All Questions
1,933 questions
0
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137
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Sample size for each trial vs Number of trials conducted for Monte Carlo Simulation
I am running some Monte Carlo Simulations on Matlab. I am wondering if running more Monte Carlo Simulation trials and taking the average value of these trials is the same as running a single trial ...
- 183
4
votes
1
answer
540
views
Can we fit extreme value distribution by build-in package?
I try to find a package in R to fit Gumbel distribution by Block Maxima Approach using maximal likelihood function (see here)
$$
G(x; \mu , \sigma)=\exp[-e^{-\frac{x-\mu}{\sigma}}].
$$
The block ...
- 747
2
votes
0
answers
259
views
Monte Carlo Power calculation for Survival analysis in R
for a project I have to analyze two survival analysis treatment groups using R. I want to calculate the power and type I error rate of a test with Monte Carlo simulation to set up a phase 3 medical ...
1
vote
0
answers
68
views
Why do we have first/every-visit in MC but not last visit [closed]
I'm studying Reinforcement Learning and I just read about first-visit and every-visit Monte Carlo, however I don't get why we are not considering last-visit MC as a possible simulation.
My "last ...
- 1,381
2
votes
1
answer
398
views
Why does Gumbel distribution have two different expressions?
Let $X_1,X_2,\dots,X_n$ be iid random variables with distribution function $F(x)$ and $M_n:=\max\{X_1,\dots,X_n\}$. By the extreme value theorem, there exist two sequences of real numbers $a_n>0$ ...
- 747
2
votes
1
answer
248
views
Extreme value theory for detrended series
I'm reading "An Introduction to Statistical Modeling of Extreme Values" by Stuart Coles, and using the pyextremes package for exploring the data which is time to return (in days). After ...
- 21
1
vote
1
answer
61
views
How to evaluate the accuracy of probability of a large set of non-repeatable events?
Assuming there are a large set ($N>1000$) of independent events $E_i$ ($i=1,2,\dots,N$), each having $M$ different outcomes. For each event $E_i$, I have an estimated discrete probability $\hat P_j(...
- 113
1
vote
1
answer
266
views
Why my fitted genextreme distribution have no mean/variance?
I have the following code for estimating a generalized extreme value distribution from scipy.
...
- 7,351
8
votes
5
answers
2k
views
When sampling a population for surveys we can often limit our sample size to hundreds, but when doing a Monte Carlo simulation we need way more. Why?
I’m a bit of a stats-noob, so I am not sure I will manage to formulate this question properly, but let me do my best.
I‘m trying to develop an intuition for sample sizes and when they are sufficient ...
- 183
1
vote
0
answers
39
views
1
vote
3
answers
310
views
Most probable value vs maximum of the distribution [closed]
Given a distribution p(x), there are two things that can be calculated.
Value of x for which p(x) is maximum.
Most probable value of x weighted over p(x).
Would these two values of x be the same?
- 113
3
votes
2
answers
119
views
Random sampling from a super level set
I have a random sampler from a region $X$. Suppose, I have a function $f: X \to \mathbb{R}$, where I can explicitly evaluate $f(x)$ and also obtain the gradient $\frac{\partial f}{\partial x}$ easily (...
- 211
0
votes
0
answers
93
views
Confidence interval for evaluating an integral via Monte-Carlo sampling
I am trying to evaluate the following integral using Monte-Carlo:
$$
\langle f \rangle = \int \mathrm{d}x~ \rho(x) f(x)
$$
where $\rho(x)$ is a normalized positive function. The integration is ...
2
votes
1
answer
204
views
Uncertainty/Standard Deviation of Monte Carlo methods
I am using a Monte Carlo method to estimate the expected value of the results of certain simulations.
Consider this simplified case: $X, Y$ are independent random variables and $g(X,Y)$ is a nonlinear ...
- 21
5
votes
1
answer
83
views
Which distribution is it?
I recently came across the following distribution
$$
\Pr(X\le x)=e^{\tfrac{1}{a}-\tfrac{1}{x}}\left(\dfrac{a}{x}\right)^{\tfrac{1}{a}},\; 0\le x< a,
$$
and the cdf is 0 for all $x\lt 0$ and 1 for ...
- 313
2
votes
1
answer
50
views
Probability of sample minimum below a certain value
I have a list of 1000 songs with their bpm (beats per minute). If I were to sample 30 songs, is there a way to find the probability that the sample minimum is below a certain value like 100 bpm?
- 23
1
vote
0
answers
187
views
How to set up a monte carlo simulation for time-series, cross-sectional / panel data in R
I am looking for tips, pointers, explainers, blog posts, and the like, on how to set up a monte carlo simulation for a time-series, cross-sectional / panel data generating process in R.
I would like ...
- 427
1
vote
1
answer
72
views
Why do we use the limiting distribution under the null hypothesis when computing power in Monte Carlo simulation?
