# Differences in bootstrap and block bootstrap

I have to be somewhat vague regarding data and such for confidentiality purposes (I'm not allowed to share whole data). I have a dataset (X) that represents transects (representing line transects of animals in space).

  Birds        area      len       transect
1            0.239310  0.478621  1
2            0.238463  0.476927  1
1            0.244382  0.488765  2
4            0.236501  0.473002  2
0            0.245832  0.491665  3
1            0.241026  0.482052  4


When I calculate the mean density of the birds, e.g.:

meandensity <- sum(X$Birds)/sum(X$area)


in the dataset, I get a mean value of ~3.63.

The problem is I've been given a MATLAB module written by someone else (and I can't read MATLAB code) who claims to be using a block bootstrap method to estimate mean and confidence intervals. When I run that module, the mean density gets estimated at ~4.6.

Now, I spoke to this person and have tried to replicate his bootstrap method and am getting a value of ~3.5.

My questions: Can the bootstrapped estimate of the mean really differ this much from the mean of the whole dataset? My understanding was that the bootstrap estimate shouldn't be super far from the mean, and differences between bootstrap methods would impact the CIs more than the estimated mean.

• Please include what "block bootstrap" is according to you and in this specific example. – Jim May 8 '18 at 16:33
• There is a block bootstrap that is used in time series analysis, but what kind of block bootstrap is being used in this situation. How does it differ from the ordinary bootstrap? – Michael R. Chernick May 8 '18 at 16:55
• Well, you seem to have spatial dependence in your data and, if the data have been collected over time as well as over space, you'll have temporal dependence. So whatever block bootstrap method you will use will have to reflect the spatial and/or temporal dependence aspects of the data. – Isabella Ghement May 8 '18 at 18:11
• Thanks for the questions. Block-bootstrapping in this case is spatial. So, the bootstrap unit is Transect ID, instead of each individual data point. – GrantRWHumphries May 8 '18 at 21:10
• @isabellaGhement there is a temporal aspect, but it's very short. These are aerial surveys, and so it's a matter of hours for an entire survey. We treat them here as "snapshots" – GrantRWHumphries May 8 '18 at 21:12