The simulation tag has no wiki summary.
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11 views
Importance Sampling: Binomial Distribution
I'm trying to estimate the probability $P(X\geq80)$, X~bin(100,p), with importance sampling.
So I came up with a Markov Chain and defined a random variable $Y$ on that Markov chain so that ...
1
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0answers
24 views
Single evaluation for using exponential sampling until past a point
I am trying to improve an algorithm that looks like the following (and am getting stumped): I am provided with a starting time, rate, and a target time. I then use an exponential distribution to ...
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1answer
130 views
Poisson Process, Exponential inter-arrival times simulation conundrum
I am trying to simulate a poisson process by using the fact that the inter-arrival times are distributed as an exponential distribution.
I want to generate patient arrival times in (say) 1 hour. So, ...
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1answer
62 views
Runge-Kutta 4 explanation
I'm a game developer and I need to write a solar system simulation. Unfortunately I'm not very good at math and most importantly I haven't got to differential equations in my maths classes at school ...
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1answer
53 views
Numerical/artifical damping in forward Euler?
I'm testing a code to find periodic solutions of nonlinear structural vibrating systems by solving a global time-discretized periodic system of equations. I am using a forward Euler (first order ...
3
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0answers
38 views
Classify knots in a closed bead-spring like polymer simulation
my problem is to detect the crossing number (or another knot invariant) of a simulated polymer. A polymer is a closed bead spring, which mean that it is represented by a set of points connected by ...
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0answers
27 views
Simulating of GBM
I have a question regarding the simulation of a GBM. I have found similar questions here but nothing which takes reference to my specific problem:
Given a GBM of the form
$dS(t) = \mu S(t) dt + ...
1
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1answer
72 views
Rejection method for beta distribution?
I have the follow function, $$\frac{8}{\pi}(x(1-x))^{1/2} 0<x<1$$
I am asked to use $U(0,1)$ as an envelope to construct a rejection algorithm for simulation samples from $Beta(3/2,3/2)$ with ...
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0answers
64 views
Approximation of SDE
I have been struggling with the following problem: If you want to find a numerical result by simulating the paths of a stochastic differential equation, in particular a geometric brownian motion I ...
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0answers
64 views
Gibbs sampler bivariate normal
Suppose that we have an observation$x = \bigl(\begin{smallmatrix}
x_{1} \\ x_{2}
\end{smallmatrix} \bigr)$ from a bivariate normal distribution with unknown mean $\mu = \bigl(\begin{smallmatrix}
...
1
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2answers
94 views
Simulation of a Gaussian process on $R^2$ with a stationary kernel using the Karhunen-Loève expansion
Assume $X(\omega, t) \sim \mathcal{N}(0, K(\cdot, \cdot))$ is a real-valued, centered Gaussian process on $R^2$, i.e., $X: \Omega \times R^2 \to R$. Let the covariance function of the process be ...
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0answers
59 views
Positive eigenvalues in differential-algebraic equations not appearing in time-domain simulation
I am solving a system of equations derived from power system applications. It consists of index-1 differential and algebraic equations in the form:
$$\dot{x}=f(x,y) \\ 0=g(x,y)$$
To get the ...
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2answers
66 views
simple (tan like shape) function needed
I need a function which initially falls slowly, then quickly and then slowly again.
Shape should be like tan but I want to be able to control the gradient
Properties needed:
$x = 0, y=0$
As $x$ ...
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0answers
52 views
Simulating the balls and bins problem in Mathematica (or similar)?
The 'balls and bins' problem
Distribute $n$ balls into $d$ bins in a way which minimises the difference between the highest and lowest loaded bins.
Reasoning for performing simulation
I have some ...
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0answers
51 views
Calculated probability not matching simulated results
I know that if you take random and uniformly continuous number that are generated by the sum of x1+x2 (so y=x1+x2), the probability $P(0.9<y<=1.8)$ the calculated results are:
y~u(0,1)
= 0.575
...
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1answer
147 views
What are the differences between the random walk and the gaussian random walk?
I know the random walk mobility model, but I can not understand what are the differences with respect to gaussian random walk.
In other words, I know how to implement the two-dimensional random walk: ...
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1answer
52 views
Moss scheduling Simulator and Standard Deviation in plain english?
source : http://www.ontko.com/moss/sched/user_guide.html
Configuration File Options standdev
n
*
The number of standard deviations from the average length of time a
process should execute ...
3
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2answers
55 views
Letter in the table with 8 trays
Here is a problem: we have a table with 8 trays. With probability $0.5$, there is a letter somewhere in the table. What is the probability that there is a letter in a last tray, given that there is no ...
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0answers
86 views
Maximizing noisy unknown function
I'm interested in maximizing a function $f(\mathbf \theta)$, where $\theta \in \mathbb R^p$.
The problem is that I don't know the analytic form of the function, or of its derivatives. The only thing ...
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2answers
531 views
Please help me solve this exponential distribution problem
Question 1 :
The time to service a customer at a bank teller's counter is exponentially distributed with mean of 60 seconds.
What is the probability that the three customers in the front of an ...
0
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1answer
46 views
How to resolve this?
I've the following problem to model and program it:
suppose that we have a central server that provides 3 different services($S_1,S_2,S_3$), there are $N$ machines connected to this server: each ...
4
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2answers
68 views
What do I need to know to simulate many particles, waves, or fluids?
I've never had a numerical analysis course so I don't know what I need to know. I'm just wondering what kind of books I should get to make me able to simulate these things. I'm wanting to simulate ...
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1answer
60 views
4 way heat distribution multiplier problem
I'm making a simple heat distribution program. It's a 2d matrix with cells holding heat value. Every iteration looks for cells near current which have lower heat value and gives them some of its heat. ...
0
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1answer
51 views
Comparing speed in stochastic processes generated from simulation?
I have an agent-based simulation that generates a time series in its output for my different treatments. I am measuring performance through time, and at each time tick the performance is the mean of ...
4
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1answer
164 views
Integral over the $\mathcal{S}^{n-1}$ sphere
I have been running into the following integral again and again:
Let $S^{n-1}= \{x \in \mathbb{R}^{n} \: | \: ||x||=1 \}$ and let $\lambda_{S^{n-1}}$ denote the surface measure over $S^{n-1}$ as ...
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0answers
94 views
Expected value involving a conditional multinomial distribution
$X|z$ has a multinomial distribution $MN(m, \mathbf{q}(z))$ where $z$ is either 0 or 1 with probability $1/2$. I need to find: $E_X[\max\{\Pr(z=1|X), \Pr(z=0|X\}]$. Is there an analytical form to ...
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0answers
84 views
Simulating first passage times
I have a Brownian motion $X_t = \mu t+\sigma W_t$, where $W_t$ standard Brownian motion. I know that the first passage time $\tau = \min\{t|X_t\leq\alpha\}$, is Inverse Gaussian distributed i.e., ...
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0answers
92 views
Fourier Transform of a Covariance Function for Spectral Simulation
I am learning about generating Gaussian random fields by spectral simulation...
If I have a covariance function $C(h)$, then the spectral density is the Fourier transform of $C(h)$:
...
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3answers
396 views
Simulation of 2-dimensional Brownian motion
I am trying to simulate (for the first time) a 2-dimensional SDE, in Matlab.
$$X(t)=F(t,X(t))\,dt + \sigma(t,X(t))\,dBt$$
I have no problem using the Euler-Maruyama method in the one dimensional ...
0
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0answers
34 views
Generating samples from $u(7,10)$
I have the following assignment:
It requires to generate samples from $u(7,10)$,the uniform distribution on the interval $2 \leq x \leq 11$. Compare the normalized histogram with the density ...
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0answers
173 views
Semi implicit integration - stability issues
I am trying to decide whether to use semi-implicit integration vs. explicit integration (particularly Position Verlet over Semi implicit Euler). Although the Verlet approach is widely used and is ...
9
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2answers
248 views
Why can't you simulate isotropic fluid flow on a square lattice?
There are easy methods for discrete simulations of gas dispersion in two dimensions. If you take a large square lattice, each cell of which is assumed to contain at most one gas molecule, and you ...
4
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1answer
160 views
Pseudo random number generator: Why not to use “too many” random variables in one application
I found statement in an article "Good Practice in ( Pseudo ) Random Number Generation for Bioinformatics Applications" that you should not use too many random variables in a single simulation. Authors ...
2
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2answers
322 views
Generating random array in Maple
I'm trying to do simulation in Maple, but I can't figure out how to do the following:
How does one generate a set of random whole numbers in an array of 24 element (in 1 column) where the sum of the ...
