Summary of research contributions

The citation for the 2001 Hannan Medal (Statistical Science) of the Australian Academy of Science read:
Professor Baddeley has done outstanding work in the difficult area of statistical analysis of digital images and spatial data. He has solved important practical problems using mathematical and statistical methods. The stereological measurement of such things as bone biopsies, skin samples and material fractures, has been fundamentally altered by his technique for measuring surface area from vertical sections. He has also introduced ways of measuring the `error' in image reconstruction, and has contributed to a broad range of other areas of spatial statistics and probability.

Research interests

Adrian Baddeley's main contributions to statistical science are in the related fields of To support research and applications in these fields, Baddeley has also made substantial contributions to statistical software.

In brief, spatial statistics is about analysing spatial data (any kind of data that involve a spatial location, such as maps, weather station records, or satellite images) and statistical image analysis is more specifically about analysing digital pictures (from satellites, cameras, microscopes etc). Stereology or `quantitative microscopy' is a kind of sampling methodology used to draw statistical inferences from microscope images. Stochastic geometry is a branch of probability theory that deals with very general kinds of `random sets'. What these fields have in common is that they combine `geometry' (spatial or geometrical information) with `probability' (random processes and statistical inference).

Research in these fields is very important to the future of statistical science. Spatial data are increasingly common, thanks to GIS technology, digital imaging, GPS tagging, and other technologies. The statistical analysis of spatial data is not a trivial extension of classical statistical methods, and indeed it creates severe difficulties for classical methods. Research on spatial data has been a fertile source of new ideas in statistics. The fields of spatial statistics and statistical image analysis played a pivotal role in many of the big developments in statistical science between 1985 and 2005. Markov Chain Monte Carlo (MCMC) methods were first invented in spatial statistics. Bayesian methods using MCMC originated in statistical image analysis.

Spatial Statistics

Spatial statistics is a branch of statistical science dealing with the analysis of spatial data - any data that are attributed to spatial locations. Examples of spatial data are maps of the locations of mineral deposits, geological faults, archaeological finds, petty crimes, bird nests etc; records of temperature, air quality or soil acidity at different locations; and satellite images, microscope images or digital camera images. In statistical science, Adrian Baddeley is recognised as a leader in spatial statistics, especially the statistical analysis of spatial point patterns. He has made important advances, ranging from fundamental theory to practical implementation.

Stereology

In the general scientific community, Adrian Baddeley is best known as a leader in the field of stereology (`quantitative microscopy') and especially as the inventor of the vertical sections technique.

Stereology is the science of interpreting microscope images. It deals with the geometrical complexities of interpreting a two-dimensional slice of a solid material (rock, metal, biological tissue) and the statistical challenges of drawing conclusions from a tiny sample of material.

A.J. Baddeley, H.J.G. Gundersen, and L.M. Cruz-Orive.
Estimation of surface area from vertical sections.
Journal of Microscopy, 142:259-276, 1986.

A. Baddeley and E.B. Vedel Jensen.
Stereology for Statisticians.
Chapman and Hall/CRC, Boca Raton, 2005.
ISBN 1-58488-405-3.

Statistical Image Analysis

Stochastic Geometry

Baddeley also worked on stochastic geometry, the fundamental geometric and statistical principles underlying all spatial information.

Statistical Software

Adrian Baddeley is a prominent developer of statistical software for spatial statistics. Over the last decade, Baddeley and Turner have implemented a software package spatstat for spatial point pattern analysis in the statistical language R. This is the leading package in its field and one of the largest packages of any kind available for R. It has had a worldwide influence on methodology for spatial point patterns. Baddeley conducts training workshops on spatial statistics using spatstat throughout Australia and New Zealand.