R help - Oct 2013 - Latin Hypercube Sample and transformation to uniformly distributed integers or classes

Hi,

I'd like to use Latin Hypercube Sampling (LHC) in the the context of
uncertainty / sensitivity analysis of a complex model with approximately 10
input variables. With the LHC approach I'd like to generate parameter
combinations for my model input variables.
Therefore I came across an simple example here on the mailing list (
https://stat.ethz.ch/pipermail/r-help/2011-June/279931.html):

Easy Example
Parameter 1: normal(1, 2)
Parameter 2: normal(3, 4)
Parameter 3: uniform(5, 10)

require(lhs)
N <- 1000
x <- randomLHS(N, 3)
y <- x
y[,1] <- qnorm(x[,1], 1, 2)
y[,2] <- qnorm(x[,2], 3, 4)
y[,3] <- qunif(x[,3], 5, 10)

par(mfrow=c(2,2))
apply(x, 2, hist)

par(mfrow=c(2,2))
apply(y, 2, hist)


However, some of my parameters are uniformly distributed integer values
and/or uniformly distributed classes. So, for example one input parameter
can be "yellow", "green", "red" with equal
probability. Of course these
attributes can be transformed into integers (1,2,3) with a uniform
distribution.

So far I've tried to use the round function:

y[,3] <- round(qunif(x[,3], 5, 10))

which does not sample the 1 and 10 eqally to 2:8 (this is discussed already
somewhere else here on the list in another context, and the function
sample() is suggested). How can this be applied here and how can a column
of the lhs-output be transformed in e.g integers 1:10 or the three colors
as mentioned above?

thanks,

Johannes

	[[alternative HTML version deleted]]

Hi
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Johannes Radinger
> Sent: Tuesday, October 08, 2013 3:38 PM
> To: R help
> Subject: [R] Latin Hypercube Sample and transformation to uniformly
> distributed integers or classes
> 
> Hi,
> 
> I'd like to use Latin Hypercube Sampling (LHC) in the the context of
> uncertainty / sensitivity analysis of a complex model with
> approximately 10 input variables. With the LHC approach I'd like to
> generate parameter combinations for my model input variables.
> Therefore I came across an simple example here on the mailing list (
> https://stat.ethz.ch/pipermail/r-help/2011-June/279931.html):
> 
> Easy Example
> Parameter 1: normal(1, 2)
> Parameter 2: normal(3, 4)
> Parameter 3: uniform(5, 10)
> 
> require(lhs)
> N <- 1000
> x <- randomLHS(N, 3)
This put 3 columns of uniformly distributed random numbers in x
> y <- x
> y[,1] <- qnorm(x[,1], 1, 2)
> y[,2] <- qnorm(x[,2], 3, 4)
> y[,3] <- qunif(x[,3], 5, 10)
> 
> par(mfrow=c(2,2))
> apply(x, 2, hist)
> 
> par(mfrow=c(2,2))
> apply(y, 2, hist)
> 
> 
> However, some of my parameters are uniformly distributed integer values
> and/or uniformly distributed classes. So, for example one input
> parameter can be "yellow", "green", "red"
with equal probability. Of
Maybe

set.seed(333)
x<-sample(c("yellow", "green", "red"), 1000,
replace=TRUE)
table(x)
x
 green    red yellow 
   334    327    339 
> course these attributes can be transformed into integers (1,2,3) with a
> uniform distribution.
I would use 

xf <- factor(x)

to transform it to numbers and still retaining labels.
> 
> So far I've tried to use the round function:
> 
> y[,3] <- round(qunif(x[,3], 5, 10))
> 
> which does not sample the 1 and 10 eqally to 2:8 (this is discussed
> already somewhere else here on the list in another context, and the
> function
> sample() is suggested). How can this be applied here and how can a
> column of the lhs-output be transformed in e.g integers 1:10 or the
> three colors as mentioned above?
Maybe cut.
as.numeric(as.factor(cut(x[,1], 10)))
factor(cut(x[,1], 3), labels=c("yellow", "green",
"red"))

Regards
Petr

> 
> thanks,
> 
> Johannes
> 
> 	[[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.

