If you are specifically worried about noise in the data from false positive or false negative detections, David Miller has a series of publications on how to model these with a recent pub from Chambert that describes a few potential avenues using occupancy. These models allow you to assign certain or unambiguous detections, along with uncertain or ambiguous detections. These mostly require repeated surveys however. I'm not sure if this is what you're looking for, but here goes....

Chambert et al.

http://www.esajournals.org/doi/abs/10.1890/14-1507.1

Miller et al.

http://www.esajournals.org/doi/abs/10.1890/10-1396.1

Thank you both for your responses. I realise my initial post wasn't particularly clear.

I am interested in a vertebrate taxon's range, which is calculated as a minimum convex polygon. The shape and size of that polygon (and hence the value of the range, in km2) are heavily dependent on the input sighting points and their location in space. The issue is that some sightings come from sources with varying degrees of reliability. I would like to use bootstrap resampling techniques (with replacement and differing inclusion probabilities) to generate a distribution of resample values of range and gain a sense for the metric's variability. In the resampling process, I would typically assign a lower probability of inclusion to these data points that come from community programmes (for instance) where observers are not necessarily as trained or experienced in animal ID, or where the recording of sighting locations is likely more prone to inaccucaries. 

I could pick an arbitrary weight (probability of inclusion) for these sightings (e.g. 0.5, which would reflect my belief that opportunistic sightings are half as reliable as other sightings) - but would like to avoid arbitrary values if possible and am on the hunt for similar studies/examples/references.

Phil -

Can you do two separate sets of estimates, one using "dedicated surveys," and the other using "opportunistic contributions," to see how closely they might agree? If they give you completely different results, and if you think the dedicated surveys were done well, you might not want to include the opportunistic contributions directly, but perhaps as something of a pilot study to guide your next dedicated surveys.

This is not my area, and I do not understand how you intend to use bootstrapping, but in any case where one has different estimates of the same thing (say here, 'abundance' totals from surveys versus contributions?), and you can estimate the variance of those two estimates, you can use a Stein/shrinkage type of estimator, such as when Bates and Granger did this to combine economic forecasts:

The Combination of Forecasts

J. M. Bates and C. W. J. Granger

OR

Vol. 20, No. 4 (Dec., 1969), pp. 451-468

Published by: Operational Research Society

Article Stable URL: http://www.jstor.org/stable/3008764

This method also appeared later in a book by Granger and Newbold. I have used it for sample survey statistics.

I guess you would need to assume the contributions were nearly random in some meaningful way to your variance estimate??

I do not know if such a technique would help in any situation for you, but it does emphasize, or de-emphasize, one estimate over another, based on variances of each estimate, and/or more involved methods. Then one estimate is multiplied by (1-a) and the other by a, where 0

Cheers Jim, this is helpful but not entirely what I am after as the areas covered by my opportunistic sightings and my dedicated surveys do not necessarily overlap.

The paper by Kern et al. (2003) is the closest thing I could find to what I am aspiring to do (Using the bootstrap and fast Fourier transform to estimate confidence intervals of 2D kernel densities - Environmental and Ecological Statistics, 10: 405-418).

With a set of sighting locations:

(1) Take a bootstrap sample of sightings, drawn with replacement.

(2) Draw a minimum convex polygon (MCP) around these points and calculate its surface area.

(3) Repeat steps 1-2 a number of times, and summarise the resulting distribution of MCP areas (mean, variance etc.).

MCPs are typically reported as single values, with no measure of variability. This should help me get a sens for how variable my MCPs are.

The idea is similar to what the function hrBootstrap of the Move R package does (see link) except that instead of choosing well-defined subsets of points of size 2, 5, 10, 20 etc. I want to conduct step (1) using a probability-based bootstrapping method where opportunistic sightings are given a lower weight (probability of inclusion) than other sightings.

For instance, I could say (arbitrarily) that opportunistic sightings are half as reliable as those from dedicated surveys and I would give them a probability of inclusion of 0.5.

I would like to find out if there are any other studies out there which could help guide my choice of probability weighting, e.g. studies that have combined different sources of data and looked at their relative trustworthiness or reliability or the such.

Thanks again for your help and responses!

https://marcosmolla.wordpress.com/2012/08/23/last-week-we-in/

"...opportunistic sightings and my dedicated surveys do not necessarily overlap."

"I could say (arbitrarily) that opportunistic sightings are half as reliable as those from dedicated surveys..."

Well, if there is any overlap, a mixture of both types, the results would vary, depending upon whether you 'weighted' by 0.4, or 0.5, or 0.6, or whatever. (If all you have is one type, it doesn't sound like weight would change results, but would impact accuracy.)

If you have a mixture, you could get results using 0.4 for that 'weight,' and then again with 0.5, etc., as a sensitivity analysis, to see how much difference it makes.