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