All Questions
1,933 questions
11
votes
1
answer
14k
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
$$
n = \...
- 111
1
vote
0
answers
74
views
Mode of Joint Posterior - Maximization Problems
I have a problem whereby I get two different answers if I try to maximize a function.
let
$ \begin{bmatrix} Y_{o}\\ Y_{a} \end{bmatrix}|\phi\sim N (0,\phi^{-1}A^{-1}) $
$\pi(\phi)=\frac{1}{\phi}$,
...
- 121
10
votes
3
answers
433
views
If $Z_i =\min \{k_i, X_i\}$, $X_i \sim U[a_i, b_i]$, what is the distribution of $\sum_iZ_i$?
Assume the following set up:
Let $Z_i = \min\{k_i, X_i\}, i=1,...,n$. Also $X_i \sim U[a_i, b_i], \; a_i, b_i >0$. Moreover $k_i = ca_i + (1-c)b_i,\;\; 0<c<1$ i.e. $k_i$ is a convex ...
- 60.8k
2
votes
1
answer
315
views
Understanding the tradeoff with regularization in SVMs
In the linear SVM model, one may have the following equation to describe how to achieve a maximal margin while still classifying the data into 2 groups:
\begin{equation}
L(w, \epsilon) = w\cdot w + \...
- 413
2
votes
2
answers
136
views
Monte Carlo Integration Interval Probability
Use MC integration to estimate the probability that X * exp(X) < 2.5, assuming that X ~ Gamma(1.2,3.7)
...
- 21
3
votes
1
answer
2k
views
Extreme value simulation with Monte Carlo
I would like to seek your help with some questions to simulating extreme values. For example, I have written the following R code to generate QQplots for a normally distributed data, varying the size ...
- 133
1
vote
3
answers
2k
views
Monte Carlo integration help needed
I'm trying to simulate these two integrals using Monte Carlo simulation:
$$
\int_{-\infty}^\infty \exp(-x^2) dx, \quad \mbox{and } \int_{-\infty}^\infty \exp(-|x|) dx .
$$
When I use ...
- 13
2
votes
0
answers
255
views
Proving that Markov Chain Monte Carlo converges
I actually asked the same question in https://math.stackexchange.com/ as well at https://math.stackexchange.com/questions/753105/proving-that-markov-chain-monte-carlo-converges but since the question ...
- 2,310
1
vote
0
answers
78
views
Sample variance and error using Monte Carlo
Asked to compute estimator for the following function,
$\theta = \int_0^\infty e^{-x^2}$
which can be solved by transforming the limits to 0 to 1 and solving the following expectation using Monte ...
1
vote
0
answers
351
views
Monte Carlo integration
I am calculating a simple integral $\int^1_{-2} \exp{x^2}(x+1)dx $
with Monte Carlo method using a linear density function $p_\xi (x) = \frac{4}{9} + \frac{2}{9} x $. Let say I have a a sample which ...
- 11
0
votes
1
answer
3k
views
Best method to fit a GEV distribution with generalised linear modelling of parameters?
I need to fit a generalised extreme value distribution to my data but I want the ability to perform generalised linear modelling of the parameters, particularly the location. Can anyone recommend the ...
- 1
3
votes
1
answer
158
views
Joint distribution of a random variable and the sample maximum
This is one necessary part of a slightly larger problem, but this part has me stumped.
We have that $X_1, X_2, ..., X_n\stackrel{iid}{\sim} U(0,\theta)$. What is the joint density of the first ...
- 39
1
vote
0
answers
113
views
Using low-discrepancy sequence for bernoulli trials in MC sim
I need to generate binomial distribution random numbers for my Carlo simulation (I need Bernoulli trials for a parameter). Thus far, I've used R "rbinom" function for that. However, as I understand, I ...
- 111
3
votes
0
answers
153
views
Effect of each parameter on a Monte Carlo Simulation
I was wondering what is the best way to determine the effect of each random parameter on the result obtained from a Monte Carlo Simulation.
I realise I have asked a similar question here, but this ...
- 293
3
votes
1
answer
331
views
Extreme value distribution for multivariate normal
I have a series of data sets. Each data set represents a measurement in 3D space relative to a global origin. I want to model the extreme values of my data. If I were to calculate the extreme radius ...
- 1,191
2
votes
0
answers
64
views
Understanding the effect of each parameter in a Monte Carlo Simulation [duplicate]
I am running a Monte Carlo simulation where I sample from Normal Distributions associated with parameters E11, E22, and GIC to get the plot in red which can be seen in the figure below. The figure ...
- 293
2
votes
0
answers
93
views
Does quasi-random number generator have a period?
