All Questions
1,933 questions
0
votes
1
answer
156
views
extreme event time series R
I'm new into time series and was wondering if there is some implementation in R for decomposing a time series into 'trend', 'extreme value', 'cyclical' and' error'.
I'm dealing with yearly weather ...
- 1
2
votes
1
answer
52
views
We know that someone identified correctly 3 out of 5 of wines he tasted. How can we answer if he can do that consistently with randomisation testing? [closed]
I don't know what should i choose as a control function for that problem. Thanks for your time.
0
votes
1
answer
2k
views
R Error - Chi-squared approximation may be incorrect
I have a dataset with salary information in various companies. I'm testing whether Job Title and Gender are dependent/independent of each other. However I'm running into an approximation error ...
1
vote
1
answer
2k
views
Standard deviation of estimated parameters in Monte carlo simulation
I am new to Monte Carlo simulation and have a question. What is the connection between the standard errors of the estimates that we normally get from a regression and standard deviation of sampling ...
- 13
0
votes
0
answers
113
views
Metropolis Hastings on hierarchical bayes update question:
[I have this somewhat complicated hierarchical bayesian model]1
Here the $y$ on $\theta$ are Poisson, $\theta$ are deterministically generated from the $att, def$ (and $home$). Then the last ...
- 1
0
votes
0
answers
32
views
Deriving quantity from two sets of data and do statistical analysis on it?
Say I have a factory that produces bottles of salt water, and there are two processes. One adds some water to a bottle and the other adds some salt.
I have stats on each process. ie. a sample of how ...
- 101
0
votes
0
answers
31
views
Antithetic variate as control variate to find optimal constant [duplicate]
Problem:
If $\hat{θ}_1$ and $\hat{θ}_2$ are unbiased estimators of $θ$, and $\hat{θ}_1$ and $\hat{θ}_2$ are antithetic, we derived that $c^∗ = 1/2$ is the optimal constant that minimizes the variance ...
- 327
0
votes
1
answer
558
views
How can you use Envelope Rejection Sampling to generate samples from a posterior distribution?
Considering two independent random variables:
$$X \sim N(-1, 2^2) \;\; \text{and} \;\;Y \sim N(1, 1^2).$$
Assume we cannot observe $X$ and $Y$ directly but instead observe: $R = \sqrt{X^2 + Y^2} + \...
- 1
0
votes
0
answers
22
views
How can Envelope Rejection Sampling be used to generate samples from a posterior distribution? [closed]
Say we have two independent variables:
$X \sim N(\mu_1, \sigma_1^2)$ and $Y \sim N(\mu_2, \sigma_2^2)$ but these cannot be observed directly.
Instead, we can observe $R = \sqrt{X^2 + Y^2} + \epsilon$ ...
- 1
2
votes
1
answer
545
views
Using Monte Carlo to sample from marginal distribution
I am defining a model on a vector, $T$, of size $n$, wherein each element $t_i \in T$ is independent and either $0$ or $1$. This model depends on 3 other parameters, $q$ (also a vector of size $n$), $\...
- 133
0
votes
0
answers
39
views
Does independence implies independence conditionally on max of the data?
Let be $X_1, ..., X_n$ I.I.D. numerical random variables with contiunous density $f$.
Note $M(X) = \max(X_1, ..., X_n)$ their maximum.
Are $X_1, ..., X_n$ independent conditionally on $M(X) = x$ for ...
- 2,629
1
vote
0
answers
143
views
Can Thomson sampling be used for better results in a 1 player-MCTS
I made a Monte Carlo tree search (MCTS) algorithm for the travelling salesman problem inspired by this paper which uses UCB1.
When I was digging to see where does the UCB1 formula comes from, I read ...
- 111
0
votes
1
answer
773
views
How to generate a random number with normal distribution given confidence intervals?
I have broken down a project in to some list of tasks. For each task, I've worked with some experts to come up with 90% confidence intervals. e.g. I'm 90% sure task A will be more than L hours and 90% ...
- 115
0
votes
0
answers
73
views
Why does the Law of the Unconscious Statistician work here for the pathwise estimator
https://arxiv.org/abs/1906.10652
So there are these two parts
"Continuous distributions have a simulation property that allows both a direct and an indirect way of drawing samples from them, ...
- 95
1
vote
1
answer
70
views
Numerical superiority necessary to beat in $L^\infty$ a population one standard deviation ahead
Suppose $m$ independent random variables $X_i$ have the distribution $\mathcal{N}(0, 1)$, and $n$ independent random variables $Y_j$ (also independent of the $X_i$) have the distribution $\mathcal{N}(...
- 11
1
vote
1
answer
2k
views
Python for ARIMA model Monte Carlo? [closed]
I'm interested in fitting a time series with an ARIMA model in Python and then performing a Monte Carlo simulation to generate many possible future paths assuming the time series follows that model.
I'...
