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Sean Grullon w/ Gary Hill
Maximum likelihood reconstruction of events using waveforms
September 2005
Sean Grullon w/ Gary Hill 2
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Overview
• Introduction & Motivation• Likelihood Formulation• wf-llh-reco project in IceTray• Results using Simulation V01-00-
04• Current Development and Future
Directions• Discussion
September 2005
Sean Grullon w/ Gary Hill 3
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Introduction & Motivation
• All reconstruction algorithms in IceRec are ported from AMANDA.
– Were originally developed for the Muon-DAQ… (TOTs, LEs, Peak Amp.)
• Need new algorithm(s) to take advantage of the full waveform information Icecube provides.
• Full Waveform information should prove powerful for high energy & non-contained events.
• A high priority since deployment has already begun.
September 2005
Sean Grullon w/ Gary Hill 4
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Likelihood Formulation
• How can you formulate a likelihood function with the full waveform at your disposal?
• Given an expected distribution of photons μp(t), what is the probability of observing a waveform f(t)?– p(t) is normalized timing probability, μ is the total
number of expected photons, given either numerically (Photonics) or analytically (e.g. Pandel)
– f(t) is your observed waveform
September 2005
Sean Grullon w/ Gary Hill 5
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Probability of f(t) given p(t)?
}{)(
}{)(
i
i
tp
ntf
•Suppose you bin the photon distributions into k bins:
September 2005
Sean Grullon w/ Gary Hill 6
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Probability of {ni } | {μi} ?
• The probability is given by Poisson statistics, as a product of Poisson probabilities over all the k bins:
i
i
en
nPk
i i
ni
ii
1 !}){|}({
September 2005
Sean Grullon w/ Gary Hill 9
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
This product turns into..
e
NnNnP
Nn
k
i i
i
ii
i
!!!}){|}({
1
September 2005
Sean Grullon w/ Gary Hill 10
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
We have our LikelihoodFunction
• Take the negative log of it
log!loglog
!loglog!loglog!log
!!!log}){|}({log
1 1
1 1
1
Nnn
NNnnN
eNn
NnP
i
k
i
k
iii
i
k
i
k
iii
Nn
k
i i
i
ii
i
September 2005
Sean Grullon w/ Gary Hill 11
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Our likelihood function – cont.
loglog}){|}({log1
NnnPk
iiiii
September 2005
Sean Grullon w/ Gary Hill 13
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
wf-llh-reco module
• The icetray implementation of this likelihood reconstruction.
• Currently looking at (non-directional) cascades.
• Uses UPandel for the timing PDF.• Uses the SIMPLEX minimizer in ROOT’s
TMinuit class. • Uses calibrated ATWD waveform directly and
not the output of the Feature Extractor • Module in the sandbox area of SVN, named
wf-llh-reco.
September 2005
Sean Grullon w/ Gary Hill 14
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Preliminary Results using Simulation V01-00-04
• 1000 100 TeV simple cascade events were generated locally in Madison by Paolo Desiati.
• Cascades were generated with a random vertex position and direction. Full IceCube simulation used layered photonics tables.
• Wf-llh-reco project results compared to cscd-llh project
September 2005
Sean Grullon w/ Gary Hill 15
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Preliminary Results Using Simulation V01-00-04: Vertex X
RMS: 38.15 RMS: 49.4
September 2005
Sean Grullon w/ Gary Hill 16
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Preliminary Results Using Simulation V01-00-04: Vertex Y
RMS: 36.32 RMS: 48.62
September 2005
Sean Grullon w/ Gary Hill 17
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Preliminary Results Using Simulation V01-00-04: Vertex Z
RMS: 29.65 RMS: 51.23
September 2005
Sean Grullon w/ Gary Hill 18
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Preliminary Results Using Simulation V01-00-04: Energy
September 2005
Sean Grullon w/ Gary Hill 19
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Scatterplot of Z resolution vs. MC Z
September 2005
Sean Grullon w/ Gary Hill 20
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Preliminary Results for an initial study of non-contained events
• 500 JULIET Toy Cascades simulated with layered photonics tables.
• Cascades simulated from 1PeV to under 10EeV
• All cascades non-contained, randomly distributed from just outside full Icecube array to 0.5 km away.
September 2005
Sean Grullon w/ Gary Hill 21
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Non contained EHE events: Preliminary Energy Resolution
September 2005
Sean Grullon w/ Gary Hill 22
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Non contained EHE cascades: Preliminary vertex resolution
September 2005
Sean Grullon w/ Gary Hill 23
IceCube Collaboration
Meeting – Imperial College
September 27th , 2005
Current Development and Future Directions
• Currently implementing Photonics as the PDF for reconstruction
• Investigate reconstructing the cascade direction• Move project from SVN sandbox to the IceRec
meta-project.• Look at some sort of hit cleaning to improve
results• Improve algorithm performance for non-
contained events.• Look at other event types • Optimize the performance