Tagged Questions

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

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3
votes
1answer
23 views

Sampling Order Statistics for Numerical Integration

This may be a stupid question. I want to do Monte Carlo integration over a region $$ {\int}_{D_{1} \geq D_{2} \geq ... \geq D_{m} \geq 0} g(d_1,\ldots,d_m) f(d_1) f(d_2) \cdots f(d_m) ...
2
votes
0answers
52 views

Simulation of Monte Carlo test

Using R, I am trying to simulate how the power of a Monte Carlo two-sample test for central tendency changes with sample size. However, my simulation results does not show power increasing with sample ...
1
vote
0answers
21 views

Combine several different sets of Linear Square Monte Carlo (LSMC) or Model Average

I am doing a project similar to LSMC (Linear Square Monte Carlo) for prediction. A Monte Carlo simulation engine is used to produce results, and a linear model is built on the same inputs and ...
1
vote
0answers
33 views

Monte-Carlo Simulations with multiple random variables

I have the following observation model : $y_i=x_i+a_i$, where $a_i$ is a Gaussian random variable whose mean is function of a uniform random variable $b_i$. I have designed, $\hat{x}_i$, an estimator ...
3
votes
1answer
39 views

What to do when rejecting a proposed point in MCMC?

I'm writing a simple Metropolis-Hastings MCMC algorithm. Every time a move gets accepted, the point is added to a list of accepted points. I wonder what exactly I should do when a proposed move has ...
0
votes
1answer
34 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 ...
0
votes
1answer
19 views

Does Accept - Reject Algorithm Monte Carlo help fit a distribution to the data?

As far as I understand the Accept - Rejection Algorithm is used to help us simulate hard to simulate densities or unknown densities by first simulating an easy density and then accepting or rejecting ...
0
votes
0answers
10 views

Simulation of CI of amount of values in different intervals by adding noise to original data

I am having a hard time trying to solve this problem, so maybe some of you guys can sort it out. I have a large data set containing a value describing the thermal comfort in buildings called PMV. The ...
2
votes
0answers
24 views

Convergence of Monte Carlo sample average for arrays of random variables

Suppose $X_1$, $X_2$ are two independent real-valued random variables. Let $F$ be a continuous (unbounded) function from $\mathbb{R^2}$ to $\mathbb{R}$. Assume that the necessary measurability and ...
0
votes
0answers
62 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 ...
1
vote
1answer
28 views

Big Data Regression Coefficient Estimation

I am working on a very large data set (n = 6.5 million) and I am trying to come up with a simple linear regression between two variables. I am working in R and using a monte carlo style simulation to ...
0
votes
0answers
14 views

Need help with importance sampling over HUGE sample space

My underlying problem is fairly simple, but the sheer size is what is causing issues. I would like to use importance sampling, but am unsure about its implementation. Problem statement: We have $N$ ...
0
votes
0answers
32 views

Monte Carlo test for spatio-temporal randomness

I have a collection of discrete spatio-temporal observations $d(x,y,z,t)$ on the surface of a sphere. The data is sparse and is in the order of ~100 points, but there is a bimodal clustering of these ...
0
votes
0answers
24 views

How many models I need?

I am doing an estimation using a bunch of sparse data. Suppose that I have a 100x100 grid and 20 data is available on this 2D grid. One solution is to use a determiastic method and estimate the other ...
0
votes
0answers
36 views

Selection of failed fitting results in MC Simuation

I recorded a set of experimental rates $r = r(c,T,P)$ at 2 values of $c$ and >15 values of $T$. $r(c,T,P)$ obeys the following functional form: $$ r(c,T,P) = ...
2
votes
1answer
34 views

Run Many Small or a Few Big Simulations to Estimate the Mean?

