Last Updated: 2009apr01


Topics in Astrostatistics

Statistics 310, Fall/Winter 2008-2009

Harvard University

Instructor Prof. Meng Xiao Li
Schedule Tuesdays 11:30 AM
Location Science Center Rm 705

Hyunsook Lee
9 Sep 2008
Computing the significance of non-nested models
slides [.pdf]
Alanna Connors (Eureka Sci), Brandon Kelly (CfA), Pavlos Protopapas (CfA)
16 Sep 2008
"Some nice problems": Introducing High-Energy Astronomy and Astrophysics
Alanna Connors [.pdf]
Brandon Kelly [.pdf]
23 Sep 2008
proposals, programs, papers
Paul Baines (HU)
30 Sep 2008
Color-Magnitude Diagrams
Abstract: The properties of stars, and clusters of stars, have important implications for understanding physical and stellar processes. We present a Hierarchical Bayesian method for determining the mass, age and metallicity of stars from photometric data. The method uses isochrone tables which map the 'expected' data to the unknown parameters in a highly nonlinear manner. Our approach allows for inference about individual star ages and masses, as well as cluster-level properties. In this talk we will discuss one aspect of the model that accounts for non-detections of stars. Some computational aspects of the model will also be discussed.
Presentation [.pdf]
14 Oct 2008
Stats grad students describe projects
Alex Blocker (BU/HU)
21 Oct 2008
Two Statistical Problems in X-ray Astronomy
Abstract: I will discuss my work on two projects in x-ray astronomy: the development of a hierarchical Bayesian replacement for "stacking" and the analysis of events in x-ray light curves. For each problem, I will outline the development of an improved model for the data and the computational methods employed. I will also discuss the unique challenges that each case has presented from a cultural perspective.
Presentation [.pdf]
Jaesub Hong (CfA)
18 Nov 2008
Peeking into the Early Universe with Coded-Aperture Imaging:
Energetic X-ray Imaging Survey Telescope (EXIST)
Abstract: A proposed Black Hole Finder probe, Energetic X-ray Imaging Survey Telscope (EXIST) is re-designed to capture and identify high red-shift Gamma-ray Burst (GRB) through X-ray imaging and onboard optical/IR spectroscopy. EXIST will probe the early Universe using GRBs as cosmic probe and survey black holes on all scales. I will review the current mission concept for EXIST and its hard X-ray imaging technique, coded-aperture imaging.
Presentation: [.pdf]; [.ppt]
Herman Chernoff (HU)
02 Dec 2008
Randomized Experiments and Hong's problem
Li Zhan (HU)
16 Dec 2008
A new tone of EM algorithm in the universe: MMT/Megacam Data
Abstract: In observing the objects in the space, there is a gap between the ones can be observed through direct observation and the one can be done through X-ray occultation. With the MMT/Megacam survey data, we are trying to fill the gap, targeting at the objects with diameter 200m-1km.
The MMT/Megacam traces the time evolution of the combined photon number from both stars and the background. By employing the EM algorithm, we aim at de-convoluting the effects of stars and finally detecting the major changes in the flux of stars in the time horizon. The change of flux of stars will give us invaluable information on our targeted objects passing the star and thus we can indirectly observe the targeted objects.
Presentation [.pdf]
Li Zhu
03 Feb 2009
Alanna Connors
17 Feb 2009
Quantifying, Summarizing, and Representing 'Total' Uncertainties in Image (and Spectral) 'Deconvolution'
Abstract: In 1998 Dixon et al. (1) used wavelets to demonsrtate a significant mis-match between their all-sky gamma-ray data versus the best physics-based models. They wrote: `The immediate question arises as to the statistical significance of this feature. ... quantification of object-wise significance (e.g., "this blob is significant at the n\sigma level") are difficult.'
Ten years later, we have cracked the problem in general (2,3); but many specific challenges remain.
We briefly describe the recent history. First, researchers tried using flexible non-parametric models (NP; e.g. wavelets and the like; 4) to represent an unknown 'true' sky image or spectrum. In both Bayesian and frequentist methods, these are embedded in a likelihood framework that includes the instrument 'smearing' ("forward-fitting"), with a prior (or complexity penalty) acting as a regularizer. Second, rather than using thresholding or an (EM) best-fit, Esch et al (2) pioneered using MCMC to generate samples of the 'true' images. Third, we included a physics-based model into the fit; with the flexible NP component used only to capture any mis-match between one's best model and the data. Fourth, extrapolating from recent classes of methods that compare the distribution of NP model co-efficients with that expected from noise, we came up with a generalized PPP method (e.g. 5). Using simple low-dimensional summary statistics, we are able to: 1/ test for significance and goodness of fit; 2/ set quantile limits on the properties of any significant 'mis-match'; and 3/ translate and display the resulting (say) +/-5% credible regions back to the image space for a different kind of object-wise significance, and limits on shape --- all the while accounting for correlations among the means of nearby bins or pixels. We do this all in the low-count Poisson limit; but our methods are more generally applicable.
