Skip to main content

Questions tagged [monte-carlo]

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

Filter by
Sorted by
Tagged with
1 vote
0 answers
10 views

How can statistical criteria be correctly validated using Monte Carlo methods?

Is it correct to say that it is impossible to determine the accuracy of a criterion in general and only possible for specific data sets or distributions? Let's say I have historical data from a ...
Романов Андрей's user avatar
1 vote
0 answers
42 views

How to get standardized coefficients of Monte Carlo method for indirect effects in lavaan/semTools?

I've run a path analysis using semTools. I'm interested to test indirect effects. I would like to report the results based on Monte Carlo confidence interval. However, the code ...
Dale's user avatar
  • 121
6 votes
3 answers
667 views

P values non-significant but Monte Carlo confidence interval does not contain zero for indirect effects

I've run a path analysis using semTools. I'm interested to test indirect effects. The p values for all indirect effects were non-significant, but the Monte Carlo confidence interval for some of them ...
Dale's user avatar
  • 121
1 vote
1 answer
38 views

Metropolis-Hastings algorithm doesn't converge to the global minimum

I calculated the total root mean squared error of 24 parameters that are estimated with metropolis hastings, I ran the algorithm for 100.000 iterations, and as the chain forward it reached a global ...
William Zhao's user avatar
0 votes
1 answer
43 views

Are the p-values obtained on the same sample using synthetic AA tests (Monte Carlo) independent values?

Let's say we have the following procedure. We take a fixed sample of size n and perform the procedure 1000 time: we divide (split) it equally into 2 groups; we calculate p value using the F function (...
Романов Андрей's user avatar
3 votes
1 answer
33 views

Understanding how to evaluate the integral causal-effect expression

I have this expression $$ p( Y \mid \text{do}(Z=z)) = \int_{B, S, W, X} dBdSdWdX \ \ P(B | S) P(W | B, S) P(X | B, S, Z=z) \left[ \int_{Z'} dZ' P(Z'| B,S,W) P(Y | B, S, W, X, Z') P(S) \right] $$ ...
Astrid's user avatar
  • 989
3 votes
1 answer
95 views

Convolution with a pathological distribution

Problem definition Consider the following random bivariate vector \begin{equation} \begin{aligned} y&=z+v \\ z&\sim p_z(z;c) \\ v&\sim p_v(v) \end{aligned} \end{equation} where $p_z$ ...
matteogost's user avatar
0 votes
0 answers
12 views

Probability of chain of events over a finite set of event with no repetition

I'm trying to tackle a problem that I suspect resembles others I'm unfamiliar with. I would love pointers for further reading. The problem is as follows: We have a finite set of actions we can take $\...
Sean's user avatar
  • 1
1 vote
1 answer
70 views

Using Rao-Blackwell to improve the estimator of P(X/Y < t)

X and Y are independent N (0, 1) random variables, we want to approximate P (X/Y ≤ t), for a fixed number t. The first part of the problem was to describe a naive Monte Carlo estimate. I described ...
stat_student123's user avatar
0 votes
0 answers
30 views

How to compute the bias of the auto-normalized importance sampling estimator

A preceding post has compared auto-normalized importance sampling with ordinal importance sampling. Beginner readers shall be directed there, but I will remind the readers of just enough elements for ...
Fernando Zhu's user avatar
0 votes
1 answer
110 views

Why weighted importance sampling is a biased estimator?

By simple math, we can have $$ E_P[f(X)] = \sum_X f(x)p(x) = \sum_X f(x)\frac{p(x)}{q(x)}q(x) = E_Q[f(X)\frac{P(X)}{Q(X)}], $$ which can be approximated by Monte Carlo sampling in two ways. 1. Normal (...
Fernando Zhu's user avatar
1 vote
0 answers
70 views

Should I use a one-sided or a two-sided confidence interval?

Context: I am teaching a subject and I prepared a multiple-choice quiz for my students. To have a feeling for which is an acceptable grade I decided to compute a baseline score, which is the score ...
rusiano's user avatar
  • 566
0 votes
0 answers
13 views

Quasi Monte Carlo: Is not grid search the ultimate low discrepancy sequence?

