All Questions
1,933 questions
4
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3
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192
views
Where did I go wrong in computing $P\left(Y-X < \frac{1}{8}\right)$ where $X \sim \mathcal{U}[0,1]$, $Y|X \sim \mathcal{U}[X,1]$?
I'm interested in an adaptation of Problem 1.3 from Mathematical Statistics by S.S. Wilks (second edition, 1962). I've added the self-study tag, however this is for ...
- 9,680
5
votes
2
answers
768
views
How to calculate Quasi-Monte Carlo integration error when sampling with Sobol's sequence?
My understanding is that QMC integration using random sampling will converge with $O(\frac{1}{\sqrt{n}})$, while using Sobol's sampling will converge with $O(\frac{(\log{n})^d}{n})$. However I'm ...
- 203
0
votes
0
answers
53
views
Combining importance sampling with enumeration for estimating expected value
I have a Monte Carlo simulation which, given an initial state, does some random stuff and outputs a scalar. Let this output be the random variable $Y$. The simulation takes place on an $K$x$K$ grid, ...
- 1
4
votes
1
answer
144
views
Rao-Blackwellization in Black Box VI
In the paper, "Black Box Variational Inference," by Ranganath et al. (2013), the authors derive a Rao-Blackwellized estimator of the gradient of the evidence lower bound with respect to a ...
- 41
1
vote
1
answer
28
views
Notation in Bayesian hierachical models: what does * indicate [closed]
I am new to Bayesian Statistics and have a question about the notation *.
What does it indicate in the context of hierarchical models ?
Cheers
- 11
0
votes
1
answer
46
views
Calculate the probability $P(S^2_{n-1}<s^2_{n-1})$ by Monte-Carlo simulation of the population distribution
i am struggling with the following problem, i have posted my attempt below, i am apparently supposed to get an answer of 0.632 with a random seed of 25 however i get a 1 as the answer. Please help i ...
- 113
0
votes
1
answer
105
views
Particle Filter Derivation based on Forward Algorithm
I have been studying the particle filter, sequential monte carlo methods, and sequential importance sampling.
I am interested in apply the particle filter equations to the standard forward algorithm:
$...
- 217
12
votes
5
answers
1k
views
Estimate the Euler–Mascheroni constant ($\gamma$) by Monte Carlo simulations
The Euler–Mascheroni constant is defined simply as the limiting difference between harmonic series and the natural logarithm.
$$\gamma =\lim_{n\to \infty}\left(\sum _{k=1}^{n}{\frac {1}{k}}-\ln n\...
- 285
1
vote
0
answers
125
views
Distribution of maximum of sample means
Let $X_1, ..., X_n$ be a sample from $N(\mu, 1)$. Fix $1 \leq m<n$ and define $$T_i= \frac{1}{m}\sum\limits_{j=i}^{i+m-1} X_j,$$ for $i \in \lbrace 1, ..., n-m+1 \rbrace$. We have the test that ...
- 111
1
vote
0
answers
37
views
How close am I to the true minimum?
This might be a trivial question but my statistics knowledge very is rudimentary:
I'm trying to measure the amount of clock cycles that my computer needs to execute a certain function. The number of ...
- 51
1
vote
0
answers
61
views
best loss function to fit model if observations contain montecarlo noise?
I have observations on the sphere and I'm trying to fit spherical-harmonic coefficients to best approximate and interpolate the observations.
I'm using a solver library for non-linear least squares ...
3
votes
1
answer
343
views
Monte Carlo or other general sampling approaches for conditional distributions?
Suppose we have a sampler – eg a Monte Carlo sampler – for the posterior probability distribution $p(x \vert D)$ of a quantity $x=(y,z)$ consisting of a pair of continuous and multidimensional ...
- 1,316
0
votes
0
answers
34
views
What test to use in order to conclude that a number of seeds/experiments is enough?
When performing a series of replicas for an experiment with a stochastic component (e.g. a Monte Carlo experiment, training a machine learning model, etc.) and averaging the results - how can I ...
- 111
0
votes
1
answer
84
views
How can i find out closest lognormal distribution parameters from a GEV distributed data in R
The question is a bit weird so i'll open it up.
So i have a table of return periods for different amounts of rain. The table has been made using GEV distribution on known data and then the mean and ...
-1
votes
2
answers
389
views
Monte Carlo simulation for generating random numbers from a distribution [closed]
Describe Monte Carlo simulation technique and mention its different steps. Also describe how would you generate random numbers from Weibull distribution with parameters (θ, β) .
In this question, I ...
- 387
1
vote
1
answer
168
views
Generating random variable from no closed-form marginal density [closed]
Suppose $u\sim N(0,I_p)$ and $Y|U\sim N(x(t),\sigma_e^2I_m)$, and the marginal distribution of $y$ is $f(y)=\int_u f(y|u)f(u)du$.
$x(t)$ is composite function of $u$, basically $x(t)$ is a function of ...
- 19
1
vote
0
answers
72
views
Extreme Value Analysis of Hurricane wind speeds
As per the theory, an EVA with annual maxima presupposes that the series is complete, i.e. all years have an event. However, hurricanes don't occur every year, and so the hurricane wind speeds in ...
