All Questions
1,933 questions
6
votes
1
answer
397
views
Monte Carlo estimation of convex hull overlap probability
This is a statistical version of my Math.SE post.
Given natural numbers $b$ and $r$, uniformly randomly choose $b+r$ points within a unit square. Call the $b$ points the blue points and the $r$ ...
- 461
5
votes
1
answer
321
views
Monte-Carlo estimation of the mean chord length in a polygon
This is a more "statistical" version of my Math.SE problem .
Question Let $\mathbf{P}$ be a convex polygon of $m$ sides. Pick two of its edges at random, and further pick a random point on each ...
- 461
12
votes
2
answers
4k
views
Finding precision of Monte Carlo simulation estimate
Background
I am designing a Monte Carlo simulation that combines the outputs of series of models, and I want to be sure that the simulation will allow me to make reasonable claims about the ...
- 121
12
votes
1
answer
20k
views
Coverage probabilities of the basic bootstrap confidence Interval
I have the following question for a course I'm working on:
Conduct a Monte Carlo study to estimate the coverage probabilities of
the standard normal bootstrap confidence interval and the basic ...
- 819
4
votes
6
answers
8k
views
What free tool can I use to do simple Monte Carlo simulations on OS X?
What free tool can I use to do simple Monte Carlo simulations on OS X?
5
votes
2
answers
7k
views
Monte Carlo experiment to estimate coverage probability
I'm working on a problem as follows for a course that I'm auditing:
Suppose a 95% symmetric t-interval is applied to estimate a mean, but the
sample data are non-normal. Then the probability that ...
user3832
2
votes
0
answers
292
views
Change of measures with Wiener process
I am trying to test importance sampling for a simple a Wiener process $W_t$ in R:
...
- 2,061
3
votes
1
answer
3k
views
Particle filter in Matlab - what is going wrong?
I posted this question on Electronics.Stackexchange and someone told me I'll be better off posting it here.
Its an implementation of the Particle Filter using MATLAB but the results never follow the ...
user3233
7
votes
1
answer
190
views
Estimate the nearest of N random points in a box in E^d?
I have N uniform-random points $p_j$ in a box in $E^d$,
$a_i \le x_i \le b_i$,
and want to estimate the expected distance of the point nearest the origin in $L_q$:
$\quad$ nearest( points $p_j$, box $...
- 3,297
14
votes
4
answers
1k
views
Unbiased estimator for the smaller of two random variables
Suppose $X \sim \mathcal{N}(\mu_x, \sigma^2_x)$ and $Y \sim \mathcal{N}(\mu_y, \sigma^2_y)$
I am interested in $z = \min(\mu_x, \mu_y)$. Is there an unbiased estimator for $z$?
The simple estimator ...
- 141
17
votes
1
answer
4k
views
Scrambling and correlation in low discrepancy sequences (Halton/Sobol)
I am currently working on a project where I generate random values using low discrepancy / quasi-random point sets, such as Halton and Sobol point sets. These are essentially $d$-dimensional vectors ...
- 5,145
13
votes
2
answers
541
views
What should I know about designing a good Hybrid/Hamiltonian Monte Carlo algorithm?
I am designing a Hybrid Monte Carlo sampling algorithm for PyMC, and I am trying to make it as fuss free and general as possible, so I am looking for good advice on designing an HMC algorithm. I have ...
24
votes
2
answers
10k
views
What are some techniques for sampling two correlated random variables?
What are some techniques for sampling two correlated random variables:
if their probability
distributions are parameterized
(e.g., log-normal)
if they have non-parametric
distributions.
The data are ...
- 617
9
votes
1
answer
3k
views
The code variable in the nlm() function
In R there is a function nlm() which carries out a minimization of a function f using the Newton-Raphson algorithm. In particular, that function outputs the value of the variable code defined as ...
- 22.4k
7
votes
3
answers
1k
views
How do extreme values scale with sample size?
Assume I have a random vector $X = \{x_1, x_2, ..., x_N\}$, composed of i.i.d. binomially distributed values. If it would simplify the problem substantially, we can approximate them as normally ...
- 8,879
6
votes
1
answer
483
views
Quantile extrapolation?
Suppose you wanted to estimate the $q$ quantile of a distribution by observing $n$ independent draws from that distribution, but with $q < \frac{1}{n}$. What methods are available, and for what ...
- 15k
3
votes
1
answer
182
views
Basics of extreme values / high-water marks?
With real-valued $X_1, X_2, \ldots$, define
$Max_n := \max(X_1,\ldots,X_n)$ record value or high-water mark
$NextMax_n :=$ the next greater high water, $Max_{n+m} > Max_n$
$Up_n := NextMax_n - ...
