A vast area which includes generating results from computer models.

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2
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0answers
27 views

Likelihood that two markov chains are derived from the same transition matrix

Forgive me for my weak statistic background, hopefully what I'm asking makes sense. So some quick background, I have one markov chain from a data set and many additional chains that I'm producing from ...
0
votes
0answers
68 views

Numerical integration of divergent functions

I am having trouble with the numerical integration of a divergent function. For example, \begin{equation} n= \int f(x)\,dx = \displaystyle\int \dfrac{\Theta(x-\varepsilon)\,dx}{\sqrt{x-\varepsilon}} \...
4
votes
3answers
49 views

Simulation of interacting Ornstein-Uhlenbeck processes

I would like to simulate the following system of interacting OU processes on $[0,T]$: $$dX_t^1=(X_t^2-X_t^1)\,dt+\sigma_1 \,dW_t^1,\quad X_0^1=x_1$$ $$dX_t^2=(X_t^1-X_t^2)\,dt+\sigma_2 \,dW_t^2,\...
0
votes
1answer
51 views

Simulating Random Vectors Based on Conditioning

I'm working on a project where I need to simulate random vectors $(Y, X_1,\dots,X_n)$ in order to understand the joint distribution $f(y,x_1,\dots,x_n)$. I wish to simulate enough random vectors so ...
2
votes
0answers
71 views

Solving Kepler's Equation

I've been working on simulating orbits. I've found that, when solving Kepler's equation, $M = E - \varepsilon\sin{E}$, I'm unsure about the solution to use. For a true anomaly $< \pi$, using the ...
2
votes
4answers
95 views

What is the statistical equilibrium for this simulation of happy bubbles?

Happy Bubbles I hope this is not too specific or practical, but I just made a simulation of sorts and seem to have hit quite close to an equilibrium (by accident). Now I am wondering if and how you ...
0
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0answers
57 views

Exlain the significance of the uniform random variable for the simulation of random variables

I can think of the "Universality of the Uniform": Given an Unif(0,1) r.v., we can construct an r.v. with any cts distribution we want. Conversely, given an r.v. with an arbitrary cts ...
1
vote
0answers
20 views

How do we derive efficiency from robustness in the virtual ant solution to the traveling salesman problem?

Using virtual ants/swarm intelligence to solve the Traveling Salesman Problem is an example of using a robust system to solve an efficiency problem. We normally think of robustness and efficiency as ...
3
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0answers
32 views

Simulating a SDE

I have a question about simulating a SDE. I want to simulate $dS=\alpha(K-S)dt+\sigma S dZ$ with use of a Euler-marayama scheme. The numerical scheme becomes: $S_{i+1}=S_{i}+\alpha(K-S_{i})dt+\sigma ...
6
votes
2answers
2k views

Implementing Ornstein–Uhlenbeck in Matlab

I am reading this article on Wikipedia, where three sample paths of different OU-processes are plotted. I would like to do the same to learn how this works, but I face troubles implementing it in ...
0
votes
1answer
30 views

Calculation of Confidence Interval for Simulation

I wrote a simulation that does 1,000,000 trials. It returns 430,200 successes. I want to calculate a probability of success with confidence interval for that probability estimate. I use $\sigma = \...
1
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0answers
167 views

distribution of the length for a random walk on an infinite 2D grid

In connection with the flatland paradox, consider a 2D-random walk $(X_n)$ on $\mathbb{Z}^2$: the four moves of length one to W,E,N, and S are equaly likely at each time. For a fixed number of moves $...
0
votes
1answer
48 views

proposal distribution for metropolis algorithm

All, I'm wondering whether it is possible to use an asymmetric distribution, eg the exponential distribution as the proposal dist'n for a metropolis algorithm (wiki) (not the metropolis-hastings). ...
0
votes
1answer
18 views

Metropolis-Hastings Algorithm Clarification

All- Could you please clarify: from wikipedia, step two states at the end if the candidate is rejected, set xt+1 = xt, instead. I don't quite understand this, so you will have two of the exact same ...
1
vote
1answer
155 views

How can I solve numerically this partial differential equation?

I am reading this paper and came across a system of differential equations with 4 ODEs and 1 PDE. The PDE is given below. My question is how to solve this numerically in MATLAB , Python or Mathematica?...
4
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0answers
157 views

How to compute this triple integral?