I read somewhere, maybe incorrectly, that the Niederreiter quasi-random generator in MKL is 32 bit, and hence as a period of 2^32.
This is pretty low, is this correct?
This made me wonder if quasi-...
user21186
1
vote
1
answer
3k
views
How to calculate max/min scales on a scatter plot
I have 3 log scatter plots that I want to establish smooth maximum and minimum lines. What is the usual mathematical method to do that? (Image and Excel file links below.)
The black lines on the ...
- 39
1
vote
0
answers
361
views
Determining the confidence interval of Monte Carlo data
I want to determine the confidence interval for my set of data. I have obtained the data by sampling from several Normal Distributions and running a Monte Carlo Simulation. I was wondering how I could ...
- 293
0
votes
0
answers
507
views
Understanding a double peaked distribution
I am running a Monte Carlo Simulation and am sampling randomly from about 65 Normal Distributions, each with a different $\mu$ and $\sigma$. I end up with the Mixture Distribution graph shown below ...
- 293
1
vote
0
answers
24
views
Newton Raphson Algorithm: negative semi definiteness [duplicate]
I would like to minimise the function $l(\theta|Y)$.
Given the Newton's method below
$$\theta^{(t+1)} = \theta^{(t)} - \left[l''(\theta\;|\;Y)\right]^{-1} l'(\theta^{(t)}\; | Y)\quad t = 0,1,...$$
...
- 1,893
11
votes
2
answers
11k
views
How does the proof of Rejection Sampling make sense?
I am taking a course on Monte Carlo methods and we learned the Rejection Sampling (or Accept-Reject Sampling) method in the last lecture. There are a lot of resources on the web which shows the proof ...
- 2,310
7
votes
1
answer
6k
views
Importance Sampling to evaluate integral in R
I have asked the question here also.
However, there might be something wrong with my theoretical understanding hence I'm asking here as it is more relevant. Kindly do not diss without looking first.
...
- 185
7
votes
1
answer
2k
views
How good is Monte Carlo Simulation when the variable distribution is unknown?
I am reading the book "how to measure everything", there is a chapter when the author encourages the usage of Monte Carlo simulation in simulating the future events in order to get a better ...
- 1,025
7
votes
2
answers
4k
views
Significance testing of cross-validated classification accuracy: shuffling vs. binomial test
I have a dataset with 2 classes and a certain way to build a binary classifier. I want to measure its performance and to test if it is significantly above the chance level. I measure its performance ...
- 107k
2
votes
1
answer
266
views
Lévy stable vs. extreme value distributions
I'm trying to understand the advantages (if any) of employing the Generalized Extreme Value distribution (GEV) vs. a stable distribution in the context of understanding the probability of crossing a ...
- 958
3
votes
1
answer
2k
views
Reweighting importance-weighted samples in Bayesian bootstrap
Typically, in Bayesian bootstrap, you have samples {$x_1,...,x_n$} of a random variable $X$.
Choose $\{p_1,...,p_n\}$ from a Dirichlet distribution, by sorting $\{0,1,u_1,...,u_{n-1}\}$ where $u_i$ ...
- 206
1
vote
0
answers
323
views
Importance Sampling MC - a couple of questions regarding PDF
I implore the good people to quickly glance through this thread over at StackOverflow to get a better idea of my question if the following isn't clear.
I have these integrals to evaluate using ...
- 185
1
vote
0
answers
49
views
Randomization Testing help
I am scratching my head over this one...any help would be greatly appreciated.
I want to know if the average travel time between Guell Park and the beach in Barcelona using the bus or the metro ...
- 11
6
votes
1
answer
10k
views
Monte Carlo simulation vs. machine learning algorithms: what is the difference in application? [closed]
I have been doing some research on different type of machine learning (ML) algorithms such as random forest/SVM etc. in order to model and best predict pharmaceutical needs of patients suffering from ...
- 63
7
votes
1
answer
1k
views
Data input uncertainty + Monte Carlo simulation + forecasting
Consider a variable $Y$ (e.g., temperature). Suppose that we were able to estimate this variable each year for the past $N$ years using some type of model. This means we have access to annual ...
- 20.9k
78
votes
7
answers
91k
views
Rule of thumb for number of bootstrap samples
I wonder if someone knows any general rules of thumb regarding the number of bootstrap samples one should use, based on characteristics of the data (number of observations, etc.) and/or the variables ...
- 1,201
3
votes
0
answers
107
views
Repairable system and the sum of GEV random variables
We know that $X\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ and $Y\sim {\mathrm {GEV}}(\alpha ,\beta ,0)$ then $X+Y\sim {\mathrm {Logistic}}(2\alpha ,\beta )$.
