All Questions
1,933 questions
11
votes
2
answers
547
views
Tail bounds on Euclidean norm for uniform distribution on $\{-n,-(n-1),...,n-1,n\}^d$
What are known upper bounds on how often the Euclidean norm of a uniformly chosen
element of $\:\{-n,~-(n-1),~...,~n-1,~n\}^d\:$ will be larger than a given threshold?
I'm mainly interested in bounds ...
- 111
4
votes
1
answer
137
views
Forming an unbiased estimator of the maximum of several parameters, given independent estimators of each parameter?
Say I have $K$ independent normals, $X_i \sim \mathcal{N}(\mu_i, \sigma_i)$ for $i = 1,...,K$. How can I form an unbiased estimator of $\max_i \mu_i$ using $X_i$'s?
- 348
8
votes
1
answer
2k
views
"Monte Carlo Kalman Filter" vs Unscented Kalman Filter
Recently, I have come across references to the Monte Carlo Kalman Filter (MCKF), which is a variant of the Sigma-Point Kalman Filter (SPKF). The key difference between the MCKF and the remainder of ...
- 695
3
votes
0
answers
783
views
Rao-Blackwellising state space for a (marginalised) particle filter
I am starting to look at particle filtering for a problem that I have. In particular, I would like to reduce the dimensionality of the particles.
The model that I have is able to be partitioned. ...
- 695
11
votes
2
answers
3k
views
Robust MCMC estimator of marginal likelihood?
I'm trying to compute the marginal likelihood for a statistical model by Monte Carlo methods:
$$f(x) = \int f(x\mid\theta) \pi(\theta)\, d\theta$$
The likelihood is well behaved - smooth, log-...
- 323
1
vote
0
answers
171
views
What is the meaning of McFaddens Axiom: Irrelevance of Alternative Set Effect?
On page 110 of McFadden,1973 - Conditional logit analysis of Qualitative Choice Behavior, Frontiers in Economics, ed Zarembka, New York: Academic Press, pp. 105-142 the following three Axioms are ...
- 1,113
8
votes
1
answer
203
views
Importance sampling of finite path of stochastic difference equation
Before passing to question, let me briefly recap what's importance sampling of random variables is about. Suppose $\xi$ is a real-valued random variable with density $f$, and let $g:\Bbb R\to \Bbb R$ ...
- 473
2
votes
0
answers
347
views
How does predictive model for the Eurovision Song Contest work?
I've encountered interesting prediction of Eurovision Song Contest http://mewo2.com/nerdery/2013/05/12/eurovision-2013-first-predictions/ it based on some kind of Bayesian model I assume but I don't ...
- 389
2
votes
1
answer
756
views
Floating point issues when transforming an arbitrary correlation matrix to positive semi-definite
I'm following Peter Jackel's book "Monte Carlo Methods in Finance", where an algorithm for transforming malformed correlation matrices into acceptable correlation matrices (positive semi-definite) to ...
- 23
5
votes
1
answer
1k
views
Asymptotic probability concerning the largest absolute value in an iid Gaussian sample
Let $v[n]$ be a vector $N$ $iid$ gaussian samples, of ~$N(0,\sigma^2)$ Also, let $v_{max}$ denote the maximum absolute value of all the samples given. (That is, if I took the absolute value of all the ...
- 1,805
5
votes
1
answer
3k
views
What do I need to consider when using the Hessian to compute S.E.'s?
I use optim() in R to do a lot of MLE. I've used the approach for a lot of problems, but the one I'm working on right now consists of fitting the parameters of the generalized extreme value ...
- 958
1
vote
1
answer
5k
views
Fitting GEV to non-stationary time series of extremes (general stationarity question?)
I'm fitting the generalized extreme value distribution (GEV) to a series of annual maxima of variable $X$. $X$ exhibits a linear trend.
When I fit the GEV to $X$, I think I have the choice to
Use ...
- 958
4
votes
2
answers
3k
views
Expected value of latent utility in logistic regression [duplicate]
I'm looking for an analytical expression for the expected value of the latent utility in a logistic regression.
Setup:
There are two choices indexed by $i \in \{0, 1\}$ with associated utilities $...
- 4,404
0
votes
1
answer
146
views
Quantifying the overlap in sort task results with cells < 5
We have data from two sort tasks where the same items (N=87) were assigned to different types of group ('g' & 'd'). We want to compare the overlap between the assignments to the 'g' groups (N=13) ...
- 155
2
votes
0
answers
204
views
Determining confidence intervals: using partial information on possible outcomes
Let's say we have a mathematical model that provides the probability of finding oil at a location in terms of a system of 10 bins with probabilities going from very low, say 2%, to 20% for the best ...
3
votes
2
answers
210
views
Condition for Law of Large Numbers, Monte Carlo
In some lecture notes I am reading, there is the following;
Consider $X_{1},...,X_{n}$, each with pdf $g$ (the instrumental distribution). Our aim is to estimate $E_{f}[h(X)]$ where $h(X)$ is some ...