I realize that subsequences won't be low discrepancy, but if I know how many samples I want and that I am operating on the unit hypercube, why not just grid search as the low discrepancy sequence in ...
lware's user avatar
  • 21
0 votes
0 answers
23 views

Monte Carlo Approximation on integral of Gaussian pdf on Convex Domain

I have hard time on estimating the following integral on convex domain ($\mathcal D$) using Monte-Carlo approximation. $$a = \int_{\mathcal D} dx f(x;\mu,\Sigma) $$ where $x \in \mathbb R^d$ and $f$ ...
Interception's user avatar
1 vote
0 answers
42 views

How can I compute the longest relaxation time?

Cross-posted at MMSE and at SciComp. In the case of Monte Carlo simulations: Autocorrelation Time ($\tau_{\text{int}}$): A measure of how many steps are needed for the correlations in the chain to ...
user366312's user avatar
  • 2,140
0 votes
0 answers
32 views

change of chi2 with Monte Carlo

I am reaching out to open this topic in order to clarify a point regarding chi-square and the influence of Monte Carlo on it. For purely informative purposes, I have decided to generate random data ...
Baguette's user avatar
3 votes
1 answer
66 views

Is this a known or valid divergence between two densities?

I am testing various metrics for learning a density estimate. Specifically, I have a sample of data from a distribution $p$, and am learning a function $f$ to estimate $p$ by minimizing a distance or ...
Travis L's user avatar
  • 181
4 votes
1 answer
148 views

Comparison of confidence intervals: bootstrap & exact resampling

Consider data $X_1,...X_n$ generated from a probability distribution $F$ with density $f$. I'm interested in constructing confidence intervals for a parameter say, $\theta(F)$. Via Monte Carlo ...
reyna's user avatar
  • 365
1 vote
0 answers
28 views

Truncated Multivariate Normal expected value approximation

I have $\vec{x} \sim N(\vec{\mu}, \Sigma)$. I would like to calculate $$E[x_i | \vec{x} \geq 0]$$ There are libraries like tmvtnorm (in R) that calculates this for me. However, it seems to be very ...
JEK's user avatar
  • 21
0 votes
0 answers
19 views

How to Visualize Integrated Risk in a GMM with the Defined Risk Function

In my Bayesian decision theory research within a Gaussian Mixture Model (GMM) framework, I've come across the need to visualize the integrated risk function, especially in the context of two ...
Alireza Ghazavi's user avatar
0 votes
0 answers
41 views

Sample size in simulation and stopping criteria

I want to estimate the average of a random variable by simulation. Also, I want to estimate a proportion by simulation. I know that there are formulas to calculate the minimum sample size so that the ...
Vicent's user avatar
  • 789
0 votes
0 answers
45 views

MLE distribution vs Bayesian posterior

Suppose that we know data is distributed according to a multivariate normal distribution $\mathbf{d} \sim \mathcal{N}(\mathbf{t}(\pmb{\theta}), \Sigma)$, where the function $\mathbf{t} : \mathbb{R}^{...
J Moore's user avatar
1 vote
0 answers
32 views

Explaining the approximation to the variational free energy in Bayes by Backprop

In the paper Weight Uncertainty in Neural Networks, Blundell et al., 2015, the authors approximate the exact cost (variational free energy) $$ \mathcal F(\mathcal D, \theta) = \mathrm{KL}[q(\mathbf w \...
user246795's user avatar
3 votes
1 answer
59 views

Montecarlo Confidence Interval of T distribution

Suppose: \begin{equation} x|\sigma^2 \sim \mathcal{N}(x; \mu, \sigma^2) \; \; st. \; \; \sigma^2 \sim \mathcal{X}^{-2}(\sigma^2; \psi, v) \end{equation} where $\mathcal{X}^{-2}$ is the inverse ...
Snowy Baboon's user avatar
2 votes
0 answers
75 views

Prior BPN based on Multi Linear Regression Model Output and Monte Carlo Simulations

On page 286 in the Prediction of road accidents: A Bayesian hierarchical approach paper. The passage describes the construction and parameter learning of Bayesian Belief Networks (BPNs), specifically ...
Mike's user avatar
  • 73
10 votes
2 answers
612 views

Why is E(θ / (1 - θ)) different than E(θ) / (1 - E(θ))?