I'm computing the power of a statistical test using Monte Carlo simulation. My test statistic is asymptotically $\chi^2$ under the null hypothesis. When I am computing the power for a given iteration ...
- 143
2
votes
1
answer
111
views
What does it mean to have a "transient state" or a "transient phase" in an Ising model?
I downloaded a simple implementation of the Ising model in C# from this link.
I have understood more or less the entire code except the following routine:
...
- 2,125
10
votes
5
answers
1k
views
Expectation of random sum of non-random numbers
I have a continuous random variable $\tau$ and I want to evaluate
$$
E\left(\sum_{i=1}^{\lfloor \tau \rfloor} Y_i\right),
$$
where $Y_i$ are known, non-random, and $\lfloor . \rfloor$ is the floor ...
- 860
0
votes
1
answer
97
views
How does one test the efficiency and completeness of an estimator using monte-carlo simulation?
How does one test the efficiency and completeness of an estimator using monte-carlo simulation?
In particular,
I want to use-montecarlo simuation to answer. Maybe the better question is how does one ...
user318514
17
votes
2
answers
1k
views
Why does this algorithm generate a standard normal distribution?
I have this algorithm which I encountered:
(1) Generate $U_1$, $U_2$ independently from Uniform(0,1)
(2) Set $Y_1 = -\log{U_1}, Y_2 = -\log{U_2}$. If $Y_2 > \frac{(1-Y_1)^2}{2}$, accept $(Y_1, Y_2)$...
- 173
1
vote
0
answers
100
views
Monte Carlo method for confidence intervals
I would like to attempt a Monte Carlo procedure to filter composite anomalies at 90% confidence level from the rest of the composite anomalies. My data is a NetCDF of hourly surface temperature that I'...
- 23
1
vote
1
answer
76
views
how to sample two random variables from different distributions and requiring one is always larger than the other
I know one way is to sample A and B independently and then reject the samples where A<B. But I wonder if there is an easier method?
1
vote
1
answer
182
views
How to use MC simulation to calculate Supremum ADF test critical values
I am replicating some techniques from Advances in Financial Machine Learning by Marcos López de Prado. In Chap 17, I am doing the Supremum ADF test and Quantile ADF test. It seems that they do not ...
- 13
1
vote
1
answer
53
views
Violation of IID in Peaks over Threshold
I'm using the peaks over threshold method to answer a researchquestion. I'm working with time-series data and the observations are not entirely independent. I know that there is some methods you could ...
- 31
1
vote
1
answer
67
views
How do I start and go about analyzing the variability of extreme rainfalls in a region?
I have a gridded dataset of monthly precipitation and would like to analyze the variability of extreme rainfall. However, aside from looking at the overview of basic statistics (mean, standard ...
- 23
1
vote
0
answers
49
views
Huge bias in IV during Monte Carlo Simulations
I am trying to see how IV performs with Monte Carlo Simulations. My model is:
$y = X \beta + p \alpha + \xi + \epsilon $. In this model $ \xi $ is not observed and $p$ is correlated with $\xi$. So I ...
- 11
1
vote
0
answers
84
views
Using p-values as an effect size measure [closed]
In the following circumstance, I believe it is valid to use p-values as a measure of effect size: am I wrong?
I have a set of objects which have a single 'observed distance' from a given spatial ...
- 61
1
vote
3
answers
245
views
Why not just run a Markov chain to get stationary probabilities?
I'm reading Performance Modeling and Design of Computer Systems which contains some analysis of Markov chains. In particular, it emphasises various analytical methods for finding the stationary ...
- 834
2
votes
1
answer
2k
views
How to ge the Monte Carlo standard deviation of the empirical standard deviation?
The authors get the Monte Carlo standard deviation of the empirical standard deviation as follows.
My question is how to get the MCSE of the EmpSE?
For bias, the MCSE of $\frac{1}{n}\sum \hat{\theta}...
- 747
4
votes
1
answer
458
views
Why does the Monte Carlo estimate not depend on the dimension
The Monte Carlo Estimator for some event probability (e.g., for the "failure probability") is defined as follows:
$$
\hat\mu = 1/N \sum_{i=1}^N I(\boldsymbol{x}_i),
$$
where $\boldsymbol{x}...
- 43
3
votes
1
answer
474
views
How to verify the convergence rate in Monte Carlo simulation?
Given a iid random samples $X\sim N(\theta,1)$, we have a unknown parameter $\theta$ and its estimator $T_n=T_n(X_1,\dots,X_n)$. If we have strictly proved that the convergence rate is
$$
|T_n-\theta|...
- 747
2
votes
1
answer
95
views
No Variance in Monte Carlo Simulation
I wanted to do a Monte Carlo simulation for some of the electoral districts in my state in the upcoming US midterms. My methodology essentially was as follows:
I have a list of populations and vote ...
- 123
1
vote
1
answer
84
views
Metropolis - Hastings algorithm on a set of countable sequences
I want to simulate $\sigma$ from a measure $\pi(\sigma)$ through the Metropolis-Hastings algorithm, where $\sigma$ is a sequence of 0's and 1's on $S = \{0, 1\}^n$, the set of all sequences of 0's ...
- 425
2
votes
1
answer
120
views
Question Concerning the Invariance of a Log-Transformed Normal Random Variable under Reciprocal Transformations
So I just started looking through through E.J. Gumbel's "Statistics of Extremes" (1958) and I came across a rather strange problem that I had never seen before. The problem is phrased as ...
- 101
1
vote
0
answers
21
views
Standard errors of Monte Carlo plus linear combination
I'm using Monte Carlo to estimate some quantity $V(x)$. To get an approximation of $V'(x)$ I would use the following
$$
V'(x)\approx\frac{V(x+h)-V(x-h)}{2h}
$$ so I can simply evaluate it with two ...
- 211
4
votes
2
answers
335
views
Monte-carlo simulation and extrapolation
I am reviewing some work and the proposed solution seems to me not to be reliable. But I fail to find any references or even consistently formulate why I think this approach does not work.
Assume you ...
- 314
1
vote
0
answers
82
views
Latent variables for spatio-temporal Extreme Value in R [closed]
Latent variables models are often used for spatial extremes modeling
see e.g., Davison, Padoan and
Ribatet. A typical application
use block maxima such as annual maxima of temperature, assumed to ...
- 5,716
1
vote
0
answers
74
views
Sampling according to a product of a known density and a probability function
Given a known density $p(x)$, I'd like to generate samples according to $q(x) \propto p(x) f(x)$, where $f(x)$ is some probability function, $\forall x f(x) \in [0, 1]$, e.g., a sigmoid function.
One ...
- 11
2
votes
1
answer
195
views
Monte Carlo Simulation of AR(1) in R but Demeaned
Suppose that I want to run $i=100$ simulations of the following AR(1) model over 10 time periods:
$ X_{t,i} = 0.5(X_{t-1,i}-\bar{X}_{t-1})+e_{t,i} $
Here $ \bar{X}_t$ refers to the mean across the $i=...
- 303
2
votes
1
answer
215
views
Comparison of frequentist methods (say, averaged over Monte Carlo simulations) and Bayesian method
I have read a lot of questions with answers like this one, How do Bayesians verify their methods using Monte Carlo simulation methods?, which stated that Monte Carlo methods are not suitable for ...
- 21
0
votes
0
answers
25
views
Find extreme values in relative frequencies
I have the relative frequencies of elements in roughly 450 samples (with varying sample sizes). These elements are organisms in fecal samples.
I am interested in finding extreme values of these ...
2
votes
1
answer
259
views
Distribution/estimation of maximum change of a stationary time series
Any help on this would be much appreciated.
Let $x_{t} = b x_{t-1} + u_{t}$, where $u_{t} \sim N(0,1)$ and $\lvert{b}\rvert < 1$.
What can we say about the distribution of $y_{t} = \max(x_{t+2},x_{...
- 21
1
vote
1
answer
89
views
What is the probability of acceptance for this algorithm?
What is the distribution of $Y$ from using the Rejection Sampling algorithm?
Repeat
Sample $X$ with distribution function $F_X = (1-(1+x^\alpha)^{-1})1_{x\ge 0}(x)$
Until $X>x_0$, where $x_0$ is a ...
- 314
4
votes
2
answers
1k
views
What is an efficient algorithm for finding the minimum of a parabola-shaped function? [closed]
I have a continuous function f(x) that is bounded on the interval (0, N), where N is a large positive integer (~10,000,000). The function is shaped like an upwards-facing parabola, however, it is ...
- 43
0
votes
0
answers
212
views
Weighing Maximum Likelihood Estimations
I'm trying to arrive at a time series of optimized parameter values $Z_t$ that maximizes the likelihood of occurrence of a specific time series $Y_t$. There is a subsample within the sample that ...
0
votes
0
answers
36
views
How to calculate the accuracy of a yes/no Monte Carlo simulation such as "throwing stones in a pond"? [duplicate]
I have a simulation that returns "yes" or "no" for each iteration, and I measure the average number of "hits" over many iterations to estimate the likelihood of "yes&...
- 605
2
votes
0
answers
177
views
Limit distribution of the joint distribution of maximum and minimum of a sequence of random variables
Assume we have a sequence $\mathsf{X}_1,\mathsf{X}_2,\mathsf{X}_3,...$ of iid random variables. Then the Fisher-Tippet-Gnedenko theorem shows that
$$ \mathbb{P}\left(\frac{\max\{\mathsf{X}_1,\mathsf{X}...
- 167
1
vote
1
answer
49
views
Estimate at which point a linear model hits a certain value (including probabilities)
I have a simple 1D set of datapoints with a trend, I want to estimate at which point $X_t$ (i.e., at which point in the future) the model will hit a certain threshold $Y_t$:
I can fit a trendline to ...
- 131