# Presentation: 363190

## Slide 1

## Overview

- Introduction & Motivation
- Likelihood Formulation
- wf-llh-reco project in IceTray
- Preliminary Results using Simulation V01-00-03
- Connections to other projects & future directions
- Discussion

- Paul Nipko, Project Controls Manager

## 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.
- A high priority since deployment has already begun.

- Paul Nipko, Project Controls Manager

## Likelihood Formulation

- How can you formulate a likelihood function with the full waveform at your disposal?
- Consider first the ideal case where the OM time response is a delta function
- Ignore any possible amplitude fluctuations for the moment.
- 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

- Paul Nipko, Project Controls Manager

## Probability of f(t) given p(t)? 

- Suppose you bin the photon distributions into k bins:

- Paul Nipko, Project Controls Manager

## Probability of {ni } | {μi} ? 

- The probability is given by Poisson statistics, as a product of Poisson probabilities over all the k bins:

- Paul Nipko, Project Controls Manager

## This product turns into something useful....

- Paul Nipko, Project Controls Manager

## ... Namely a multinomial distribution, the probability of arranging exactly N events into k bins, multiplied  by the Poisson probability of these N events occurring. 

- Paul Nipko, Project Controls Manager

## We have our Likelihood	Function

- Take the negative log of it

- Paul Nipko, Project Controls Manager

## Where is this applicable?

- We assumed we knew the photon arrival times precisely, or have a waveform made from the superposition of many photons.
- If we have a non-delta function time response, this form is still applicable as long as *our PDF is slowly varying *over the region described by the OM time response.
- Should be the case for our optical modules, typical pulse widths are narrow relative to the scale of expected photon arrival time distribution.

- Paul Nipko, Project Controls Manager

## wf-llh-reco module 

- The icetray implementation of this likelihood reconstruction.
- Currently looking at (non-directional) cascades.
- Uses UPandel for the timing PDF and PHit-PNoHit to get the expected PEs.
- Uses the MIGRAD minimizer in ROOT’s TMinuit class.
- Module in the sandbox area of SVN, named wf-llh-reco.

- Paul Nipko, Project Controls Manager

## Preliminary Results using Simulation V01-00-03	

- Newest version of Simulation meta-project just released over the weekend.
- 500 100-GeV cascade events were simulated with the vertex at the origin.
- Three reconstruction modules compared in icetray: CFirst, cscd-llh and wf-llh-reco.

- Paul Nipko, Project Controls Manager

## Preliminary Results Using Simulation V01-00-03: Vertex X

- Paul Nipko, Project Controls Manager

## Preliminary Results using Simulation V01-00-03: Vertex Y

- Paul Nipko, Project Controls Manager

## Preliminary Results using Simulation V01-00-03: Vertex Z

- Paul Nipko, Project Controls Manager

## Preliminary Results using Simulation V01-00-03: Vertex T

- Paul Nipko, Project Controls Manager

## Future Directions	

- First and foremost, continue development and check the algorithm.
- Incorporate Photonics as the “PDF of choice” for waveform reconstruction.
- Look at other event types (directional cascades, muon tracks, high energy tracks, etc)
- Optimize the minimization, perhaps use another minimizer?

- Paul Nipko, Project Controls Manager

## Discussion

- Thoughts and Comments
- Possible connection with other waveform based algorithms?

- Paul Nipko, Project Controls Manager