I was just running some simulations on tossing a coin given certain conditions, to test out some ideas I had. I was trying to find the ratio $\frac{\mathtt{successful\ tosses}}{\mathtt{total\ ...
0
votes
2answers
83 views

Normal Distribution with random mean and standard deviation

When trying to code this in R, I'm getting very confused about what to do. Apologies if my terminology is incorrect but I would be grateful for any advice. The Problem: I have been given two normal ...
6
votes
3answers
188 views

Simulation involving conditioning on sum of random variables

I was reading this question, and thought about simulating the required quantity. The problem is as follows: If $A$ and $B$ are iid standard normal, what is $E(A^2|A+B)$? So I want to simulate ...
2
votes
0answers
27 views

Testing if points on a line are over/under dispersed

I have a series of about 1000 points on a chromosome and I want to know if they are clumped, over-dispersed, or neither. The chromosome can be viewed as a 1-dimensional. I've looked over some ...
0
votes
0answers
11 views

significant differences between time series - Monte Carlo simulation

I would like to test if there are significant differences between 3 time series. First, I thought to run a simple chi square test, then a Monte Carlo simulation. Comparing the two methods: P-values ...
0
votes
0answers
13 views

Restricted Boltzman Machine Non-Hidden Layer Approach

An RBM is defined by the joint probability distribution $$p({\bf x},{\bf h})=\exp(-E({\bf x},{\bf h}))/Z$$ where $$E({\bf x},{\bf h})=-{\bf h}^TW{\bf x} - {\bf c}^T{\bf x} - {\bf b}^T{\bf h}$$ ...
2
votes
0answers
134 views

Forward Filtering Backwards Sampling (FFBS) and Look-Ahead Bias

Assumptions / Context: Let's assume that I have data that can be modeled as a dynamic linear model. To estimate the parameters (e.g., covariance matrix of the state/system equation), I use a Gibbs ...
2
votes
1answer
36 views

Refining Monte Carlo predictions using observed measurements

I'm trying to build a monte-carlo simulation that can revise it's distribution of outcomes of a project based on observed measurements after the project has started. I have a few questions about the ...
2
votes
0answers
34 views

Monte Carlo simulation of investment account

I'm trying to estimate performance of an investment account over 20 years. The question is, have I set up the Monte Carlo simulation correctly? I've used Excel. I've assumed 8% average return and 13% ...
1
vote
1answer
44 views

Monte Carlo computation of expectation when there is dirac delta

Let $Z \sim N(0,1)$ and let $Y=Z$. Suppose I wish to perform the following weird computation: $f(z)=\int f(z|y)f(y)dy=E_Y[f(z|y)]$ and then use Monte Carlo to estimate $E_Y[f(z|y)]$. The problem is ...
0
votes
1answer
126 views

Particle filter (sequential Monte Carlo) for a non-Gaussian hierarchical model

I have the following, which I am attempting to model with a particle filter. \begin{align*} y_{i,t}&\sim\mathrm{Poisson}\left(\lambda_{i,j,t}\right)\\ ...
6
votes
2answers
79 views

Seeking a continuous, parametric, bimodal sampling distribution for proportions

I am seeking a parametric probability model whose pdf has the following characteristics: (1) it is supported on a variate axis that is bounded between 0 and 1; (2) it is continuous; and (3) it is ...
0
votes
0answers
47 views

Demand Forecasting : Montecarlo Simulation

I am trying to build a demand forecasting model for human resource team. I have thought of using monte carlo simulation method to do it. Is it the right technique for it? Has anyone used it to ...
5
votes
1answer
49 views

Advantage of multiple simulations in old-fashioned Monte Carlo?

The spirit of this question comes from "Ordinary Monte Carlo", also known as "good old-fashioned Monte Carlo" Suppose I have a random variable $X$, with $$\mu := E[X]\\ \sigma^2:=Var[X] $$ Both are ...
1
vote
0answers
20 views

Simultaneous multiple perturbations in Markov chain Monte Carlo

I'm coding a McMC algorithm for geophysical applications. Using the Metropolis–Hastings scheme to accept/reject the proposed models is something that I thought I understood completely, but I don't. ...
1
vote
0answers
33 views

pairing algorithm in R

I have two sets of elements M and N, and a scalar-valued distance/similarity function between one element from M and one from N. The problem is to generate a set of pairs (one item from M and one ...
0
votes
0answers
18 views

Is Monte Carlo simulation more appropriate than parametric tests for constructing confidence intervals for weighted means?

