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A common problem in my field (climate science) is that we want to assess the statistical significance of a 2D spatial field. This field is typically obtained by taking the temporal mean of a subset of the data.

We might test the statistical significance of this field by generating many bootstrap samples from the full sample by randomly selecting time slices, then computing the means of the bootstrap samples, and comparing this set of 2D fields with the 2D field we want to test the significance of. The effect size for each spatial point is compared to the equivalent point of the many bootstrap samples, and we can compute p-values to determine whether each spatial point in the field is "significant" or "not significant".

My question is, does this procedure tell us anything about the specific spatial pattern of the 2D field we are testing?

On the one hand, we are only sampling along time, thus each random draw will be a spatially-coherent field. This suggests to me that the 'uniqueness' of the spatial field we're testing is implicitly accounted for. On the other hand, we are testing each spatial point individually; there is no specific accounting for the spatial structure.

Let's also assume that we have properly accounted for multiple testing - I'm interested in the interpretation of the final result, which would look like a 2D spatial field, with the "significant" points marked on the field.

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  • $\begingroup$ The classic bootstrap assumes statistical independence among the resampled variables. On the face of it this seems like a bad idea for spatial data since statistical dependence (e.g. spatial autocorrelation) is common. $\endgroup$
    – Galen
    Jul 4, 2023 at 3:54
  • $\begingroup$ Thanks for your comment, @Galen. I tried to keep the details of the exact procedure to a minimum. If it helps, I control the False Discovery Rate, which to my understanding accounts for multiple testing and is only modestly sensitive to spatial autocorrelation (from this paper: journals.ametsoc.org/view/journals/bams/97/12/…). Bootstrapping spatial data in this way is very common in my field - what would you suggest as an alternative to explore? $\endgroup$
    – boro141
    Jul 5, 2023 at 0:41
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    $\begingroup$ My broad advice is to model the statistical dependence. Sampling from a statistical model that approximates the statistical dependence will allow you to make probabilistic inferences about your estimand. This is easier said than done and the generality of the notion of statistical dependence makes it impossible for me to guess what will be appropriate from summary description. But to give you at least something to look further into, kriging is one family of approaches that can do well with spatial dependence. $\endgroup$
    – Galen
    Jul 5, 2023 at 1:45

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