[arxiv:0906.3662] The Statistical Analysis of fMRI Data by Martin A. Lindquist
Statistical Science, Vol. 23(4), pp. 439-464

This review paper offers some information and guidance of statistical image analysis for fMRI data that can be expanded to astronomical image data. I think that fMRI data contain similar challenges of astronomical images. As Lindquist said, collaboration helps to find shortcuts. I hope that introducing this paper helps further networking and collaboration between statisticians and astronomers.

List of similarities

• data acquisition: data read in frequency domain and image reconstruction via inverse Fourier transform. (To my naive eyes, It looks similar to Power Spectrum Analysis for cosmic microwave background (CMB) data).
• amplitudes or coefficients are cared and analyzed, not phase nor wavelets.
• understanding data:brain physiology or physics like cosmological models that describe data generating mechanism.
• limits in/trade-off between spatial and temporal resolution.
• understanding/modeling noise and signal.

These similarities seem common for statistically analyzing images from fMRI or telescopes. Notwithstanding, no astronomers can (or want) to carry out experimental design. This can be a huge difference between medical and astronomical image analysis. My emphasis is that because of these commonalities, strategies in preprocessing and data analysis for fMRI data can be shared for astronomical observations and vise versa. Some sloggers would like to check Section 6 that covers various statistical models and methods for spatial and temporal data.

I’d rather simply end this posting with the following quotes, saying that statisticians play a critical role in scientific image analysis.

There are several common objectives in the analysis of fMRI data. These include localizing regions of the brain activated by a task, determining distributed networks that correspond to brain function and making predictions about psychological or disease states. Each of these objectives can be approached through the application of suitable statistical methods, and statisticians play an important role in the interdisciplinary teams that have been assembled to tackle these problems. This role can range from determining the appropriate statistical method to apply to a data set, to the development of unique statistical methods geared specifically toward the analysis of fMRI data. With the advent of more sophisticated experimental designs and imaging techniques, the role of statisticians promises to only increase in the future.

A full spatiotemporal model of the data is generally not considered feasible and a number of short cuts are taken throughout the course of the analysis. Statisticians play an important role in determining which short cuts are appropriate in the various stages of the analysis, and determining their effects on the validity and power of the statistical analysis.

When it comes to survey, the first thing comes in my mind is the census packet although I only saw it once (an easy way to disguise my age but this is true) but the questionaire layouts are so carefully and extensively done so as to give me a strong impression. Such survey is designed prior to collecting data so that after collection, data can be analyzed according to statistical methodology suitable to the design of the survey. Strategies for response quantification is also included (yes/no for 0/1, responses in 0 to 10 scale, bracketing salaries, age groups, and such, handling missing data) for elaborated statistical analysis to avoid subjective data transformation and arbitrary outlier eliminations.

In contrast, survey in astronomy means designing a mesh, not questionaires, unable to be transcribed into statistical models. This mesh has multiple layers like telescope, detector, and source detection algorithm, and eventually produces a catalog. Designing statistical methodology is not a part of it that draws interpretable conclusion. Collecting what goes through that mesh is astronomical survey. Analyzing the catalog does not necessarily involve sophisticated statistics but often times adopts chi-sq fittings and cast aways of unpleasant/uninteresting data points.

As other conflicts in jargon, –a simplest example is H_o: I used to know it as Hubble constant but now, it is recognized first as a notation for a null hypothesis — survey has been one of them and like the measurement error, some clarification about the term, survey is expected to be given by knowledgeable astrostatisticians to draw more statisticians involvement in grand survey projects soon to come. Luckily, the first opportunity will be given soon at the Special Session: Meaning from Surveys and Population Studies: BYOQ during the 213 AAS meeting, at Long Beach, California on Jan. 5th, 2009.

A review paper on LASSO and LAR: [stat.ME:0801.0964] T. Hesterberg et.al.
   Least Angle and L₁ Regression: A Review
Model checking for Bayesian hierarchical modeling: [stat.ME:0802.0743] M. J. Bayarri, M. E. Castellanos
   Bayesian Checking of the Second Levels of Hierarchical Models

• [astro-ph:0802.0042] Y. Kubo
  Statistical Models for Solar Flare Interval Distribution in Individual Active Regions (it discusses AIC)

• [astro-ph:0802.0131] J.Bobin, J-L Starck and R. Ottensamer
  Compressed Sensing in Astronomy

• [astro-ph:0802.0387] J. Gaite
  Geometry and scaling of cosmic voids

• [astro-ph:0802.0400] R. Vio & P. Andreani
  A Modified ICA Approach for Signal Separation in CMB Maps

• [astro-ph:0802.0498] V. Balasubramanian, K. Larjo and R. Sheth
  Experimental design and model selection: The example of exoplanet detection

• [astro-ph:0802.0537] G. Dan, Z. Yanxia, & Z. Yongheng
  Support Vector Machines and Kd-tree for Separating Quasars from Large Survey Databases