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I have a significant background in statistics, and I'd like to learn more about spatial statistics (and statistics associated with geospatial data).

Are there any especially good resources for someone looking for an overview of the field?

I am not looking to solve a specific problem at this point. Just want to understand the field and how it differs with statistical applications on non-spatial data.

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Spatial statistics, like most statistical methods, is a large topic. If you would like spatial statistical theory presented in a statistical/mathematical framework my favorite is Cressie's book "Statistics for Spatial Data".

Since Diggle's point process book is out of print, A good alternative, specific to point pattern analysis, is "Statistical Analysis and Modelling of Spatial Point Patterns".

A great overview of spatial statistics in ecology is Fortin & Dale's "Spatial Analysis: A Guide for Ecologists.

For implementation of spatial Hierarchical Bayesian Modelling there is "Hierarchical Modeling and Analysis for Spatial Data".

I really like Gilks "Markov Chain Monte Carlo in Practice" for an introduction of Monte Carlo approaches.

For an introduction to geostatistics the standard is Isaaks & Srivastava's "An Introduction to Applied Geostatistics"

This is by no means a comprehensive list but are some of the books that I refer graduate students to.

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    +1 Ripley's seminal book (Spatial Statistics, Wiley, 1981), even though everything in it has been supplanted by material in the later texts (such as Cressie's magnum opus) is also a good choice because it's still widely cited and is quite accessible to people with statistical backgrounds. – whuber Jan 22 '13 at 19:28
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You can start by checking the Geospatial Analysis - A comprehensive guide.

The entire book is online: http://www.spatialanalysisonline.com/

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Since spatial statistics are very often implemented in R, my go-to book is Applied Spatial Data Analysis by Bivand et al. 2008. This book is great in describing how to tie together spatial data with spatial statistics. For example, how do you go from a collection of XY coordinates describing tree locations to determining whether or not they are clustered, random or uniformly distributed? There are many books that describe the intricacies of spatial statistics, yet few of those actually describe how to implement these statistics.

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http://resources.arcgis.com/en/communities/analysis/017z0000001m000000.htm has everything ArcGIS-related on the topic of spatial statistics.

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Applied spatial statistics for public health data by lance Waller was recommended to me by a Biostats professor for the same reason. But its been out of stock on Amazon. Diggle's works are also a good reference on the bayesian side. Esri may have recommendations as well.

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