I am trying to do this triple integral $$\int_{0}^{\infty }\int_{0}^{\infty }\int_{0}^{\infty }(u+w)e^{-\frac{(u+w)^2}{2}}(v+w)e^{-\frac{(v+w)^2}{2}}(u+v)e^{-\frac{(u+v)^2}{2}}e^{-(\mu +\lambda )u}e^{-...
1
vote
1answer
146 views

How to generate integer random numbers that equal to another random number?

I am running a simulation in Excel, and need to generate a group of integer random numbers summing up to another random integer, how can I possibly do it? For instance I have an integer random number ...
0
votes
1answer
168 views

Time between arrivals Distribution

I am simulating a hair parlor queue with m number of queues and 3 different types of services (queues). I was doing the time between arrival with a uniform distribution with a min value and a max ...
1
vote
0answers
60 views

Simulating r.v.'s from a joint density by rejection sampling in R. Continued

I wish to sample variables $v$ and $w$ from the joint density $$(v+w)e^{-\frac{(v+w)^{2}}{2x_{0}}-2\mu v-(\mu -\lambda )w},$$ where $x_0$, $\mu$ and $\lambda$ can be seen as positive constant. Since ...
-1
votes
1answer
45 views

Finding density and distribution functions [closed]

I have been trying to understand probability by attempting past paper question and I have been stuck on this question all day and night. I am not quite sure how to go about finding the functions ...
0
votes
0answers
22 views

Stability of boostrap confidence intervals

As a word of background, I want to show that certain result is stable when averaging over a large number of simulations, but could be just a lucky draw with a small number of simulations. I have a ...
2
votes
1answer
82 views

Simulating r.v.'s from a joint density by using rejection sampling in R

I wish to sample variables $v$ and $w$ from the joint density $$(v+w)e^{-\frac{(v+w)^{2}}{2x_{0}}-2\mu v-(\mu -\lambda )w},$$ where $x_0$, $\mu$ and $\lambda$ can be seen as positive constant. Since ...
1
vote
0answers
96 views

Personal Experiences with Probability Simulation

Simulations methods are increasingly used in theoretical and (especially) applied probability. Personally, I have used simulation for purposes that range from recreational Q&A to applications of ...
0
votes
2answers
95 views

exponential distribution with probability about texts

It is 9:00 p.m. The time until Joe receives his next text message has an exponential distribution with mean 5 minutes. A text has not arrived for 5 minutes. Find the probability that none will arrive ...
0
votes
2answers
34 views

Sinusoid with zero boundary conditions on $[0,1] \times [0,1]$ grid

I want to make a sinusoidal plot (any shape is welcome) on a $[0,1] \times [0,1]$ grid, with boundary conditions equal to zero. It should resemble a membrane fixed along its edge. I tried out some ...
1
vote
3answers
836 views

Evaluating Difficult Monte Carlo Integration in R

I recently posted a simple version here (Simple Monte Carlo Integration). I was able to verify that the answer was indeed close to 1/3 when I wrote the following R code, and got a mean of X of ~1/3: ...
0
votes
1answer
29 views

Difference and confidence intervals

I performed a few series of simulation to evaluate values of two parameters. Let's say, the results can be presented like this: ...
1
vote
0answers
51 views

Is Principal Component Analysis applicable to this type of situation?

I'm trying to model the response of ant populations to pheromones in this way: The ants are simulated as Self Propelled Particles with internal energy. They undergo acceleration due to their internal ...
0
votes
1answer
43 views

Is it possible to estimate $e$ based on $N$?

Consider a sequence of random numbers $u_1,\dots,u_n$ obtained from a continuous distribution $F$. Let $N$ be the first one that is greater than its immediate predecessor. In othe words, $$N=\min_n\{...
2
votes
1answer
138 views

Simulate correlated $\chi^2$ distribution

I understand that when one have multiple independent variable that follows $N\sim(0,1)$, denoted as $A$ if we have a correlation matrix $R$, we can generate correlated variables $B$ that are normally ...
1
vote
1answer
110 views

mean and std deviation from little's law

I have a service node with a queue The arrival rate in this service node is exponential(0.4) The service time is exponential(0.2) Running a simulation i've calculated the average population of the ...
1
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0answers
183 views

Monte Carlo sampling and Kolmogorov–Smirnov test in practice

I have two deterministic algorithms, Algorithm 1 and Algorithm 2. The first has $m$ inputs and one output, and the second has $n$ inputs and one output. The distributions of the inputs of the ...
1
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0answers
129 views

Statistics Marble Simulation

Given the jar containing 20 red, 5 white, and 10 blue marbles, Joey thinks a more interesting problem would be to find the number of marbles you would have to draw, without replacing them in the jar, ...
3
votes
1answer
50 views

Can you simulate from a cantor distribution?

