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

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Calculating probability of full house and royal straight in R poker simulation

Given a poker simulation in R using vectors for the denomination and class of playing card in a loop, how would one go about identifying a given hand containing a full house or a royal straight. I'm ...
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23 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 ...
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34 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) = ...
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1answer
31 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\ ...
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2answers
52 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 ...
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3answers
151 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 ...
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25 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 ...
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9 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 ...
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12 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 $$E({\bf x},{\bf h})=-{\bf h}^TW{\bf x} - {\bf c}^T{\bf x} - {\bf b}^T{\bf h}$$ ...
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54 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 ...
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1answer
35 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 ...
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26 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% ...
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1answer
40 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 ...
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1answer
110 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)\\ ...
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2answers
68 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 ...
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40 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 ...
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1answer
47 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 ...
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17 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. ...
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31 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 ...
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17 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 ...
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1answer
11 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 ...
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28 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 ...
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1answer
47 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 ...
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27 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 ...
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22 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 ...
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1answer
26 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 ...
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15 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 ...
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50 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 ...
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2answers
232 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 ...
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19 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 ...
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1answer
62 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 ...
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17 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 ...
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1answer
58 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 ...
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1answer
58 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 ...
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44 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 ...
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41 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 ...
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96 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 ...
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1answer
27 views
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143 views

Why use the parametric bootstrap?

I am currently trying to get my head around some things concerning parametric bootstrap. Most things are probably trivial but i still think i may have missed something. Suppose i want to get ...
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33 views

Box-Muller algorithm and Monte Carlo Integration

Can someone help me out here? Using Box-Muller would generate N(0,1) however X ~ N(-1, 4). How do I transform the variables to the distribution of X? And would the pseudocode include the usage of ...
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24 views

Integration via importance sampling - expectation and variance

I need to calculate $$\int_A f(x) \; dx$$ via Monte Carlo Importance Sampling and, for simulations purposes, I need to calculate the variance and mean of my estimator. In importance sampling ...
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1answer
41 views

Importance Sampling Simulation

I need to calculate an integral using importance sampling method and, for the stopping criteria of the simulation, it is given an relative error. I've found that the relative error is defined by the ...
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1answer
69 views

Monte Carlo Simulation…?

I just have 2 questions: (1) If we can obtain samples from the posterior distribution, is there any need to try to compute posterior expectations and intervals analytically...? (2) Also, I know ...
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3answers
162 views

Monte Carlo integration aim for maximum variance

I have a question about Monte Carlo integration. As I understand it the method takes a region S of known volume V which contains the region T specified in the definite integral. $T \in S$. Then ...
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0answers
34 views

Monte Carlo Based A-Priori Power Calculation for Logistic Regression

I have been wanting to get a Monte Carlo based power calculation working for Logistic Regression cases for a little bit. I have put together a workflow with some assisstnace and I wanted to ask the ...
6
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1answer
162 views

Required number of simulations for Monte Carlo analysis

My question is about the required number of simulations for Monte Carlo analysis method. As far as I see the required number of simulations for any allowed percentage error $E$ (e.g., 5) is $$ n = ...
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50 views

Use of Monte Carlo vs predictive modeling?

I am building a scoring model for rating an individual on trustworthiness. The parameters of the model are not fixed and I have no historical data to test. So to test the validity of the parameters ...
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42 views

Monte Carlo method

I need to write a report on what is Monte Carlo method suitable for and for what it is not suitable for, however, I can't find a lot of material regarding this information. What is it suitable for ...
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2answers
51 views

Monte Carlo Integration Interval Probability

Use MC integration to estimate the probability that X * exp(X) < 2.5, assuming that X ~ Gamma(1.2,3.7) ...
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1answer
75 views

Extreme value simulation with Monte Carlo

I would like to seek your help with some questions to simulating extreme values. For example, I have written the following R code to generate QQplots for a normally distributed data, varying the size ...