
$(E,\mathcal E,\lambda)$ be a measure space
$f:E\to[0,\infty)$ be $\mathcal E$-measurable with $\lambda f<\infty$
$q:E\to[0,\infty)$ be $\mathcal E$-measurable with $\lambda q=1$ and $$\{q=0\}\...
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Estimate $\lambda\frac{|f-\lambda f|^2}p$ without looping twice
Let $(E,\mathcal E,\lambda)$ be a measure space, $p$ be a probability density on $(E,\mathcal E,\lambda)$ and $f\in\mathcal L^2(\lambda)$. Say I want to estimate $$\int_{\{\:p\:>\:0\:\}}\frac{|f-\...
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Convergence of Diffusion Process Monte-Carlo
Let $X_t$ be a $d$-dimensional diffusion process initialized at $x \in \mathbb{R}^d$; given as the strong solution to the SDE
$$
X_t = x + \int_0^t a(t,X_t)dt + \int_0^t b(t,X_t)dW_t;
$$
where $a$ and ...
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Use of the inversion method in sequential sampling to "invert" a random walk
Let $M\subseteq\mathbb R^3$ be Borel measurable, $\lambda$ be a $\sigma$-finite measure on $\mathcal B(M)$, $k\in\mathbb N$, $I:=\{0,\ldots,k\}$, $q$ be a probability density on $\left(E^I,{\mathcal E}...
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Issue about confidence interval on OLS intercept
Let us assume this simple linear model: $Y|X=\beta_0+\beta_1X+\epsilon $
where $X \sim N(\mu,\sigma^2)$ and $\epsilon \sim N(0,\sigma_{\epsilon}^2)$
Suppose also that $X$ and $\epsilon$ have all ...
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Minimizer of $\int\mu({\rm d}x)\int\kappa(x,{\rm d}y)|g(x)-g(y)|^2$ for a jump kernel $\kappa$ of the Metropolis-Hastings algorithm
Let $\kappa$ be a sub-Markov kernel on a measurable space $(E,\mathcal E)$ and $\mu$ be a probability measure on $(E,\mathcal E)$ reversible with respect to $\kappa$. Assume $\kappa$ and $\mu$ admit a ...
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Use both historical prices and fundamentals data for predicting portfolio profit?
Get highly accurate probability distribution for the future price of portfolio using all the data available.
Each stock has two historical data - daily prices (scalar time series updated daily) and ...
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How to understand 4 steps of Monte Carlo tree search?
From many blogs and this one https://web.archive.org/web/20160308070346/http://mcts.ai/about/index.html
We know that the process of MCTS algorithm has 4 steps.
Selection: Starting at root node R,...
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Evaluating Likelihood in Bootstrap Particle Filter
I am currently struggling with an attempt to apply a bootstrap particle filter to a linear, Gaussian state-space model
$$s_t=A\,s_{t-1}+B\,\nu_t\qquad\text{( transition equation )}$$
$$\qquad z_t=C\,...
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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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Intuition for MCMC and stationary distribution?
Studying up on Markov-chain Monte Carlo sampling and the theory behind the stationary distribution, I want to validate it.
Say we have a stochastic transition matrix $p$ describing events in space $\...
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Estimating probability density function of big amount of data coming from MC simulations
I am trying to estimate Probability Density Function (PDF) of a big amount of data ($1e^6$ , $1e^7$, and higher) coming from Mote Carlo (MC) simulation.
My objective is to estimate the PDF (e.g. with ...
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Monte Carlo Simulation (or bootstrapping ) mutually exclusive events
Say event A probability of happening in a day is 1%; event B probability of happening in a day is 5%. Assuming they are independent, if I want to build a simulation model to simulate 1000 days, and ...
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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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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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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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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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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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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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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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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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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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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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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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