R help - Mar 2008 - How can I sample from a two-dimensional grid of points

Hi everyone,
   
  My goal is to sample from a two-dimensional grid. Consider the following
example of code:
   
  n.grid <- 500
muA.grid <- seq(-4,4, length=n.grid)
muB.grid <- seq(-4,4, length=n.grid)
mu.p <- matrix(NA, nrow=n.grid, ncol=n.grid)
for(i in 1:n.grid){
  for(j in 1:n.grid){
    mu.p[i,j] <- dnorm(muA.grid[i], 0, 1)*dnorm(muB.grid[j], 0, 0.5)
    }
}
   
  mu.p <- mu.p/sum(mu.p)
   
  I would now like to sample the grid of points from the probabilities in mu.p.
Im using the multivariate normal here for illustration as my real problem is a
more complicated probability density. If this problem were only one-dimensional,
this is easy:
   
  n.samples <- 1000 
  # assuming mu.p and muA.grid are now the appropriate vectors
  mu <- sample(muA.grid, n.samples, replace=T, prob=mu.p)
   
  However, im not sure how to do this in two-dimensions in R.
   
  Thanks in advance for any help.
   
  All the best,
  Gregory Gentlemen

       
---------------------------------

	[[alternative HTML version deleted]]

you can still use sample(), e.g.,

n.grid <- 500
muA.grid <- seq(-4, 4, length = n.grid)
muB.grid <- seq(-4, 4, length = n.grid)

vals <- data.matrix(expand.grid(muA.grid, muB.grid))
mu.p <- dnorm(vals[, 1]) * dnorm(vals[, 2], sd = 0.5)
mu.p <- mu.p / sum(mu.p)

ind <- 1:nrow(vals)
samp.ind <- sample(ind, 1000, TRUE, mu.p)
mu <- vals[samp.ind, ]
head(mu, 10)


I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
     http://www.student.kuleuven.be/~m0390867/dimitris.htm

----- Original Message ----- 
From: "Gregory Gentlemen" <gregory_gentlemen at yahoo.ca>
To: <r-help at stat.math.ethz.ch>
Sent: Monday, March 10, 2008 3:32 PM
Subject: [R] How can I sample from a two-dimensional grid of points

> Hi everyone,
>
>  My goal is to sample from a two-dimensional grid. Consider the 
> following example of code:
>
>  n.grid <- 500
> muA.grid <- seq(-4,4, length=n.grid)
> muB.grid <- seq(-4,4, length=n.grid)
> mu.p <- matrix(NA, nrow=n.grid, ncol=n.grid)
> for(i in 1:n.grid){
>  for(j in 1:n.grid){
>    mu.p[i,j] <- dnorm(muA.grid[i], 0, 1)*dnorm(muB.grid[j], 0, 0.5)
>    }
> }
>
>  mu.p <- mu.p/sum(mu.p)
>
>  I would now like to sample the grid of points from the 
> probabilities in mu.p. Im using the multivariate normal here for 
> illustration as my real problem is a more complicated probability 
> density. If this problem were only one-dimensional, this is easy:
>
>  n.samples <- 1000
>  # assuming mu.p and muA.grid are now the appropriate vectors
>  mu <- sample(muA.grid, n.samples, replace=T, prob=mu.p)
>
>  However, im not sure how to do this in two-dimensions in R.
>
>  Thanks in advance for any help.
>
>  All the best,
>  Gregory Gentlemen
>
>
> ---------------------------------
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 

Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm