“You must attend the AMSI Summer School since it is highly
worth it. Not only you will enhance your knowledge and skills
in the area of mathematical sciences, but also you can broaden
your networking.”

Abdul Hadi Asfarangga, The University of Adelaide

Spatial Statistics

Lecturers

Dr Charlotte Jones-Todd, The University of Auckland NZ

Synopsis

This course will focus on the theory and application of modelling spatially referenced data. Students will be introduced to methods for the analysis of geostatistical, lattice, and point pattern data. From summary statistics to model inference & validation this course will introduce students to a wide range of techniques, which will enable them to appropriately analyse spatial data. Much of the course will have a practical element involving using the statistical programming language R; there will be a particular focus on statistical modelling and inference of spatial data from a wide range of research fields (e.g., ecology, physics, international relations, criminology).

Course Overview

  • Week 1:
    • Introduction to spatial data, what it is and how to visualise it in R.
    • Spatial dependence and spatial covariance functions.
  • Week 2:
    • Introduction to point pattern data.
    • Spatial stochastic processes.
    • Kriging techniques and likelihood techniques.
  • Week 3:
    • Introduction to hierarchical models, likelihood approximation, and Bayesian spatial statistics.
    • Using Gaussian Markov Random Fields (GMRFs) in hierarchical models.
  • Week 4:
    • Introduction to spatiotemporal data: modelling and inference.
    • Joint likelihoods and marked point patterns.

There will be a series of two assignments alongside low-stakes tasks and a final take home exam to reinforce the taught material.

No prior knowledge of spatial statistics is required; however, students are expected to be confident in R programming.

Prerequisites

Students should be familiar with the Bayesian paradigm, comfortable with the concept of maximum likelihood and OLS, and be aware of the theory of stochastic processes. This course will use the programming language R and fit models using TMB and INLA. Students should bring their own laptop to both lectures and tutorials where possible.

Assessment

  • Final assessment details to be confirmed

Attendance requirements

  • For those completing the subject for their own knowledge/interest, final attendance requirements to be confirmed

Resources/pre-reading

  • TBC

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Dr Charlotte Jones-Todd, The University of Auckland NZ

Increasing amounts of spatio-temporally indexed data are available from different disciplines ranging from disaster resourcing to species distribution. Charlotte develops point process models that incorporate stochastic structures to better inform the complex temporal and spatial evolution of these data.