# Questions tagged [monte-carlo]

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

1,316 questions
Filter by
Sorted by
Tagged with
1 vote
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 ...
1 vote
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 ...
• 121
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 ...
• 121
1 vote
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 ...
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 (...
33 views

### Understanding how to evaluate the integral causal-effect expression

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

### Convolution with a pathological distribution

Problem definition Consider the following random bivariate vector \begin{aligned} y&=z+v \\ z&\sim p_z(z;c) \\ v&\sim p_v(v) \end{aligned} where $p_z$ ...
• 373
12 views

1 vote
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 \...
• 101
59 views

### Montecarlo Confidence Interval of T distribution

Suppose: $$x|\sigma^2 \sim \mathcal{N}(x; \mu, \sigma^2) \; \; st. \; \; \sigma^2 \sim \mathcal{X}^{-2}(\sigma^2; \psi, v)$$ where $\mathcal{X}^{-2}$ is the inverse ...
• 321
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 ...
• 73
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)....
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 ...
• 453
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. ...
• 261
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 ...
• 373
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 ...
• 51
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 ...
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 ...
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 ...
1 vote
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 ...
1 vote
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 ...
• 11
1 vote
31 views

• 157
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 ...
• 21
1 vote
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 ...
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 ...