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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Estimation Error Calculation
I'm learning about variance reduction for Monte Carlo methods and I am confused about how to calculate the "estimation error" of a given method.
My question is how should I interpret "...
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Integral of normal likelihood and multivariate normal prior
I'm updating cluster assignments in the context of a non-parametric Bayesian mixture model. When computing the probability of starting a new cluster, in the absence of cluster parameters (and using a ...
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Estimating standard deviation of a posterior generated by importance sampling MC uncertainty propagation [closed]
If I want to the esimate the statistical properties of a black-box model with uncertain parameters with known distributions, I can quite easily run an MC simulation to generate a histrogram of model ...
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Monte Carlo simulations and sum of normal distributions
I am trying to predict the revenues of a portfolio of items. I want to simulate the revenues in a particular market situation in which they might increase. Each item's revenues is made up of 3 ...
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Can I do a meta-analysis by Monte-Carlo synthetic data?
I'm trying to do a meta analysis of ~30 studies (total N = ~2000) on the correlation (X, Y). However, the heterogeneity is soooo high. My hypothesis (and what has been suggested in the literature) is ...
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In practice, should I use k-fold cross-validation or repeated random sub-sampling validation as my default choice of evaluating the model performance?
I was wondering if someone can shed some light on which cross-validation method should I, in general, use more often: k-fold cross-validation or repeated random sub-sampling validation.
From Wikipedia,...
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What are correlated errors and why are they important?
I am looking for help on correlated systematic errors, and their meaning. I have some quantities $x,y,z$ which determine a function I need to calculate. These 3 quantities are determined by a ...
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How to compute a rectangular credible region from samples
Given high-dimensional Monte Carlo samples $\bf{X_1},...,\bf{X_N}$ from a probability distribution $p({\bf x})$ in $\mathbb{R^d}$, I want to estimate a rectangular highest-density credible region for $...
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Monte Carlo Integration Results in Heavy Tailed Distribution
I am running a Monte Carlo simulation that results in an heavy-tailed distribution. The image below shows the distribution of 1,200 runs of the Monte Carlo simulation, where each run consists of ...
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Which are the statistical methodologies to consider when examining study group death rates but without considering time to death?
I have a dataset for a group of 66,000 subjects diagnosed with a dangerous condition, and the time it takes for death to occur (the “event”) or to not occur (survival or “censored”). I am pursuing ...
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Compare variance estimators in complex sampling designs by simulations
I need to find the best variance estimator of my parameter $\theta$ using complex sampling data. My survey data with dimension N are drawn with a two-stages stratified sampling.
I thus began from my ...
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Question on Equation 5.2 of Reinforcement Learning by Sutton and Barto
I'm currently studying the textbook Reinforcement Learning by Sutton and Barto. I can't seem to understand the derivation in Equation 5.2:
How did (a) become (b)?
In particular, why is the ...
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Effect of Simulation Error on the Monte Carlo Estimator
Given a random variable $X$ with known pdf $f$ and some computer simulation model $g(x): \mathcal
R \rightarrow \mathcal R$, mapping samples $x \sim f$ to a scalar metric $g$, we can estimate the ...
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Averages in Monte Carlo error propagation
I'm doing a Monte Carlo error propagation, so for $10^5$ iterations I:
generate a curve $y(x)$ choosing the parameters using a multivariate gaussian distribution.
generate a random point $x_k$ using ...
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How to choose priors for bounds on circular truncated distributions?
I am considering choices of priors for truncated distributions on a circle. Let's take the truncated normal distribution on the unit circle as an example. It has parameters $\mu \in [-\pi, \pi]$ and $\...
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How to use Monte Carlo simulation to get the conditional mean
Given the following assumptions:
$Z,Z'\in\mathbb{R}^4$ where $(Z,Z')\sim N(0,\Sigma)$, for some known $\Sigma\in\mathbb{R}^{8\times 8}$.
$Y=f(Z,u,\epsilon)=Z_1\boldsymbol{1}\Big[u<\frac{\exp(Z_3)}{...
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How to empirically check a PDF
Intro
Let $Y$ be a random variable whose PDF is $p_Y(\cdot)$. Let's say that $Y$ is a function $g(\cdot)$ of another random variable $X$ whose PDF $p_X(\cdot)$ is given. Then, you do your calculation ...
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Why does First-Visit Monte Carlo Prediction (Policy Evaluation) converge?
