1. New Software Bob Nichol ICG, Portsmouth Thanks to all my colleagues in SDSS, GRIST & PiCA Special thanks to Chris Miller, Alex Gray, Gordon Richards, Brent Bryan, Chris Genovese, Ryan Scranton, Larry Wasserman, Jeff Schneider

2. Phystat 2005 Oxford Outline 1.Cosmological data is exploding in both size and complexity (see Szalay’s talk) 2.Can present software handle this data quality and quantity? 3.Also present models lack detail to understand the data which drives us towards non-parametric techniques. 4.Important synergies between CS, statistics and domain sciences Jim reviewed existing statistical software, I will discuss new software we may need

3. Gravity correlates everything The 2-point function (  (r)) has a long history in cosmology (Peebles 1980). It is the excess joint probability (dP 12 ) of a pair of points over that expected from a Poisson process. dP 12 = n 2 dV 1 dV 2 [1 +  (r)] dP 123 =n 3 dV 1 dV 2 dV 3 [1+  23 (r)+  13 (r)+  12 (r)+  123 (r)] dV 1 dV 2 r Also, marked correlation functions

4. Same 2pt, different 3pt Motivation for the N-point functions: Measure of the topology of the large-scale structure in universe

5. Multi-resolutional KD-trees  Scale to n-dimensions (although for very high dimensions use new tree structures)  Use Cached Representation (store at each node summary sufficient statistics). Compute counts from these statistics  Prune the tree which is stored in memory! (Moore et al. 2001 astro-ph/0012333)  Many applications; suite of algorithms!  See Alex Gray’s talk tomorrow

6. Top Level 1st Level 2nd Level 5th Level

7. Just a set of range searches Prune cells outside range Also Prune cells inside! Greater saving in time

8. Phystat 2005 Oxford N1N1 d max d min Usually binned into annuli r min < r < r max Thus, for each r transverse both trees and prune pairs of nodes No count d min < r max or d max < r min N 1 x N 2 r min > d min and r max < d max N2N2 Therefore, only need to calculate pairs cutting the boundaries. Scales to n-point functions also do all r values at once Dual Tree Algorithm

9. Can also parallelize on the Grid! bins Survey size

10. Phystat 2005 Oxford Code Available The code is freely available http://www.autonlab.org/autonweb/showSoftware/127/ http://www.autonlab.org/autonweb/showSoftware/127/ Added “Monte carlo sampling” to code for faster answers: approximate answers Added to AstroGrid suite of algorithms: “aimed at building a data-grid for UK astronomy, which will form the UK contribution to a global Virtual Observatory” VOtech is an EU-funded R&D project to explore the use of advanced algorithms in the IOVA infrastructure Broker developed to handle submission of jobs to National Grid Service (NGS) - the UK's core production computational and data grid service. Also using US Teragrid (5000 correlations in one weekend).

11. Phystat 2005 Oxford

12. EuroVO The Euro-VO Data Centre Alliance (DCA): –A collaborative and operational network of European data centres who publish data and metadata to the Euro-VO and who provide a research infrastructure of GRID-enabled processing and storage facilities. The Euro-VO Facility Centre (VOFC): –An organization that provides the Euro-VO for centralized resource registry, standards definition and promotion as well as community support for VO technology take-up and scientific program support using VO technologies and resources. The Euro-VO Technology Centre (VOTC): –A distributed organisation that coordinates a set of research and development projects on VO technology, systems and tools.

13. Phystat 2005 Oxford EuroVO: VOTech Project 6.6M Euro Design Study under EU FP6, Aims: –Complete all technical preparatory work necessary for the construction of the European Virtual Observatory, –Responsible for development of infrastructure and tools: Intelligent resource discovery (ontology and the semantic web), data interoperability, data mining, and visualisation capabilities. –Provide the ability to offload mass scale computational process onto the Enabling Grids for E-sciencE (EGEE) backbone.