Finally, in our Bayesian framework, we are able to incorporate increasingly complex prior information in a hierarchical way. Thus, we can also incorporate instrumental uncertainties, following the approaches of Drake et al and Kashyap et al.
However many challenges remain. These include:
  • Better summary statistics;
  • Better, more robust and efficient ways to represent and incorporate instrumental calibration uncertainties;
  • Better representation of 'significance' than scatter plots or histograms of 'null' vs 'interesting' results;
  • More complex physics-models -- fitting at same time;
  • Incorporating higher-level physics model-uncertainty;
  • Keeping it a 'convex' (i.e. unimodal) problem when adding different kinds of components;
  • Higher dimensions (E and t as well as X and Y); and other coordinate systems (Fermi's "Healpix", etc..)
(1) Dixon, Hartman, Kolaczyk, et al, New Astronomy 3 (1998) 539.
(2) Esch, D. N., Connors, A., Karovska, M., and van Dyk, D. A. (2004). Ap.J. 610, 1213
(3) Connors, A. and van Dyk, D. A. (2007). In SCMA IV (Editors: E. Feigelson and G. Babu), vol. CS371, 101
(4) Nowak, R. D. and Kolaczyk, E. D. (2000). IEEE Transactions on Information Theory 46, 1811
(5) Protassov, R., van Dyk, D. A., Connors, A., Kashyap, V., and Siemiginowska, A. (2002). Ap.J. 571, 545.
Presentation slides [.pdf]
Alanna Connors
03 Mar 2009
Doubts and Challenges: The Untidiness of Real Examples
Abstract: We will again have the Geiger counter and radioactive source to use to help define the problem, and to summarize the machinery we are proposing to use as solutions (Bayes with physics-based plus multi-resolution -- i.e. wavelet-like -- models, via MCMC and D.A.). We will look at preliminary results from several kinds of Monte Carlo tests, using our new methods. We will also introduce "skeptical astronomers" with several kinds of doubts. As time permits, we will also show several more examples of interesting data from X-ray and Gamma-ray telescopes --- each with its own challenges.
Presentation slides [.pdf]
Li Zhu
31 Mar 2009
Wavelet analysis of RMFs
Abstract: In this presentation, I will talk about analyzing uncertainty of redistribution matrix functions(RMFs) with wavelet decomposition. I used wavelet (haar and db4) to do decomposition on both log(RMF) and the difference between log(RMF) and log(default RMF). I will present the characteristic of wavelet coefficients for both cases, especially the similarity of wavelet coefficients between different true energies and correlations between wavelet coefficients. After that I will suggest several different Bayesian models which include base function and error term with specific variance structure which I will use to do the further analysis.
Erik Kolaczyk
07 Apr 2009
Multiscale methods for Poisson count data: a review
Abstract: I will review a handful of methods designed for multiscale analysis of Poisson count data, based on Haar wavelets, multiscale likelihood factorizations, and piecewise polynomial bases on recursive partitions. These methods were designed to translate the power of wavelet-based methods in the standard Gaussian noise model to the context of count data.
Victoria Liublinska
21 Apr 2009
Differential Emission Measure analysis of high-resolution X-ray Spectra
Abstract: Access to substantial amount of data in the high-energy range gives us an opportunity to extend our knowledge of stellar coronal composition and temperature structure by analyzing the entire spectrum as a whole. Moreover, data from detectors with high spectral resolution will provide additional constraints on atomic data measurements being conducted in laboratories on the ground. In particular, the best atomic emissivity databases created by physicists still have missing, misplaced or poorly estimated lines and the goal of our analysis is to provide ways of identifying lines that were omitted and improve our estimates of stellar Differential Emission Measure and plasma abundance by incorporating the information about them.
Presentation [.pdf]
Nathan Stein
05 May 2009
The White Dwarf Initial-Final Mass Relationship
Abstract: Stars lose mass during their evolution. A star's initial mass helps determine both its rate of evolution and whether it becomes a white dwarf, a black hole, or a neutron star. Since most stars end their lives as white dwarfs, astronomers are eager to understand the relationship between white dwarf masses and the initial masses of their progenitor stars, but large theoretical and observational uncertainties remain. I will suggest a method for obtaining inferences on the initial-final mass relationship by extending statistical models for analyzing star cluster color-magnitude diagrams.
Fall/Winter 2004-2005
Siemiginowska, A. / Connors, A. / Kashyap, V. / Zezas, A. / Devor, J. / Drake, J. / Kolaczyk, E. / Izem, R. / Kang, H. / Yu, Y. / van Dyk, D.
Fall/Winter 2005-2006
van Dyk, D. / Ratner, M. / Jin, J. / Park, T. / CCW / Zezas, A. / Hong, J. / Siemiginowska, A. & Kashyap, V. / Meng, X.-L.
Fall/Winter 2006-2007
Lee, H. / Connors, A. / Protopapas, P. / McDowell, J., / Izem, R. / Blondin, S. / Lee, H. / Zezas, A., & Lee, H. / Liu, J.C. / van Dyk, D. / Rice, J.
Fall/Winter 2007-2008
Connors, A., & Protopapas, P. / Steiner, J. / Baines, P. / Zezas, A. / Aldcroft, T.
Fall/Winter 2008-2009
H. Lee / A. Connors, B. Kelly, & P. Protopapas / P. Baines / A. Blocker / J. Hong / H. Chernoff / Z. Li / L. Zhu (Feb) / A. Connors (Pt.1) / A. Connors (Pt.2) / L. Zhu (Mar) / E. Kolaczyk / V. Liublinska / N. Stein