In Barto and Sutton's "Introduction to Reinforcement Learning" book, in Section 5.1 (Monte Carlo Prediction), they describe the First-visit (and every-visit) Monte Carlo (MC) methods for ...
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How to handle physically meaningless values in sampling?
I'm working on stochastic optimization for optimal energy dispatch, where the uncertainty of photovoltaic power output should be considered with monte carlo sampling and scenario reduction technique. ...
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Evaluate integral using R [closed]
I need to evaluate $\displaystyle{\int_{1}^{1}\int_{1}^{1}\int_{1}^{1}(y)e^{x+}}dxdz}$ using in R.
Here is my attempt:
...
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Data point selection from large unlabeled data pool in active learning
I am interested in using a Neural Network with Monte Carlo Dropout in my active learning pipeline, but my case is quite different from the examples described in the literature. I was inspired by the ...
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Generate a point cloud distributed according to a Boltzmann-Gibbs distribution with prescribed marginals
Let $p$ be a probability density on $\Omega\in\mathcal B(\mathbb R^d)$ for some $d\in\mathbb N$ (I'm primarily interested in $\Omega=[0,1)^d$). We can approximate $p$ by $$A_x(y):=\sum_{i=1}^k\varphi_{...
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Monte Carlo Dropout as surrogate model for Bayesian Optimization
I am interested in using Monte Carlo Dropout as a surrogate model for Bayesian optimization. I noticed that the paper states:
The use of dropout (and its variants) in NNs can be interpreted as a ...
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Simulation of correlated Bernoulli Random Variable [duplicate]
Let $\zeta_x$ and $\zeta_y$ be two Bernoulli random variables with value in $\{-1,+1\}$, and correlation$(\zeta_x, \zeta_y)=\rho$.
We know the values of $p^{x,y}=\mathbb P(\zeta_x=x,\zeta_y=y)$ with $...
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Subtracting Standard Deviation with Monte Carlo
I am looking for a way to reduce the variance/standard deviation of one distribution by another where the two distributions are not necessarily the same.
I have found that adding or subtracting two ...
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Suppose $f: \mathbb{R}^n \to [0, 1]$ is known, how to sample $x \in \mathbb{R}^n$ such that $f(x)$ follows uniform distribution? [closed]
Suppose $f: \mathbb{R}^n \to \mathbb{R}$ is known, where evaluation and gradient computation is easy. How can I sample $x \in \mathbb{R}^n$ such that $f_x \in \mathbb{R}$ follows uniform distribution? ...
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Is there a variant of the Metropolis-Hastings algorithm with proposal and/or acceptance function depending on the history?
Is there a version of the Metropolis-Hastings algorithm where either
the proposal kernel; or
the acceptance function
might depend on the whole history (or at least a part of it) of the chain so far?
...
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Example for Resampling in Sequential Monte Carlo
I am currently looking into SMC methods and especially resampling in this context. I know and understand the weight-degeneracy problem when leaving out the resampling step.
However, I am wondering if ...
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How to sample from a predictive distribution of a transformed quantity
Typically, it's easy to simulate from the predictive distribution for next observation, say $\tilde{y}$, after obatining the posterior distribution for $\theta$. We may first simulate a large number ...
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How to go about an optimization problem where posterior denstiy is involved
I am currently reading a paper by Yao et al.(2018) where they discussed about stacking bayesian prediction distribution for K models. I got the idea but I am not sure how you will implement it in ...
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Estimating fit parameter variance when the true distribution is unknown and systemic errors exist
I have a novel model for the errors that affect many types of qubits (quantum bits) and want to show my theory is correct. Visually it is great, but that is not quantitative.
I'm a theorist, while my ...
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Is this the correct approach to apply a MC simulation to a time series forecast?
I have a stationary time series. I have generated a daily forecast using a TBATS model to reflect seasonality at weekly and annual level for three months (with true values held back) based on three ...
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Is there a variant of the Metropolis-Hastings algorithm where the acceptance probabiltiy can depend on all states generated so far?
I wasn't able to find anything on google, but is there a variant of the Metroplis-Hastings algorithm where the acceptance probability (not the proposal kernel) in the $i$th iteration might depend on ...
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What is the expression for covariance in the context of Monte-Carlo estimator? [duplicate]
I am trying to calculate the variance:
$$
\langle(\bar{O}-<O>)^2\rangle
$$
of the Monte-Carlo estimator
$$
\bar{O}=\frac{1}{M}\sum_{m=1}^M{O_m}
$$
For uncorrelated samples.