- 13
0
votes
2
answers
237
views
Sum of squares for a Dirichlet distribution
I have some data that takes the form of vectors $(a_0,...,a_n)$ lying on the simplex $\Sigma a_i = 1$ (all $a_i$'s non-negative). I have noticed that the maximum $\max_i a_i$ is very highly correlated ...
- 3
3
votes
2
answers
329
views
Why are extreme correlations so common in this Monte Carlo simulation? [duplicate]
Consider the following simple Monte Carlo:
...
- 9,680
6
votes
2
answers
433
views
Do you need large amounts of data to estimate parameters in extreme value distributions?
There is probably not a hard answer for this, but I am wondering if you need to collect more data when trying to estimate the parameters of generalized pareto distribution well?
The reason I ask is ...
- 99
4
votes
0
answers
75
views
Estimation of the density at the bound of the support of a real random variable
Let $X$ be a random variable with real values and with density $f$.
Assume the support $f$ is bounded with supremum $m$ and has a positive value at that supremum:
$$\forall x > m, f(x) = 0 \text{ ...
- 2,629
10
votes
1
answer
642
views
Distribution of argmax of beta-distributed random variables
Let $x_i \sim \text{Beta}(\alpha_i, \beta_i)$ for $i \in I$. Let $j = \operatorname*{argmax}_{i \in I} x_i$ (ties broken arbitrarily). What is the distribution of $j$ in terms of $\alpha$ and $\beta$? ...
- 1,033
0
votes
0
answers
76
views
Normalization of $M_{n} = \max(U_{1}, ... , U_{n})$
Let $M_{n} = \max(U_{1}... , U_{n})$ be the maximum of a sample size $n$ from $U(0 , 1)$ distribution.
In my statistics textbook it says that $M_{n}$ normalized is equal to $n(1 - M_{n})$ but I'm not ...
- 107
9
votes
1
answer
443
views
Intuition about the coupon collector problem approaching a Gumbel distribution
The coupon collector's problem
Let there be $n$ different types of coupons and we try to collect all of the types.
We do this by independent random draws of coupons in which each type of coupon has an ...
- 86.5k
9
votes
3
answers
2k
views
Monte Carlo simulations for arbitrary functions
I'm familiar with MC methods for approximating PDF integrals. But in this question, I'm curious how we might adapt these methods for other problems. For example evaluating $\int_{0}^{1} x^2 dx$ . I ...
- 3,520
2
votes
1
answer
270
views
Calculate certainty of Monte Carlo simulation
(Hi, sorry, this is probably a very entry level question for this site. Let me know if something is not OK.)
Let's say that we use the Monte Carlo method to estimate the area of an object, in the ...
0
votes
0
answers
220
views
mixture of exponential and gamma distribution
I'm not particularly good at statistics and whatever elementary statistics I have had exposure to are now rusty. However, I am working on a problem that I am hoping to gain some insights into:
My goal ...
- 251
1
vote
0
answers
90
views
Comparing two types of confidence intervals in R using Monte Carlo: trouble understanding what's going on
In a course I'm taking, my professor includes the following code in his slides.
I'm trying to understand what this code does, but perhaps more importantly I'm also trying to understand the ...
- 601
3
votes
1
answer
440
views
Finding a right way of sampling 1/X knowing X follows the Moschopoulos distribution (sum of Gamma distribution with different (shape/rate parameters)
I can generate, with COGA R library (with rcoga function), a sample from a random variable ...
user226073
5
votes
2
answers
1k
views
CDF of maximum of $n$ correlated normal random variables
The maximum of $n$ normal i.i.d. random variables
$$Y=\max\{x_1,...,x_n\},$$
$$x_i \sim N[0,1]$$
has the CDF
$$P(Y\le y)=\Phi(y)^n $$
but how does the CDF look like, if the variables are identically ...
- 1,250
0
votes
1
answer
139
views
Why set factor means to 0? Monte Carlo simulation
I am using structural equation modeling (SEM). My model is a simple mediation model with latent variables (each latent variable has 3 indicators).
I want to run a Monte Carlo simulation to estimate if ...
0
votes
0
answers
82
views
SVM random sampling permutation for imbalanced data: class & score weighted vs non weighted
I have been running the dataset of 2 classes with imbalanced numbers with python.
Class one is 61, and class two is 66.
When I built up the SVM model and did the random sampling permutation (monte-...
1
vote
1
answer
2k
views
Return level plots for GEV-distribution
I was reading An Introduction to Statistical Modeling of Extreme Values by Stuart Coles, and I ran into a problem whilst trying to replicate a basic return level graph in R. For context, I first ...
- 79
0
votes
1
answer
141
views
Stochastic simulation, what to do after generate the initial random sample
I don't have a background in statistics but currently learning the basics.
I want to do a stochastic simulation, which I assume here I should iterate my simulation multiple times. And I am stuck now ...
- 1
0
votes
0
answers
27
views
Issues with sampling distribution over bootstrapped monte carlo simulations
Facebook posed an interview question (see ~49 min mark), how many days would it take (in days) to sample every user from a population of 1000, given that you sample 10 users/day each day? Analytically,...