- 398
1
vote
0
answers
28
views
Generating random variable from mixture representation [duplicate]
Suppose $u\sim N(0,I_p)$ and $Y|U\sim N(x(t),\sigma_e^2I_m)$, and the marginal distribution of $y$ is $f(y)=\int f(y|u)f(u)du$.
$x(t)$ is composite function of $u$. The problem is I need to generate ...
- 19
8
votes
2
answers
763
views
Intuition behind Weibull distribution?
I don't understand the physical meaning of Weibull distribution's $k$ parameter. Here is a simplified formula of cumulative probability function of Weibull in the simplest form:
$$p(\xi \geq x) = e^{-(...
- 378
3
votes
1
answer
299
views
Method of collecting and comparing outliers from sets of sets of populations
Background
I am a PhD student co-supervising a Master's student in our lab. I am mostly familiar with discrete mathematics, signal processing, and programming simulations. My statistics background ...
2
votes
1
answer
786
views
Von Neumann acceptance-rejection technique for 2 or more variables
I need to generate random numbers that follows a given distribution f(x). Consider the following acceptance-rejection method:
I generate two random numbers, $r_1$ and $r_2$, both from 0 to 1 that ...
- 25
1
vote
0
answers
205
views
How does Particle Filters work?
I'm trying to figure out how particle filter works.
Assume that I have selected propability function called $a \sim Gauss(\mu, \sigma)$. We call it proposial (Gaussian) Distribution.
Then we have ...
- 425
4
votes
1
answer
353
views
How to extract the shape parameter of a Fréchet fitted model using the R SPREDA package?
I'm trying to follow this post, which fits a Frechet distribution to some wind measurements as follows:
...
- 26.9k
0
votes
0
answers
46
views
Do I need to know the distribution of the noise before I'm using Monte Carlo Sampling?
I'm going to use Particle Filter, which is a Monte Carlo Sampling.
My simple question is: Do I need to know the distribution of the noise before I'm using Monte Carlo Sampling?
Or can I just use a ...
- 425
3
votes
1
answer
914
views
Fat tails equal higher probability of non-extreme values according to Nassim Taleb?
I just came across the following passage written by Nassim Taleb Link:
The fattest tail distribution has just one very large extreme deviation, rather than many departures form the norm. [...] if we ...
- 1,129
4
votes
1
answer
486
views
Student's t as a power law distribution
I'm currently reading about power laws and I have came across an answer stating:
The density function of a Student's t-distribution with $n$ degrees of freedom is:
$$f(x) \sim (1 + x^2 / n)^{-(n+1)/2}...
- 750
4
votes
1
answer
319
views
computing $P\left(\max(U_{(1)}, U_{(2)}-U_{(1)}, \cdots,U_{(n)}-U_{(n-1)} ) <a\right)$
Let $U_{1}, \, ... \, ,U_{n}$ be a random sample of uniform random variables $U_i \sim \mathrm{Uniform}(0,1)$. Let $U_{(1)}, \, ... \, , U_{(n)}$ be the order statistics of the sample. My problem is ...
1
vote
1
answer
256
views
Expectation of Maximum and Minimum of Partial Sums of Normal Random Variables
Peggy Strait, 1974, Pacific Journal of Mathematics
ON THE MAXIMUM AND MINIMUM OF PARTIAL SUMS OF RANDOM VARIABLES
Gives a nice result (4.3) and (4.4) in terms of "standard normal random variables&...
- 241
6
votes
1
answer
107
views
Estimate $E[X_1 | X_1>X_2>\cdots>X_k]$ with simulation
Suppose Random variables $(X_1,X_2,\cdots,X_k)$ are mutually independent, but not identically distributed. I want to estimate $E[X_1|X_1>X_2>\cdots>X_k]$ with simulation. I am wondering if ...
- 657
4
votes
1
answer
200
views
How to reproduce the distribution of p-values in a Monte Carlo?
In whichever program (R preferred, but pseudo-code would do), could I get an idea of how Nassim Taleb simulated the distribution of p-values - I guess under the alternative hypothesis - on this MOOC?
...
- 26.9k
1
vote
0
answers
203
views
Calculation of Variance from a 2 order Taylor expansion - Expecting a better estimation than with 1st order Taylor expansion
I tried to compute the variance of a squared ratio of 2 Gaussians random variables (not the same means and standard deviations between both). I generate the samples by Monte-Carlo method.
I expect ...
user226073
6
votes
1
answer
10k
views
Trying to calculate confidence intervals for a Monte-Carlo estimate of Pi. What am I doing wrong?
I trying to implement the classic Monte-Carlo simulation of $\pi$ to better understand how confidence intervals (CI) decrease with more trials. There are a lot of examples of how to do the former, but ...
- 415
1
vote
0
answers
105
views
What are some methods to choose a $n$ for Quasi Monte Carlo Integrations?
When studying "simple" Monte Carlo integration methods, such as Hit or Miss, Crude , Importance Sampling, etc. A common problem for first time learners is to choose a number $n$ of points ...
- 11
1
vote
1
answer
563
views
Correct methodology using $g$-computation to estimate Average Treatment Effect on the Treated ($ATT$)?