I am wondering, what will be $X+Y+Z$ ...
- 328
3
votes
0
answers
671
views
Conceptual or mathematical motivation for the three extreme value distribution types?
What motivates, justifies, gives rise to the differences between the Gumbel, Fréchet, and Weibull distributions? Glen_b's comment indicates that they are distributions for extreme values generated by ...
- 1,108
4
votes
1
answer
172
views
Reasons not to use fuzzy numbers instead of pds to represent uncertainty
Can someone explain why (if at all) it would be a bad idea to use fuzzy numbers in order to represent uncertainties in model parameters instead of probability distributions?
To motivate my question - ...
- 217
1
vote
0
answers
99
views
Fitting of bivariate data to a self-defined probability density function
I have a bivariate set of data points which I want to fit to a self-defined distribution (i.e. not standard normal or chi-square or like that, a different, let's say "new" density function). I would ...
- 11
3
votes
1
answer
4k
views
Fitting a linear model with non gaussian noise
I am trying to evaluate the elasticity of prices of some goods. I am concerned about the gaussianity of the noise in the prices. With non gaussianity I am referring to the non existence of the firt/...
- 2,098
1
vote
1
answer
784
views
Plotting the coverage of the confidence interval as a function of sample size using Monte Carlo in R
I have a distribution $x\sim\text{exponential}(\lambda)$ and I know that $\hat{\lambda}=\bar{x}$ and Fisher's information to be $\lambda^{-2}$. Now, I need to use R ...
- 11
1
vote
0
answers
67
views
Optimising test re-test reliability through randomly generating hypothetical repeated trials
I have had a look around the forum, and despite some similar questions on measurement error, no one appears to have asked this question specifically.
I have developed a test where a small group of ...
- 23
4
votes
1
answer
590
views
expected lowest value of 10 normally distributed values
Consider 10 values that follow a standard normal distribution. What would you expect to be the lowest value?
I tried to simulate this problem in R. I basically just simulated 100000 standard normal ...
- 311
2
votes
0
answers
1k
views
maximum gap between order statistics of normally distributed random variables [closed]
I am currently working on a not-that-easy problem involving order statistics. As I am unsure as to how I could solve it, I thought it might already possess a solution. So here I am, my questions is: ...
- 21
5
votes
2
answers
2k
views
Delta function in monte carlo sampling
I am confused by the dirac delta function in the formulation of monte carlo sampling. http://www.cs.ubc.ca/~arnaud/doucet_johansen_tutorialPF.pdf, for instance, defines in section 3.1 page 8 the ...
- 51
2
votes
1
answer
265
views
KL divergence minimisation equation
I am looking at some literature on KL divergence minimisation and am having trouble understanding the derivation of the second order moment. So, if we have a distribution from the exponential family, ...
- 4,730
7
votes
1
answer
125
views
Measurement error in maximum counts
I'm familiar with the concept of a mean value of data and the variation around the mean. Is it possible to quantify variation around maximum values?
For example, take the below data collected across ...
- 14.6k
2
votes
1
answer
937
views
Fitting a probability distribution to non i.i.d. data? [closed]
I have temperature time series data that I have determined is not independently and identically distributed (from looking at the autocorrelation plots and Ljung-Box tests).
However, I am still able ...
- 21
7
votes
1
answer
249
views
Compare maxima of two Gaussian samples
Suppose $X$ and $Y$ are both normally distributed, with $X \sim \mathcal{N}(0,1)$ and $Y \sim \mathcal{N}(c,1),$ where $c > 0$. Consider $n$ independent draws of both $X$ and $Y$. As $n \rightarrow ...
- 874
3
votes
1
answer
322
views
Selecting uncorrelated samples from a set of bulk data that contains correlated and dependent samples
i have a set of data that is generated by expensive computational model evaluations, on a total data set of 10000 samples in 40 dimensions. This sample data set is composed of different data sets, ...
- 151
6
votes
3
answers
306
views
conditional sampling of bivariate normals
I would like to generate random samples from a bivariate normal distribution under a condition. First normal variable is $\varepsilon_1$ , and second normal is $\varepsilon_2$. The condition is $\...
- 607
2
votes
2
answers
2k
views
Most suitable algorithm for optimizing Maximum likelihood function
What is the most suitable optimization algorithm for optimizing maximum likelihood estimator? In excel I used GRG non linear optimization algorithm, is that good enough?
I want to write my own code ...
- 205
1
vote
1
answer
298
views
Overlap Probability of Empirical Distributions
I have a load versus capacity problem, and I'm trying to determine the likelihood of failure. Here's a simple example of what I mean.
I have load and capacity discrete pdfs that were determined ...
- 13