- 3,297
7
votes
0
answers
328
views
Help in setting up and solving a transportation / traffic problem [closed]
Traffic light synchronization nowadays is not a tedious project, Image:
For a personal research project I'm trying to build a statistical model to solve such problems in two and higher dimensions.
...
- 1,459
10
votes
5
answers
6k
views
Generate random multivariate values from empirical data
I'm working on a Monte Carlo function for valuing several assets with partially correlated returns. Currently, I just generate a covariance matrix and feed to the the ...
- 627
12
votes
2
answers
7k
views
How can one do an MCMC hypothesis test on a mixed effect regression model with random slopes?
The library languageR provides a method (pvals.fnc) to do MCMC significance testing of the fixed effects in a mixed effect regression model fit using lmer. However, pvals.fnc gives an error when the ...
- 19k
9
votes
2
answers
2k
views
Sampling from bivariate distribution with known density using MCMC
I tried to simulate from a bivariate density $p(x,y)$ using Metropolis algorithms in R and had no luck. The density can be expressed as $p(y|x)p(x)$, where $p(x)$ is Singh-Maddala distribution
$p(x)...
- 35.4k
2
votes
1
answer
1k
views
Finding the mode of a function by MCMC sampling
When trying to find the mode of a nonnegative function $f$ (i.e. maximize the function), one way to do it is to sampling the function viewed as an unnormalized density of some distribution via MCMC.
...
- 19.8k
7
votes
3
answers
4k
views
Minimization of a function by Metropolis-Hastings algorithms
When minimizing a function by general Metropolis-Hastings algorithms, the function is viewed as an unnormalized density of some distribution.
(1) As density functions are required to be nonnegative, ...
- 19.8k
3
votes
0
answers
568
views
Averaged continuous Kernel Density Estimates in lieu of a discrete Kernel Density Estimate in Monte Carlo Proceedure
I am thinking of using this code in a Monte Carlo routine to generate Kernel Density Estimates for subsequent use in a Naive Bayes Classifier (see this earlier post).
The author of the code states ...
- 4,869
7
votes
1
answer
1k
views
Random permutation of a vector with a fixed expected sample correlation to the original?
Suppose you have an $n$-vector $X$. For a fixed real number, $r$ between $-1$ and $1$, can one generate a random permutation of the integers $1,2,\ldots,n$, call it $i_1,i_2,\ldots,i_n$ such that the ...
- 15k
6
votes
4
answers
2k
views
Difference between Excel's RAND(), RAND()*RAND(), etc
I plotted below the standarized results of:
RAND()
RAND() * RAND()
...
RAND() * RAND() * RAND() * RAND() * RAND() * RAND()
It seems that the results are getting to zero, is that because you're ...
- 1,459
14
votes
5
answers
10k
views
Is Matlab/octave or R better suited for monte carlo simulation?
I started to do Monte Carlo in R as a hobby, but eventually a financial analyst advised to migrate to Matlab.
I'm an experienced software developer.
but a Monte Carlo beginner.
I want to construct ...
- 681
5
votes
2
answers
836
views
Is there an analytical expression for the distribution of the max of a normal k sample?
For example:
k <- 100
R <- 10000
max.g <- numeric(R)
for(i in 1:R) max.g [i] <- max(rnorm(k))
hist(max.g) # We can see it's right tailed...
I ...
- 21.9k
13
votes
6
answers
4k
views
How should one approch Project Euler problem 213 ("Flea Circus")?
I would like to solve Project Euler 213 but don't know where to start because I'm a layperson in the field of Statistics, notice that an accurate answer is required so the Monte Carlo method won't ...
- 233
7
votes
1
answer
2k
views
Tangency portfolio in R
I am trying to solve for an efficient portfolio in R. How do I translate my constraints for a tangency point for 2 risky asset portfolio, and a given risk free rate to R solve.QP function? So ...
- 2,799
9
votes
3
answers
10k
views
What is the expected MINIMUM value drawn from a uniform distribution between 0 and 1 after n trials?
Assume you draw a uniformly distributed random number between 0 and 1 n times. How would one go about calculating the expected minimum number drawn after n trials?
In addition, how would one go ...
- 597
9
votes
4
answers
855
views
Why is the average of the highest value from 100 draws from a normal distribution different from the 98th percentile of the normal distribution?
Why is the average of the highest value from 100 draws from a normal distribution different from the 98% percentile of the normal distribution? It seems that by definition that they should be the ...
- 19k
83
votes
3
answers
105k
views
How is the minimum of a set of IID random variables distributed?
If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general?
- 941