On 08/10/2013 9:37 AM, Johannes Radinger wrote:
> Hi,
>
> I'd like to use Latin Hypercube Sampling (LHC) in the the context of
> uncertainty / sensitivity analysis of a complex model with approximately 10
> input variables. With the LHC approach I'd like to generate parameter
> combinations for my model input variables.
> Therefore I came across an simple example here on the mailing list (
> https://stat.ethz.ch/pipermail/r-help/2011-June/279931.html):
>
> Easy Example
> Parameter 1: normal(1, 2)
> Parameter 2: normal(3, 4)
> Parameter 3: uniform(5, 10)
>
> require(lhs)
> N <- 1000
> x <- randomLHS(N, 3)
> y <- x
> y[,1] <- qnorm(x[,1], 1, 2)
> y[,2] <- qnorm(x[,2], 3, 4)
> y[,3] <- qunif(x[,3], 5, 10)
>
> par(mfrow=c(2,2))
> apply(x, 2, hist)
>
> par(mfrow=c(2,2))
> apply(y, 2, hist)
>
>
> However, some of my parameters are uniformly distributed integer values
> and/or uniformly distributed classes. So, for example one input parameter
> can be "yellow", "green", "red" with equal
probability. Of course these
> attributes can be transformed into integers (1,2,3) with a uniform
> distribution.
>
> So far I've tried to use the round function:
>
> y[,3] <- round(qunif(x[,3], 5, 10))
Why round()?  floor() would make more sense.  And why have a lower limit 
of 5?  I would use 0.

When I do that I get reasonable results:

table(floor(qunif(runif(100000), 0, 10)) + 1)

(You should put in your lhs values instead of runif.  You will run into 
problems if they are ever exactly equal to 1; runif() would never do that.)

Duncan Murdoch
>
> which does not sample the 1 and 10 eqally to 2:8 (this is discussed already
> somewhere else here on the list in another context, and the function
> sample() is suggested). How can this be applied here and how can a column
> of the lhs-output be transformed in e.g integers 1:10 or the three colors
> as mentioned above?
>
> thanks,
>
> Johannes
>
> 	[[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.

Johannes Radinger <johannesradinger <at> gmail.com> writes:
> 
> Hi,
> 
> I'd like to use Latin Hypercube Sampling (LHC) in the the context of
> uncertainty / sensitivity analysis of a complex model with approximately 
10
> input variables. With the LHC approach I'd like to generate parameter
> combinations for my model input variables.
> Therefore I came across an simple example here on the mailing list (
> https://stat.ethz.ch/pipermail/r-help/2011-June/279931.html):
> 
> Easy Example
> Parameter 1: normal(1, 2)
> Parameter 2: normal(3, 4)
> Parameter 3: uniform(5, 10)
> 
> require(lhs)
> N <- 1000
> x <- randomLHS(N, 3)
> y <- x
> y[,1] <- qnorm(x[,1], 1, 2)
> y[,2] <- qnorm(x[,2], 3, 4)
> y[,3] <- qunif(x[,3], 5, 10)
> 
> par(mfrow=c(2,2))
> apply(x, 2, hist)
> 
> par(mfrow=c(2,2))
> apply(y, 2, hist)
> 
> However, some of my parameters are uniformly distributed integer values
> and/or uniformly distributed classes. So, for example one input parameter
> can be "yellow", "green", "red" with equal
probability. Of course these
> attributes can be transformed into integers (1,2,3) with a uniform
> distribution.
> 
> So far I've tried to use the round function:
> 
> y[,3] <- round(qunif(x[,3], 5, 10))
> 
> which does not sample the 1 and 10 eqally to 2:8 (this is discussed 
already
> somewhere else here on the list in another context, and the function
> sample() is suggested). How can this be applied here and how can a column
> of the lhs-output be transformed in e.g integers 1:10 or the three colors
> as mentioned above?
> 
> thanks,
> 
> Johannes
> 
> 	[[alternative HTML version deleted]]
> 
> 
Johannes,

I would modify my example (quoted above) as follows to meet your needs.  
Please feel free to email me directly about the lhs package if necessary.

require(lhs)
N <- 1000
set.seed(1919)

x <- randomLHS(N, 4)
y <- x
# uniform on 1-10
y[,1] <- ceiling(qunif(x[,1], 0, 10))
# three colors 1,2,3
y[,2] <- ceiling(qunif(x[,2], 0, 3))
# other distributions
y[,3] <- qunif(x[,3], 5, 10)
y[,4] <- qnorm(x[,4], 0, 2)

par(mfrow=c(2,2))
dummy <- apply(x, 2, hist, main="")

par(mfrow=c(2,2))
plot(1:10, c(table(y[,1])), type="h", col="blue", lwd=2,
ylim=c(0,120),
ylab="Frequency", xlab="y[,1]")
plot(1:3, c(table(y[,2])), type="h", col="blue", lwd=2,
ylim=c(0,400),
ylab="Frequency", xlab="y[,2]")
hist(y[,3], main="")
hist(y[,4], main="")

# change to color names
z <- as.data.frame(y)
z[,2] <- factor(y[,2], labels=c("R","G","B"))
z[1:10,]

Rob