- 427
3
votes
1
answer
742
views
Monte Carlo Rejection Sampling Method
I have the following passage from a set of lecture notes I am working on that I would like to understand a little better.
$\underline{\text{Algorithm for Rejection Sampling}}$:
Given two densities $...
- 427
3
votes
2
answers
3k
views
Can I do parallel analysis with any type of exploratory factor analysis/principal component analysis?
I wish to perform parallel analysis to determine how many factors I should extract from my maximum likelihood exploratory factor analysis. I have been referred to a program that calculates the ...
- 5,104
1
vote
0
answers
516
views
Variance of average of estimate computed by importance sampling
I have a random variable X of which I sample N values [$x_{1}$...$x_{N}$]. From these values I calculate the estimate P of function H(x) using Importance Sampling, i.e. $P = \sum_{i=1}^{N} w_{i}H(x_{i}...
- 23
1
vote
1
answer
2k
views
Variance for hit-and-miss Monte Carlo method and importance sampling
Variance for Hit-and-Miss Monte Carlo is given by $Var(\theta)=\frac{\Theta*(1-\Theta)}{N}$ where $\theta$ is the estimated probability of Hit and N is the number of simulations. Can someone explain ...
- 23
8
votes
4
answers
496
views
How can I sample from a distribution with incomputable CDF?
Semi-computer science simulation related problem here.
I have a distribution where
P(x) = $\frac{(e^b-1) e^{b (n-x)}}{e^{b n+b}-1}$
for some constants b and n, and x is an integer such that $0\leq ...
- 2,163
1
vote
1
answer
41
views
How to test the significance of increase in sample interval range(s)?
Suppose we have two samples of a variable taken under different conditions: e.g. A1 without medical treatment and A2 after medical treatment. These are not necessarily normally distributed. Suppose A1 ...
2
votes
2
answers
428
views
Program for Sequential Monte Carlo Algorithm [closed]
Does anybody has the
example of the program which
simulates Sequential Monte Carlo Algorithm?
In any software. I'm trying to write such
kind of program but there constantly are
question and problems I ...
- 661
2
votes
1
answer
235
views
Sequential Monte Carlo for hierarchical models
Does anybody know,
can Sequential Monte Carlo
be applied for multi-dimensional
problems i.e. simulating more
than 1 distribution like in
hierarchical models?
Maybe you know some following literature
- 661
3
votes
0
answers
1k
views
Confidence intervals for extreme value distributions
I have wind data that i'm using to perform extreme value analysis (calculate return levels). I'm using R with packages 'evd', 'extRemes' and 'ismev'.
I'm fitting GEV, Gumbel and Weibull distributions,...
- 951
3
votes
2
answers
717
views
Where can i find a good book that teaches MCMC in R?
I am looking for a good book that will teach me MCMC in R , in particular Block Gibbs and Collapsed MCMC. Preferably with R pseudocode supplemented within the book as well.
Does anyone have any ...
- 1,256
4
votes
0
answers
79
views
Non-Analytic extrapolation
I have some samples of a stable real-world process. Its is polymodal, and does not cleanly fit any of the "textbook" analytic distributions. I need to make very accurate estimates of the maximum ...
- 9,853
4
votes
0
answers
168
views
How to estimate the given function using Rao Blackwellization approach?
I have a function $X$ which is lognormal (0,1)
and then another function
$\log Y = 4 + 2 \log(X) + \epsilon$
where $\epsilon \sim \mathcal N(0,1)$
I want to estimate $E(Y|X)$ as a Rao Blackwellized ...
- 41
3
votes
2
answers
547
views
Finding the integral of a fitted function
I have a function obtained by fitting some data, and I do not have access to the data itself. The fitting parameters of the function have confidence bounds. I need to obtain an expression for the ...
- 131
2
votes
1
answer
749
views
positive skewness in simulation results
I am using simulations to make a calculation. I generate many random numbers from a distribution for each input and then I take the mean and standard deviation of the outputs.
I noticed that the mean ...
- 435
7
votes
2
answers
190
views
Metropolis Sampling and invalid states
I have a short question about Monte Carlo integration with Metropolis sampling. I have a continuous state space, but only certain parts of this state space are valid. It is possible that the ...
- 71
2
votes
1
answer
847
views
Monte Carlo: generating autocorrelated data from empirical distribution
my problem is the following: having a distribution function of daily casfhlows resulting from electricity trading, I need to calculate a yearly 99% VaR, i.e. the 1% percentile of yearly casfhlows ...
- 139
49
votes
5
answers
41k
views
K-fold vs. Monte Carlo cross-validation
I am trying to learn various cross validation methods, primarily with intention to apply to supervised multivariate analysis techniques. Two I have come across are K-fold and Monte Carlo cross-...
