[R-sig-Geo] sample with varying intensity according to local density

[Tom Philippi]

Nicholas--
You might also want to consider the spsurvey package (in the spatial task
view or http://cran.r-project.org/web/packages/spsurvey/index.html).  It
supports stratified and unstratified unequal probability independent random
sampling, which is how I interpret your first aspect if it is stand-alone.

If you need #1 and #2 in the same sample design, spsurvey also supports
generalized random tessellation stratified (GRTS) sampling, which is a
slick and useful design that is almost as spatially-balanced or spread as
grid sampling, but is also a probability design, so it works well for both
design-based estimators and model-based estimators such as kriging.  GRTS
samples are also easy to enlarge or reduce if some points are unsampleable,
which isn't possible with grid sampling.  GRTS works for sampling from both
continuous domains (e.g., areas) or finite domains (sets of spatial
locations), and supports stratification as well as unequal probability
sampling within and between strata.  And, the package includes functions
for analyses of the resulting data, including a neighborhood variance
estimator for GRTS.  It might not meet your needs, but I recommend you
consider it.

Tom 2

On Mon, Oct 20, 2014 at 1:09 AM, Rolf Turner <r.turner at auckland.ac.nz>
wrote:

> On 20/10/14 17:03, Nicolas Meurisse wrote:
>
>> Hi all,
>>
>> I want to sample locations within a defined area, but also optimize
>> the spatial arrangement of my sample locations in order to:
>>
>> 1.       sample some parts of the area more intensively (e.g. as a
>> function of previous findings intensity, as it could be illustrated
>> by a density map)
>>
>> 2.       sample at regular intervals within each area, as opposed to
>> pure random sampling (e.g. "regular" or "stratified random" as
>> defined in sp package)
>>
>> Here an example dataset:
>> n <- 10000
>> x1  <- matrix(rnorm(n), ncol = 2)
>> x2  <- matrix(rnorm(n, mean = 3, sd = 1.5), ncol = 2)
>> x   <- rbind(x1, x2)
>> # scatterplot with smoothed densities color representation
>> smoothScatter(x)
>> # random sampling (not appropriate, as we want an arrangement that
>> optimizes conditions 1 and 2)
>> points(sample(x[,1],20), sample(x[,2],20), col="red", pch=16)
>>
>> I would greatly appreciate any insight someone might have as it seems
>> there are lot of potential applications using  such "stratified"
>> sampling.
>>
>
> It seems to that desideratum #1 can easily be effected using the rthin()
> function from the spatstat package.
>
> I'm not clear what you actually want to do in respect of desideratum #2,
> but it is at least conceivable that this could be effected in the same
> way:  Provide an image or function specifying the intervals (regions?) from
> which you wish to sample.  I.e. make an image (object of class "im") or
> function which takes the value 1 within the regions from which you wish to
> sample and 0 outside those regions.
>
> cheers,
>
> Rolf Turner
>
> --
> Rolf Turner
> Technical Editor ANZJS
>
>
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