A colleague suggested that Monte Carlo simulation should be preferred for constructing confidence intervals for weighted means calculated from a sample. How and why exactly might Monte Carlo perform ...
0
votes
1answer
14 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 ...
1
vote
0answers
29 views

Question about Hybrid Monte Carlo

In a Hamiltonian system, the Hamiltonian is always preserved, but in HMC algorithm, new state is accepted by probability $\min(1,\frac{\exp(-H_{new})}{\exp(-H)})$, I think increase or decrease in ...
3
votes
1answer
59 views

Error Bars for Monte Carlo Experiment

Suppose we have a random variable $X$, where $\mathbb{E}(X)$ and $\text{Var}(X)$ are known. I have computed $N$ number of MC-type samples from the distribution of $X$. Let $\bar{x} = \frac{1}{N}\sum ...
1
vote
0answers
29 views

Distribution of number of values less than cutoff within symmetric Dirichlet

Assume have a symmetric Dirichlet distribution with $a_1= \dots =a_k = a$ $ (X_1, \ldots, X_K)\sim\operatorname{Dir}(a) $ I am trying to determine the distribution of the number of values less than ...
0
votes
0answers
23 views

Showing that the variance increases with the dimension of the random vector

This is actually related to a more complex question; but I want to re-ask it by trying to simplifying it as possible: 1- We have $n$ dimensional functions of the form $f_n:\mathbb{R}^{n} \mapsto ...
0
votes
1answer
31 views

Is it possible to randomly sample from single data set (Monte Carlo style) to create new data sets?

Background I understand Monte Carlo methods only superficially, but I understand you can repeatedly randomly sample, with or without replacement, from your data set to estimate population parameters ...
1
vote
0answers
21 views

Uniform convergence of Monte Carlo approximation

Usually Monte Carlo method is used to compute integration. For example, let $g(x,\theta)$ be a continuous function about $x$ and $\theta$, $f(x \mid \theta)$ is a continuous pdf with parameter ...
0
votes
0answers
62 views

Triangular distribution and simulation monte carlo

How can I do to incorporate Monte Carlo simulation on a triangular function. I'm trying to do this using JavaScript and found a very interesting bibliioteca http://jstat.github.io/distributions.html ...
4
votes
2answers
243 views

Misunderstanding of Monte Carlo Pi Estimation

I am fairly sure that I understand the how Monte Carlo integration works but I am not understanding the formulation of how it is used to estimate Pi. I am going by the procedure outlined in the 5th ...
2
votes
0answers
25 views

How to show that the variance of Sequential Importance Sampling estimates increase with the dimension?

I am trying to understand the Particle Filter and the motivation to use it over the regular Sequential Importance Sampling. As far as I understand until now: 1- We try to estimate the expectation of ...
-1
votes
1answer
66 views

NP hard implementation optimisation using Monte Carlo method

I need to implement an algorithm ( or find an implementation) and optimise it using Monte Carlo method. This must be an NP hard such as the Travelling Salesman problem or the Knapsack problem. How can ...
1
vote
0answers
18 views

Tail probabilities and the GHK simulator

I am trying to use the GHK simulator to estimate the probabilities $F(\mathbf{x} > k\mathbf{a})$ that the values of a high dimensional ($n>1000$), correlated random vector $\mathbf{x}$ will ...
0
votes
1answer
69 views

10 minutes wind speed data to 1 second wind speed data

I have a wind speed data series .txt file (1 year long), in which in each register I have the following info: date; hour; 10 minute wind speed average; 10 minute max value; 10 minute sigma An ...
1
vote
1answer
66 views

NP-Hard optimisation problems that require approximate methods

What are some examples of NP-hard optimisation problem that requires approximate methods (such as Monte Carlo? I have done a lot of research but I can't find a suitable problem to implement apart from ...
3
votes
0answers
53 views

Combining unbiased estimators with unknown variance

Say we are given a sequence of independently (but not identically) distributed random variables $X_1,...,X_n$ which are known to be bounded, $X_t \in (a,b)$, and to have the same mean, $\mathbb{E}X_t ...
0
votes
0answers
42 views

Monte Carlo Optimisation

I have been doing a LOT of research about this but I can't figure out exactly how to do it. I need to find a problem that can be solved using Monte Carlo Optimisation (it is important that it is an ...
3
votes
0answers
98 views

How to mathematically prove that we are sampling from same distributions?

The content of this question is about rigorously proving something which is otherwise considered easily correct intuitively. Let's assume we have a multivariate distribution $g(x_1,x_2,...,x_n)$ over ...
0
votes
1answer
30 views