14. Phystat 2005 Oxford Existing infrastructure VOTech is tasked with building upon existing infrastructure: In particular: –IVOA for standards, –AstroGrid for middleware: Web Services based, Presumably IVOA will continue to look towards other standards bodies: –World Wide Web Consortium (W3C), –Global Grid Forum (GGF), –…

15. Phystat 2005 Oxford IVOA Standards (Recommendations) VOTable Format Definition Version 1.1: –An XML language, Flexible storage and exchange format for tabular data: Emphasis on astronomical tables, –Allows meta data and data to be stored separately with links to remote data. Resource Metadata for the VO Version 1.01: –For describing what data and computational facilities are available, and once identified how to use them. Unified Content Descriptor (UCD) (Proposed): –A formal (and restricted) vocabulary for astronomical data. IVOA Identifiers Version 1.10 (Proposed): –Syntax for globally unique resource names.

16. Phystat 2005 Oxford AstroGrid Components MySpace: Distributed file store for workflows,results, Common Execution Architecture (CEA): –Codes need wrapping before use, –Take command line apps and present as a Web Service. Algorithm Registry: –Meta data from wrapped codes are published in a yellow pages, for searching. Portal: –Web interface for interacting with preceding services, –Workflow: Coordinate data flow/control of components within a larger system of work, –Submit jobs and observe status, and access files in MySpace. Dashboard/Workbench: –Interact with MySpace, Registry, CEA from any language that provides XML-RPC library. Web Start application.

17. Phystat 2005 Oxford AG Portal AG rollout and access via portal

18. Phystat 2005 Oxford Non-parametric Techniques The complexicity and wealth of the data demands non-parametric techniques, ie., can one describe phenomena using the least amount of assumptions? The challenges here are computational as well as psychological

19. Phystat 2005 Oxford CMB Power Spectrum Before WMAP WMAP data Are the 2 nd and 3 rd peaks detected?

20. Phystat 2005 Oxford In parametric models of the CMB power spectrum the answer is likely “yes” as all CMB models have multiple peaks. But that has not really answered our question! Can we answer the question non-parametrically e.g., Y i = f(X i ) + c i Where Y i is the observed data, f(X i ) is an orthogonal function (  i cos(i  X i )), c i is the covariance matrix. The challenge is to “shrink” f(X i ), we use Beran (2000) to strink f(X i ) to N terms equal to the number of data points - optimal for all smooth functions and provides valid confidence intervals Monotonic shrinkage of  i - specifically nested subset selection (NSS) See Genovese et al. (2004) astro-ph/0410104

21. Phystat 2005 Oxford Results (optimal smoothing through bias-variance trade-off) Concordance Our f(X i ) Note, WMAP only fit is not same as concordance model

22. Phystat 2005 Oxford Testing models The main advantage of this method is that we can construct a “confidence ball” (in N dimensions) around f(X i ) and thus perform non-parametric interferences e.g. is the second peak detected? Not at 95% confidence!

23. Phystat 2005 Oxford Information Content f h (X i ) = f(X i ) + b*h Beyond here there is little information

24. Phystat 2005 Oxford Using CMBfast we can make parametric models (11 parameters) and test if they are within the “confidence ball”. Varying  b we get a range of 0.0169 to 0.0287 Gray are models in the 95% confidence ball ASA “Outstanding Application of the year” (2005)

25. Phystat 2005 Oxford Testing in high D Now we can now jointly search all 11 parameters in the parametric models and determine which models fit in the confidence ball (at 95%). Traditionally this is done by marginalising over the other parameters to gain confidence intervals on each parameter separately. This is a problem in high- D where the likelihood function could be degenerate, ill-defined and under-identified This is computational intense as billions of models need to searched, each of which takes ~minute to run Use Kriging methods to predict where the surface of the confidence ball exists and test models there.

26. Phystat 2005 Oxford 7D parameter space 400000 samples Cyan : 0.5  Purple: 1  Blue : 1.5  Red : 2  Green : >2  Bimodal dist. for several parameters

27. Phystat 2005 Oxford Other applications Physics of CMB is well-understood and people counter that parametric analyses are better (including Bayesian methods) [however, concerns about CI] Other areas of astrophysics have similar data problems, but the physics is less developed –Galaxy and quasar spectra (models are still rudimentary) –Galaxy clustering (non-linear gravitational effects are not confidently modeled) –Galaxy properties (e.g. star-formation rate)

28. Phystat 2005 Oxford Summary Existing statistical software can’t scale-up to the next generation of datasets. Nor does it exploit the “Grid” Need to explore non-parametric statistics Software will be made available via AstroGrid and IVOA - seemless access to data, computational resources and algorithms