Using (pseudo-)random numbers to simulate the random behavior of a real system.
0
votes
0answers
11 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 $g:\Bbb R\to \Bbb R$ ...
2
votes
0answers
44 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 ...
1
vote
0answers
28 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 ...
0
votes
1answer
32 views
Monte Carlo Tree Search : Expansion Step
The algorithm asks to "Start at root node, recursively select optimal child nodes until a leaf node L is reached.", and then "If L is a not a terminal node (i.e. it does not end the game) then create ...
1
vote
0answers
38 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 ...
1
vote
1answer
49 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 ...
1
vote
1answer
54 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 ...
0
votes
0answers
11 views
Functions of Scenario-based Probability Distributions
I am considering monte carlo simulations of some probability distributions over time. For instance, I might simulate multivariate distributions $\widetilde{X}_{t+1}$ and $\widetilde{X}_{t+2}$ where ...
2
votes
2answers
62 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 ...
0
votes
0answers
28 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} ...
0
votes
1answer
52 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 ...
6
votes
4answers
210 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 ...
0
votes
0answers
41 views
Program for Sequential Monte Carlo Algorithm
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 ...
0
votes
0answers
73 views
Value at risk by Monte Carlo using generalized Pareto distribution
I have created a VBA program to calculate VaR by using Monte Carlo, I have simulated Brownian Motion. This method might be ok for 100% equity portfolio, but let's say this portfolio may have fixed ...
1
vote
1answer
30 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
2
votes
2answers
124 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 ...
2
votes
0answers
31 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 ...
1
vote
0answers
63 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 ...
1
vote
1answer
57 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 ...
5
votes
2answers
52 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 ...
1
vote
1answer
83 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 ...
0
votes
0answers
125 views
Randomly selecting x number of cases from 4 groups - script modification
I managed to get together the code (1) below. It's essentially a monte carlo discriminant function script that also uses oms to output.
It runs a given number of cases through discriminant function ...
1
vote
0answers
94 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 ...
3
votes
0answers
65 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:
$\mathrm{E}[f(x)]\mathrm{E}[g(x)]=\sum_x P(x) f(x) \sum_x P(x) g(x)$
with $N$ Monte Carlo samples $(x_1,x_2,...,x_N)$ from $P(x)$:
...
1
vote
3answers
87 views
How to simulates random variables according to the law of a pregiven data sample
Say I have the following sample:
...
2
votes
0answers
89 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 ...
1
vote
1answer
66 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 ...
3
votes
0answers
75 views
Estimating parameters using Kullback-Leibler and 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 ...
2
votes
1answer
180 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 ...
1
vote
1answer
50 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 ...
2
votes
0answers
38 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 ...
3
votes
0answers
38 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 ...
1
vote
1answer
59 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
...
0
votes
0answers
74 views
particle filtering importance weights
In theory, 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 ...
3
votes
1answer
227 views
How to create a random variables in a simulation using skewness and kurtosis as well as average and standard deviation input?
I am curious to learn whether there are any best practises in creating random variables for a Monte Carlo simulation using input such as skewness and kurtosis information of a particular distribution. ...
0
votes
0answers
115 views
Defining this simulation approach (Bootstrap, Monte Carlo)
I am currently carrying out simulations based on two different longitudinal (multi-state) models. In practice, these two models are aimed at parametrically estimating the transition probabilities ...
3
votes
2answers
69 views
Estimating covariance of the difference of directional distributions derived from Gaussian mixtures
Given Gaussian mixtures $X_1, X_2 \in \mathbb{R}^p$ defined as $$P(X_i = x) = \sum_s \omega^{(s)}_i \mathcal{N}(x; \mu^{(s)}_i, \Sigma_i)$$ where the superscript $(s)$ indexes the $s$-th component of ...
5
votes
0answers
85 views
Rao-Blackwellization of sequential Monte Carlo filters
In the seminal paper "Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks" by A. Doucet et. al. a sequential monte carlo filter (particle filter) is proposed, which makes use of a ...
1
vote
0answers
87 views
Confidence Interval in Monte Carlo integration
I want to integrate
$\int_{\mathbb{R}_+}\mathbb{1}_A(x) d\mathbb{P}(x)$, in other words I am interested in $\mathbb{P}(A)$. I did this numerically with two Monte Carlo steps.
First, I drew, say a ...
3
votes
0answers
109 views
Deriving priors for MCMC implementation
I have been working on an assignment lately wherein the object is to implement an MCMC approach to simulate from a generated posterior distribution.
The posterior distribution is generated from a ...
0
votes
0answers
41 views
How to track a curved object using the particle filter algorithm?
I have implemented the condensation algorithm in order to track a moving object in image streams. If the moving object is simple, the object's state can be represented only by the coordinates of the ...
1
vote
0answers
42 views
A motion model to track a moving object using the condensation algorithm
I have implemented the condensation algorithm in order to track a moving object in video sequences, however the predictive step does not work properly, so the samples moves excessively compared to the ...
2
votes
1answer
160 views
MCMC and data augmentation
I have been looking at an MCMC data augmentation question; the general form of the question is as follows:
Suppose data gathered on a process suggests $X_{i} \sim \text{Pois}(\lambda)$ and a prior ...
0
votes
1answer
140 views
Preparing Bayesian conditional distributions for Gibbs sampling
I was looking at the Gibbs Sampler when I stumbled upon the following example:
Suppose $y = (y_{1}, y_{2}, \ldots, y_{n})$ are iid observations from an $N(\mu, \tau^{-1})$
Furthermore, suppose there ...
4
votes
1answer
156 views
Is there a better way to create variables with a certain correlation and one of them is heteroskedastic?
My goal is to generate two variable which are correlated and one of them is heteroscedastic with regards to an grouping variable.
To create two variables with a desired correlation the common way to ...
3
votes
1answer
263 views
What are pure random sampling and orthogonal sampling?
I'm working on a project to calculate the Area of Mandelbrot Set by Monte Carlo method. I implemented my code by generating standard random numbers and throwing them into the area.
I used simple ...
2
votes
0answers
219 views
Monte Carlo calculation of value at risk
I want to calculate the VaR with Monte Carlo Simulation, I am referring to this page:
http://financetrain.com/calculating-var-using-monte-carlo-simulation/
which was created to the JP Morgan ...
2
votes
1answer
231 views
Using the rejection sampling with the method of inversion
I am hoping to write some rejection algorithm code in R to approximate a $\text{Gamma}(k,\lambda)$ distribution.
The problem is more for educational purposes than real-world implementation.
Given an ...
3
votes
2answers
109 views
Confusion related to MCMC technique
I have this confusion related to Monte Carlo Markov Chain method. I know that Monte Carlo method is used to get the sample mean instead of calculating the high dimensional integration which is not ...
3
votes
1answer
106 views
Confusion related to calculation of pi
I was referring to this lecture http://videolectures.net/mlss09uk_murray_mcmc/. However, I didn't get how the pi value was calculated. Here is a screenshot
As far as I know the integral gives the ...