In order to do so, I ...
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What is a mathematic rigorous definition of "blue noise"?
Let $d\in\mathbb N$, $I$ be a finite nonempty set, $(x_i)_{i\in I}\subseteq[0,1)^d$, $(w_i)_{i\in I}\subseteq[0,\infty)$ with $\sum_{i\in I}w_i=1$ and $$\sigma:=\sum_{i\in I}w_i\delta_{x_i}.$$
I ...
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Is it possible to calculate the SD of observations for a RR based solely on the confidence interval and mean?
Set up:
I have a epidemiological study with a dose-response curve with a series of relative risk estimates (risk ratio of mortality risk exposed compared to mortality risk unexposed) along a curve. ...
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Time complexity of Metropolis-Hastings and potential speed-up?
The MH algorithm essentially involves generating a sample destination state from a proposal distribution, computing the acceptance probability as a function of that sample, and checking whether a ...
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Does measurement non-invariance between groups matter in difference-in-difference designs?
Claim:
If a measure has a difference in measurement invariance (i.e. the measures are non-invariant) between two groups (say treatment and control), which is constant across time, then a difference-...
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Using Gibbs sampling to verify the analytical solution of 2D Ising Model
Suppose a 2-D Ising model on a period lattice $L\times L.$ I want to apply Gibbs sampling to verify the analytic solution of spontaneous magnetization in 2D Ising model given the Hamiltonian $H=-J\...
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Is there a Quasi-Monte Carlo variant of the Metropolis-Hastings algorithm which also works on a possibly inifinite dimensional state space?
In his thesis MARKOV CHAIN MONTE CARLO ALGORITHMS USING COMPLETELY UNIFORMLY DISTRIBUTED DRIVING SEQUENCES Tribble proves consistency of the Metropolis-Hastings estimator when the input sequence of ...
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Sampling from a distribution in Quasi-Monte Carlo methods
I'm new to Quasi-Monte Carlo, so this might be a dump question. Did I get this right that we assume that every sample is created by uniformly distributed random numbers on $[0,1)$ and we replace this ...
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Generate data from posterior predictive distribution [closed]
I am new to Bayesian. I want to draw data from the posterior predictive distribution p(y|D).
Do we need to find the CDF of the posterior predictive distribution and use the monte Carlo method or is ...
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How many Monte Carlo simulations must I run to get a 95\% confidence interval for some error $E$
Suppose I want to use Monte Carlo to compute some probability $p$. A single MC simulation will run for $R$ iterations and calculate $p$ as the fraction of 'successes'.
Say I want to compute $p$ within ...
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The Monte Carlo of the mean square error of the maximum likelihood estimates
I try to get mean square error of the maximum likelihood estimators in R (using Monte Carlo).
I can write the calculation for the MLE that is repeated once, but I need to repeat the Monte Carlo ...
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Sample size for each trial vs Number of trials conducted for Monte Carlo Simulation
I am running some Monte Carlo Simulations on Matlab. I am wondering if running more Monte Carlo Simulation trials and taking the average value of these trials is the same as running a single trial ...
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Monte Carlo Power calculation for Survival analysis in R
for a project I have to analyze two survival analysis treatment groups using R. I want to calculate the power and type I error rate of a test with Monte Carlo simulation to set up a phase 3 medical ...
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Why do we have first/every-visit in MC but not last visit [closed]
I'm studying Reinforcement Learning and I just read about first-visit and every-visit Monte Carlo, however I don't get why we are not considering last-visit MC as a possible simulation.
My "last ...
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How to evaluate the accuracy of probability of a large set of non-repeatable events?
Assuming there are a large set ($N>1000$) of independent events $E_i$ ($i=1,2,\dots,N$), each having $M$ different outcomes. For each event $E_i$, I have an estimated discrete probability $\hat P_j(...
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Structural prediction for a binary sequence when dynamic programming is too slow
I have a model of an event process. The process can be considered to be a 1D binary sequence, for example: [0, 0, 0, 1, 1, 0, 0]. The axis is time, but that's not ...
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How many samples in each group for a standard error of the variance calculation should I take?
I am working on a problem where I am using Monte Carlo simulation to generate the variance of a function over random points, with the goal being to calculate (i.e, estimate) the average variance for ...