Has someone run across a method for generating random variates from a Cantor Distribution? It seems like its abstract definition prevents this. In essence, can one "invert" the Cantor Function?
1
vote
2answers
56 views

How to efficiently simulate successes of several trials if probabilities are inhomogeneous

If I'm doing a simulation with $n$ trials, each with probability $p$, a quick way to select the successful trials is to choose a binomially distributed random number. Then randomly choose that many ...
0
votes
1answer
34 views

What platform is best for simulating a stochastic process on a graph/network?

I'm simulating a dynamic process which was so far done only on a lattice, and Matlab was quite sufficient for that. However, I can't seem to find a convenient way to model such a process on a graph ...
1
vote
1answer
49 views

Permutation algorithm for simulating random variables $X,Y,Z \in [0,1]: X+Y+Z = 1$ and $X,Y,Z \sim U(0,1)$

Edit: Sorry, I tend to jump back and forth between math notation and computer science notation....often to the chagrin of my more rigorous colleagues (and Math.SE folks ;-) Also, I accidentally ...
0
votes
1answer
46 views

Looking for Method to evaluate the optimal node rate vs number of simulation rate in a Monte Carlo simulation

I am currently working on evaluating an American Option using a Monte Carlo simulation, and I am getting answers but they vary quite a bit. The two variables that I can alter are number of simulations ...
0
votes
1answer
58 views

uniqueness of svd decomposition and its role in statistical analysis

let us consider following model according to following link http://www4.ncsu.edu/~ipsen/REU09/chapter4.pdf it says that : The singular values are unique, but the singular vector matrices are ...
2
votes
2answers
117 views

Probability that winner of tournament is best player

There are $2^n$ players with skills $1, 2, \ldots, 2^n$ where the probability of Player A winning any game (against B) is $\text{skill}(A)/(\text{skill}(A)+\text{skill}(B))$. Set up a tournament of $n$...
3
votes
1answer
52 views

Simulating elastic collision

I wrote a simple program where i can move around some objects. Every object has a bounding box and I use hooke's law to apply forces to the colliding objects. On every tick, I calculate the forces, ...
1
vote
1answer
34 views

Tissue Deformation Simulation using FEM

I need to simulate tissue deformation using FEM. Is it advisable to represent the object as a triangle mesh or a ...
4
votes
1answer
102 views

Applying MCMC Metropolis algorithm

I'm interested in all possible paths (on the grid $\mathbb{N}^2 $) that goes from $ (0,0) $ to $ (n, n) $. At each step there are two possibilities: go right or go up. The path is a sequence $ z=(z_0,...
0
votes
2answers
238 views

Calculating a Cardgame

I was send here from stackoverflow because they thought maybe you can help me. Here my original post: http://stackoverflow.com/questions/26799476/a-faster-way-then-doing-14-for-loops What I want: ...
0
votes
1answer
189 views

Incomplete Cholesky decomposition conjugate gradient method in Matlab

I have a problem in finding the numerical material that describing in detail for incomplete Cholesky combined with conjugate gradient method by using Matlab. Someone can help me? Many thank in advance....
0
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1answer
73 views

Angular momentum superposition

I am doing a space simulation. I have a spaceship and this spaceship has engines that don't push the spaceship through its center of gravity. These engines can therefore give the spaceship angular ...
0
votes
1answer
53 views

Generate a random chain with cauchy distribution using C language

Here is my question: I want to simulate a random variable using cauchy distribution with C language. Scale and position must be setted manually. I fuond the GSL library wich contain the function: ...
0
votes
0answers
92 views

Uniform Sampling over Convex Polytope (not full-dimensional)

I want to simulate a uniform distribution on a convex polytope that is not full-dimensional for optimization purposes (to generate random points on the set I want to minimize over). The polytope is ...
3
votes
1answer
66 views

Hypercomputation & Higher Dimensional Variants of Conway's Game of Life

Conway's Game of Life is a simple and important mathematical game with some rules of evolution in a two dimensional space. It appears in many subjects in mathematics, artificial intelligence and ...
2
votes
0answers
34 views

Are these two approaches to calculating return rate mathematically consistent?

I have coded two C# programs, which use two different approaches to evaluate the outcome of a certain casino-style game (casino-style in the sense that the user pays points to take a turn, and ...