- 3,520
0
votes
1
answer
379
views
Monte Carlo approximation to find expected value of gradient square
I need to to calculate this term:
$
\mathbb{E}\left[S(Y, L,\theta)S(Y,L,\theta)^\prime\right]
$
Where
$
S(Y,L,\theta) =\frac{\partial}{\partial\theta}
l(Y,L,\theta)
$
With $\theta$ = maximum ...
- 35
2
votes
1
answer
63
views
A front-loaded Gumbel-like distribution
I'm looking for a distribution that is somewhat like the Gumbel distribution and I was wondering if anyone could help.
The parameters are a positive integer $n$ and real numbers $\mu>0$ and $\sigma&...
- 1,248
1
vote
1
answer
407
views
Bayesian A/B testing and decision metrics
Say I need to test two different product features ({existing/control: blue} vs {new/treatment: red} font on webpage, for example), and need to boil my analysis down a to a single go/don't go criteria ...
- 3,520
7
votes
1
answer
371
views
How can you combine control variates with antithetic variates
Is there a benefit of combining control variates with antithetic variates and if so how should it be done ?
In my specific case I would like to add control variates to the formulation in this paper :
...
- 173
1
vote
1
answer
178
views
Understanding the probability distributions behind a Monte Carlo experiment
A colleague and I are trying to model the expected maintenance cost/h (E[C/h]) of a component A on an aircraft over its life based on its reliability distribution. As the component fail, it's replaced ...
- 181
0
votes
1
answer
32
views
comparing odds of two gaussians
I am trying to compare the odds of two events happening (what are the odds of one happening first). I know that the first one occurs in an average of 10 months with a sigma of 3 months. The second ...
1
vote
1
answer
367
views
How to generate random points from a custom curve? [closed]
my question is how to generate random points ($\theta_1,\phi_1$) on a curve determined by :
$
\arccos\left(\cos(\theta_1)cos(\dfrac{\pi}{6})+\sin(\theta_1)\sin(\dfrac{\pi}{6})\cos(\phi_1)\right) = \...
- 11
1
vote
0
answers
61
views
Importance sampling vs acceptance-rejection [duplicate]
In both importance sampling as well as acceptance-rejection, we sample from some alternate distribution to simulate some expression from an original distribution of which we know the PDF. The ...
- 2,630
0
votes
0
answers
127
views
Estimate argmax of function that is measured at discrete points
I have gathered simulation data of a function $f(x)$, where $x$ is a continuous variable. I measure $f$ at discrete points $x_k$. Since the underlying process is stochastic, I performed Monte Carlo ...
1
vote
0
answers
45
views
Does this distribution with polynomial tails have a name?
I have $N$ random variables which are identically and independently distributed with complementary CDF:
$$Pr[X \geq x] = \frac{a}{X} + \frac{b}{X^2}$$
for $x \geq 1/2 \sqrt{a^2 + 4 b} + a/2$.
This ...
- 359
3
votes
0
answers
43
views
Computationally + Statistically Efficient Unbiased Estimation of Chebyshev Polynomials of Expectations
Let $T_n$ denote the $n^\text{th}$ Chebyshev polynomial, defined by the recursion
\begin{align}
T_0(x) &= 1,\\
T_1(x) &= x,\\
T_n(x) &= 2x \cdot T_{n-1} (x) - T_{n-2} (x).
\end{align}
Now, ...
- 1,356
2
votes
1
answer
238
views
Sampling from bivariate joint cumulative distribution function
Given two variable $x,y$, they are subjected to a joint probability density function:
$
f(x,y) = \dfrac{1}{3}(3x^2 + 4xy + 3y^2)\\
0\leq x \leq 1;0\leq y \leq 1
$
Obviously, its corresponding ...
- 21
1
vote
0
answers
71
views
Distribution of Geometric Brownian Motion drawdowns from realizations of multivariate Normal and Laplace distributions
I am trying to simulate the distribution of Geometric Brownian Motion drawdowns from realizations of multivariate Normal and Laplace distributions under the same covariance structure. Drawdowns are ...
- 41
2
votes
0
answers
118
views
Distribution of sample p-values with a known true p-value
N. Taleb in his book Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications (Technical Incerto), page 349 (chapter 19: Meta-distribution of p-values and p-...
- 26.9k
0
votes
0
answers
67
views
How to generate uniformly distributed random numbers between 1 and 26 with a die [duplicate]
I want to generate uniformly distributed random numbers between 1 and 26 with a die: Is this correct:
I have assembled the following algorithm using the Monte Carlo Method:
{1, 2, 3, 4, 5, 6} {7, 8, 9,...
1
vote
0
answers
36
views
Given 5 variables, all independently normally distributed, what is the probaility that variable A is lower than the other 4 variables?
Suppose variables A B C D and E are independent, normally distributed, with known variance and mean.
What is the probability that A is less than B and C and D and E?
Essentially, I have model ...
- 11