I have a question about the $g$-computation methodology for estimating the Average Treatment Effect on the Treated ($ATT$) in the following article.
The authors recommend estimating the $ATT$ by first ...
- 6,286
0
votes
1
answer
271
views
Are the two $\epsilon$-greedy policies different?
I found 2 diffefent versions of $\epsilon$Greedy policy for monte carlo and q learning:
For monte carlo:
$\pi (a|s)=\epsilon /m +1-\epsilon$ to choose the best action and $\pi =\epsilon /m$ for other ...
- 1
0
votes
1
answer
40
views
Can I create an own p.d.f to apply it in a Monte Carlo study?
I need to generate few random numbers, but they need to be distributed in a very specific (continuous) function $R(x)$. Once I do not have much background in the topic, I would like to ask 2 questions:...
- 25
0
votes
0
answers
71
views
Minimum of Multivariate Pareto
Suppose I have a multivariate Pareto distribution with cdf,
$$ Prob(Z_{1}<z_{1},\dots,Z_{n}<z_{n}) = H(\textbf{z}) = 1 - \left( \sum_{i=1}^{n} (T_{i}z_{i}^{-\theta})^{\frac{1}{1-\rho}} \right)^{...
- 253
0
votes
1
answer
412
views
Question about MCMC independent proposals
I've a question re MCMC proposals, I was hoping you could help me with that. I need to implement for work an Independent Metropolis-Hastings algorithm to sample from a 10-dimensional posterior. I am ...
- 3
2
votes
1
answer
282
views
Importance Sampling: using Target Distribution as Proposal Distribution to approximate normalizing constant
Importance Sampling is a method use to approximate expectations of a test function $\phi$ with respect to $p$ by instead sampling from a proposal distribution $q$
$$
\mathbb{E}_{p}[\phi(x)] = \int \...
- 667
1
vote
0
answers
238
views
Sampling marginal distribution from joint density
Suppose we know that random vectors $x, y$ have joint density $p(x, y) \propto \exp(-U(x_1, \ldots, x_m, y_1, \ldots, y_n))$, and we want to draw a random sample from the marginal $p(x)$ (i.e. we want ...
- 111
8
votes
2
answers
516
views
Estimating $f(\mathbb{E}[X])$ with a guaranteed error performance
Given "black-box" sample access to a random variable $X$**, are there results that give an algorithm that approximates $f(\mathbb{E}[X])$ with a user-specified error bound, ideally using as ...
- 1,194
1
vote
0
answers
232
views
Maximum absolute from complex Gaussian distribution
Consider a random variable $Y$ with complex Gaussian distribution, i.e $Y \sim \mathcal{C N}(\mu,\sigma^2)$. We can write $Y$ as real ($Y_r$) and imaginary component ($Y_j$) as $Y = Y_r + i Y_j$. ...
- 121
0
votes
0
answers
24
views
Estimating Actual Ranking Amongst Other Quiz Takers
Problem
The New York Times has a multiple choice "quiz" to evaluate their readers' understanding of recent news. They normally have a feature that reports your performance compared to other ...
0
votes
1
answer
635
views
Monte Carlo Approximation of a Normalizing Constant [duplicate]
I know that one can approximate expectations of a function with respect to a pdf as such
$$
\mathbb{E}_{p(x)}[\phi(x)] = \int \phi(x) p(x) dx \approx \frac{1}{N}\sum_{i=1}^N \phi(x^{(i)}) \qquad\qquad ...
- 667
-1
votes
1
answer
135
views
Calculating Monte-Carlo Error For Confidence Interval Estimation [closed]
I am simulating from a Categorical process such that each $x_i \in \mathbb{R}$ is an independent sample. After drawing $N$ samples, I want to use my samples to estimate the standard error of the ...
4
votes
1
answer
453
views
Residuals in Generalized Pareto Distribution
I'm learning generalized Pareto distribution for fitting extreme value data. I came across an R package evir that is able to plot residuals. Residuals from a GPD ...
- 8,655
0
votes
0
answers
676
views
How to model distributions of correlated variables and pick from it for montecarlo simulation
I have time data. Different variables with some degree of correlation among them. What I would like is to pick a sample from the distribution of those who have no or low correlation with the others ...
- 213
1
vote
1
answer
218
views
Finding a proposal distribution in acceptance-rejection method
I'm learning the Acceptance-Rejection method but I am having a hard time finding a g(x) except using uniform distribution to simulate the f(x).
How could we find a g(x) that has a simple pdf and is ...
- 11
1
vote
0
answers
29
views
Uses of MCMC samplers outside of Bayesian Inference? [duplicate]
I'm curious if there are applications of MCMC outside of Bayesian Inference?
this conversation started when discussing Monte Carlo methods vs Markov Chain Monte Carlo methods with a coworker. He asked ...
- 3,520
2
votes
0
answers
134
views
Do Particle Filters actually approximate the posterior distribution?
Im reading a tutorial paper about particle filters (Link) in which it is stated that as the number of samples tends to infinity the approximated posterior density given by
$p(x_k|z_{1:k}) \approx \...
- 21