- 633
3
votes
0
answers
142
views
Distribution of variable
How to find the distribution of $$\sum_{i=1}^n (X_i - X_{1:n}),$$ where $X_i$ are i.i.d. random variables and $X_{1:n} = \min(X_1,X_2,...,X_n)$?
I need to find the distribution in a particular case, ...
- 31
5
votes
1
answer
560
views
In a Monte Carlo approximation of a product of expectations, can the same samples be used for both expectations?
I am trying to approximate a product of expectations:
$\operatorname{E}[f(x)]\operatorname{E}[g(x)]=\sum_x P(x) f(x) \sum_x P(x) g(x)$
with $N$ Monte Carlo samples $(x_1,x_2,...,x_N)$ from $P(x)$:
$...
- 1,115
1
vote
0
answers
501
views
Probability of exceedance and reliability of a sample range estimation
Consider that $P$ is the water pressure coming out of a valve $A$. Let $P_{dif}$ be the difference between the maximum and the minimum pressure of valve $A$:
$$P_{dif}≔P_{max}-P_{min}$$
Now, what I ...
- 131
3
votes
3
answers
239
views
How to simulate random variables according to the law of a pregiven data sample
Say I have the following sample:
...
- 399
2
votes
2
answers
25k
views
Determine density of $\min(X,Y)$ and $\max(X,Y)$ for independently uniform distributed variables
Two independent random variables, $X$ and $Y$, are uniformly distributed on the unit interval $(-1,1)$.
Determine the density for $U=\min(X,Y)$ and for $W=\max(X,Y)$
- 23
4
votes
0
answers
348
views
Gibbs sampling from full conditionals
I have the following joint density:
$p(x_1,x_2,y_1,y_2) \propto \exp\left(−\left(x_1^2+x_2^2+c_1(y_2-y_1)^2+c_2(y_2-y_1)^4\right)\right)$
Can I use Gibbs sampling to sample from that? How can I get ...
- 41
2
votes
1
answer
532
views
Calculation of confidence interval of a population parameter (the range)
Consider that $P$ is the water pressure coming out from a valve A. Let $P_{dif}$ be defined as the difference between the maximum and the minimum pressure of valve A:
$$P_{\text{dif}}:= P_{\text{max}}...
- 131
1
vote
1
answer
210
views
Pointers on how to perform a Monte Carlo Analysis
Im looking for some pointers on how to perform a Monte Carlo simulation. Say im conducting a survey of how late flights are for a certain airline. I amass 1000 records, and plot a cumulative sum of ...
- 209
6
votes
0
answers
194
views
Estimating parameters using Kullback-Leibler or Kolmogorov-Smirnoff via Nelder-Mead
I want to find the parameters of a model which specifies a set of classification probabilities, for say M classes. (I'll use the parameters in another model later.)
Given a set of parameters $\theta$,...
- 379
4
votes
1
answer
9k
views
Spearman correlation in the presence of many ties - how to spot a problem?
I'm testing the hypothesis that there's a monotonic relationship between two variables. I think I should use a Spearman rank correlation test, since my data don't necessarily meet normality ...
- 694
1
vote
1
answer
129
views
Learning to predict maximum of parameterized function class
I am interested in a multi-task regression problem: I have a parametrized function $f_x : \mathcal{R}^n -> \mathcal{R}$ where $x \in \mathcal{R}$ is a real-valued parameter. For some values of $x$, ...
- 73
1
vote
1
answer
164
views
Simulation of woman's age of getting breast cancer (cumulative incidence rate)
I am writing a programme to simulate the age at which women will get breast cancer. I have data on the cumulative incidence rate for the whole population.
What I am doing right now is using Monte ...
- 183
4
votes
0
answers
77
views
Random walk with restricted graph knowledge
I have a very large graph and a function of its vertices, and want to estimate mean value of this function.
It's not possible to sample vertices uniformly in this problem, so a reasonable choice for ...
- 63
3
votes
0
answers
135
views
Relation between statistical randomness, uniform distribution and independence
In Monte Carlo simulation, we often consider how well a sequence of generated points are. If I am correct, one aspect is statistical randomness:
A numeric sequence is said to be statistically ...
- 19.8k
1
vote
1
answer
531
views
How to generate iid samples from the linear congruent method?
Given a uniform random number generator (such as the linear congruent method), how shall I generate a sequence of i.i.d. random
samples?
Are samples generated in a successive sequence i.i.d., or
...
- 19.8k
7
votes
2
answers
9k
views
Particle filtering importance weights
In theory, the importance weight of a particle has to be a probability, i.e., $w_{s_t} = p(z_t|s_t)$.
My question is: Since we eventually normalize the weights with their sum and get a probability ...
- 532
24
votes
6
answers
48k
views
Why doesn't k-means give the global minimum?
I read that the k-means algorithm only converges to a local minimum and not to a global minimum. Why is this? I can logically think of how initialization could affect the final clustering and there is ...
- 589