I've encountered a problem question: The probability of success for a random variable follows a Beta(5, 3) distribution. The posterior mean is θ = 0.625. The odds of success is defined as θ / (1 - θ)....
alexandrosangeli's user avatar
4 votes
1 answer
100 views

Check if a coin flips randomly, but it can have a different number of sides each toss

I would like to check if a coin flips randomly, based on observational data. The catch is, the coin can have two sides, but also three, four, up to nine. The number of sides differs in each ...
Nucular's user avatar
  • 453
2 votes
0 answers
112 views

I am confused about the histogram distribution and confidence interval

I have a dataset of 12627 records (value and sd) and want to get the sum and overall uncertainty of the sum. I ran Monte Carlo analysis with 10000 simulations. I got the statistical result as below. ...
Elizabeth's user avatar
  • 261
7 votes
1 answer
518 views

Understanding importance sampling in Monte Carlo integration

Introduction I'm studying importance sampling and I'm trying to figure out by myself, with a couple of examples, what are the main benefits with respect to standard Monte Carlo integration. I'm not ...
matteogost's user avatar
2 votes
1 answer
46 views

Monte carlo estimator using samples from normal distribution

I am following the Physically Based Rendering: From Theory To Implementation book. In the exercises from Chapter 2 (Monte carlo integration) they ask to write a program to compute numerical ...
ElPotac's user avatar
  • 51
0 votes
1 answer
81 views

(Perhaps dumb) question about Monte Carlo simulation [closed]

I am experimenting with Monte Carlo simulations and have a question about the applicability of the method to my particular problem. In this problem, I have a parameter $\phi$ which is normally ...
gth802s's user avatar
2 votes
1 answer
114 views

Proof of Rejection Sampling: Flawed reasoning about continuous random variables

I recently studied Rejection Sampling as part of one of my University courses. When justifying why Rejection Sampling makes sense (to "prove", so to speak, that samples drawn using Rejection ...
aren't eistert's user avatar
0 votes
0 answers
33 views

Adaptive piecewise linear regression of empirical distribution function

I need to find the best, in the mean-squared sense, piecewise linear regression of an emprical density function (eCDF, which I do not know but can be sampled online) on the largest possible ...
user169291's user avatar
1 vote
0 answers
35 views

How to generate random samples for the Poisson Bivariate Distribution like `np.random.poisson` in Numpy? [duplicate]

I am working with the Poisson Bivariate Distribution and I need to generate random samples to apply in a Monte Carlo simulation, but so far I haven't found too much about it on the internet. I saw ...
José Thomaz Antunes Soares's user avatar
1 vote
0 answers
19 views

Accept Rejection Mante carlo simulation and simulation mean [closed]

I read that in Monte Carlo simulation results, the larger the sampling, the mean sample results from the simulation close to normal distribution, but does this also apply to Monte Carlo accept ...
Bun's user avatar
  • 11
1 vote
0 answers
31 views

Efficient sampling of a high dimensional random vector

I have a $D$ dimensional random vector $\mathbf{X}=[X_1, X_2,\dots,X_D]$, where each dimension is independent and follow some probability distribution: $X_i \sim p_i(.)$.My goal is to get samples of $\...
Tom Bennett's user avatar
1 vote
2 answers
54 views

Estimating error variance for simulated path analysis

I want to run a simulation using lavaan and simsem to determine the sample size to use in a study using path analysis. The ...
kathryn's user avatar
  • 13
0 votes
0 answers
30 views