2
votes
1answer
120 views
Simulation of diffusion processes on the canonical space $C([0,t],\mathbb{R})$
I'm currently reading the article "Exact and computationally efficient likelihood-based estimation for discretely observed diffusion processes" by Beskos, Papaspiliopoulos, Roberts and Fearnhead. I'm ...
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1answer
83 views
Any simple function which behaves like this?
I'm looking for this behavior to simulate the movement of the recoil of a gun.
I'm not sure the recoil exactly has this shape, that's a wild guess.
I'm looking for a function that does this ...
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2answers
157 views
Random and Pseudo-random number generation
I heard that computation results can be very sensitive to choice of random number generator.
I wonder whether it is relevant to program own Mersenne-Twister or other pseudo-random routines to get a ...
2
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1answer
2k views
Can't understand a simple wave equation matlab code
I'm trying to figure out how to draw a wave equation progress in a 2D graph with Matlab.
I found this piece of code which effectively draw a 2D wave placing a droplet in the middle of the graph (I ...
0
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1answer
244 views
Why are random numbers necessary for a Monte Carlo simulation?
This may be somewhat of a question with an obvious answer, but I can not seem to understand the necessity of "truly" random numbers to make a Monte Carlo simulation a good one.
I understand that not ...
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0answers
51 views
Continuum limit of cellular automata
Is there any function defined for say the plane, that has interesting nontrivial behaviour similar to Conway's Game Of Life, but where every point's on/off status is decided by something like the ...
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0answers
125 views
Optimization via Simulation
I want to minimize and objective function $\hat{B_i}$ $i\in l$, which can be computed by a matlab code (assume $\operatorname{findB}(a, b, c)$ returns $B$. I have the following optimization problem:
...
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0answers
149 views
Markov Chains - Using Gibbs & Metropolis algorithm.
Suppose $f_x,_y$ is bivariate normal distribution. I was given the parameters $(μ_1, μ_2, σ_1^2, σ_2^2)$ and $ρ=0.95$ the correlation coefficient. I want to generate $(x_1,y_1), ...
2
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1answer
261 views
Monte Carlo - Control Variates & Antithetic method
Supposing $g(x)=\sqrt[3]{x}$, I want to calculate the expected value of g, $E(\sqrt[3]{x})$, using Monte Carlo method, by generating $x_i$ from a Weibull distribution with parameters $(1,5)$.
After ...
3
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0answers
162 views
Simulation and Stochastic Processes
Supposing we want to take a sample from the distribution $p(x)=cp^*(x)$
where $c$ is the normalization constant and $p^*(x)$ is given by
$$p^*(x)=0.5\exp(-(x-\mu_1)^2)+0.5\exp(-(x-\mu_2)^2).$$
...
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1answer
148 views
Algorithms and Simulation
Supposing we want to take a sample from a $N(0,1)$ distribution and i can take a sample from a $N(0,σ^2)$.
(a) Construct a disposal/rejection algorithm with function $N(0,σ^2)$, which generates a ...
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1answer
113 views
simulation and algorithms
A variant method of squeezed rejection algorithm for the simulation of the exponential distribution $\exp(1)$ truncated to $(0,2)$ interval can be written as:
(a) generate $Y \sim U(0,2)$ , $U\sim ...
3
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2answers
131 views
Finite differences of function composition
I'm trying to express the following in finite differences:
$$\frac{d}{dx}\left[ A(x)\frac{d\, u(x)}{dx} \right].$$
Let $h$ be the step size and $x_{i-1} = x_i - h$ and $x_{i+ 1} = x_i + h$
If I ...
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2answers
269 views
Is there a simulation for the Birthday Paradox?
Is there a simulation for the Birthday Paradox problem? Something that uses data from Facebook would be ideal.
0
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1answer
78 views
Simple physics for a graphical user interface widget
I have developed a spinner view for an Android application. It's like the spinner wheel on the Price Is Right with Bob Barker (If you're not familiar with that show watch this video).
I am looking ...
3
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2answers
650 views
Numerical approximation of Levy Flight
I'm trying to produce a computer simulation of a Levy Flight in 2-dimensions; an approximation would be ok. Please excuse the simplistic level of this question: my maths is very rusty.
My proposed ...