Boostrapping from Exponential Sample to estimate the quantiles

I have the problem where I want to estimate the quantiles of a distribution by bootstrapping. Fortunately I do know the original DGP which I chose to be an Exp(1/4) distribution and so the theoretical ...
jjjcjjj893's user avatar
2 votes
1 answer
241 views

Monte-Carlo integration with importance-sampling

I came across a paper, where (section 3.2) importance sampling is used to estimate an integral. I think I understand what importance sampling is but I don't understand how they got the solution. The ...
harsanyidani's user avatar
1 vote
0 answers
197 views

Monte Carlo simulation vs. Discrete event simulation

I'm trying to understand the difference between a Monte Carlo simulation vs. a Discrete event simulation. I learned from googling( for eg.: https://bookdown.org/manuele_leonelli/SimBook/types-of-...
user2450223's user avatar
1 vote
1 answer
91 views

Is there anything inherently wrong to use the Black-Scholes-Merton model to simulate BTC pricing rather than only using it for Options pricing?

My understanding of the Black Scholes model is that it can be used to simulate options pricing for stocks in traditional financial markets. But this article uses the model to forecast/simulate bitcoin ...
KubiK888's user avatar
  • 1,187
2 votes
2 answers
369 views

How could Lilliefors use Monte Carlo if the estimand is not distribution-free?

Lilliefors test is a well-known statistical test for normality. Its idea is based on the Kolmogorov-Smirnov test, except the CDF is replaced by the CDF of the normal distribution with $\mu, \sigma^2$ ...
Student's user avatar
  • 235
0 votes
2 answers
85 views

Apply Monte Carlo simulation to historical data to determine probability of event to happen

I have the data below and We have a game, that has a prize jackpot. The jackpot prize starts at 1,000 credits and every round you play the jackpot increases, until someone wins the jackpot and it ...
firmo23's user avatar
  • 149
0 votes
0 answers
40 views

How do you sample from a Poisson distribution when the observed count is zero?

I have some data showing the count of deaths in a population. The data are stratified by age. For example, the data might show that at age 40 there were 30,000 years of observation and 300 deaths. In ...
Dan's user avatar
  • 595
0 votes
1 answer
239 views

How to apply the antithetic variates method for an exponential distribution?

I'm trying to complete an exercise in R related to Monte Carlo estimation for the shortest path in the bridge network problem. The exercise asks me to first perform the estimation using the plain ...
Mr Economics's user avatar
3 votes
1 answer
96 views

Quantile function of multivariate distributions from empirical samples

Let's say I have a k-dimensional multivariate normal distribution $MVN(0,\Sigma)$. Denote random vector $X \sim MVN(0,\Sigma)$ as $X = (x_1, x_2, \dots, x_k)$. It is trivial to find $P(x_1 \leq c_1, ...
David Wang's user avatar
2 votes
0 answers
22 views

Intuition behind testing seasonality hypothesis

In this post to prove the statistical significance of a statement about a seasonality of a timeseries (every april returns are high) the author simulates alternative paths using the Monte Carlo method ...
gournge's user avatar
  • 21
1 vote
0 answers
25 views

Why do we need the Markovian property in Markov chains Monte Carlo?

Adaptive Markov Chains Monte Carlo (MCMC), unlike traditional MCMC methods that rely on fixed proposal distributions, dynamically adjust their proposal distribution based on the information gathered ...
user avatar
0 votes
0 answers
57 views

Adaptive Metropolis For Multidimensional Parameter

Hi recently I want to implement the adaptive Metropolis algorithm. However I dont know how to deal with multidimensional parameters. The normal step of the adaptive MCMC is to update the covariance ...
stander Qiu's user avatar
3 votes
0 answers
25 views

How to illustrate the validity of bootstrap with monte carlo simulation?

Suppose I have a random sample $S_n=\{W_i\}_{i=1}^n$ where $W_i\sim F $, and I have an estimator $\widehat{\beta}$ computed using this sample. I want to illustrate that the bootstrap approximation ...
ExcitedSnail's user avatar
  • 2,914

1
2 3 4 5
27