Applications of change point detection in Gravitational Wave Data Analysis

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Applications of change point detection in
Gravitational Wave Data Analysis

• Soumya D. Mohanty
• AEI

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Plan of the talk

• Brief introduction to change point detection and
  its relevance to GW data analysis
• Contrast with prevalent methods
• Three applications in different areas

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What is a change point?
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Signals and Change points

• The most elementary signature of a signal is to
  introduce a change in the distribution of data
• Isolating a subset of given data that is
  significantly different from the rest is the most
  general signal detection method
• This division is subject to statistical
  uncertainty

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Mathematical Statement

• Data described by a joint probability density
  p(x).
• CP detection Can the data be divided into
  disjoint sets y, z (x y?z), such that p(y) is
  different from p(z)? Not required to know p(y)
  or p(z) themselves.
• Adaptive detection Somehow deduce or estimate a
  noise p(x). Then given new data y, test if it
  could have come from p(x).

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Pros and Cons

• Change point detection
• Can go from full prior information to no prior
• Less sensitive
• Possible to tune away response to different types
  of inhomogeneity
• Post analysis definition required of what is a
  signal and what is noise

• Adaptive detection
• Needs prior information and assumption of
  stationarity
• More sensitive provided prior information is
  correct
• Tuning is a complicated process if at all
  possible
• Signal noise pre-defined

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Applications

• Change point detection in the time-frequency
  plane burst detection
• Change point detection in a multivariate time
  series Data/Detector Characterization Robot
• Two sample comparison GRB-GW association

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Bursts in time-frequency plane

• Time frequency plane arena for burst detection
• Example split time series into segments and FFT
  each one.
• Basic signature of a burst changes the
  distribution of samples in some region of the
  time-frequency plane.

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• Most Burst detection algorithms try to look for
  this effect in different ways
• Excess power thresholds the average (band
  limited rms)
• Tfclusters thresholds cluster size
• PSDCD (Mohanty, PRD,99) tests for difference in
  sample distributions of blocks in TF plane.
• PSDCD is a change point detector, others are
  adaptive detectors.

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Non-parametric CP detection

• Non-parametric detection the false alarm rate is
  independent of noise distribution by
  construction. Sets it apart from other burst
  detectors.
• A non-stationary time series can be thought of as
  a sequence of transitions from one noise model to
  another (e.g. 1? ?10??...). A non-parametric
  detector should maintain a constant false alarm
  rate even for non-stationary noise.
• CP detection can be tuned to prevent triggering
  on known technical features.

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KSCD

• Power Spectral Density Change Detector DMT
  Monitor
• Kolmogorov-Smirnov test based Change Detector
  (KSCD)
• KSCD improvement in detection efficiency and
  implementation

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Trial run on GEO S1 data

• Uncalibrated h(t). 3.47 days (some breaks).
• Plagued by fast non-stationarity in the lt1.5kHz
  band.
• 90 - 95 of MTFC triggers could be attributed to
  this fast non-stationarity.
• These false triggers skew the interpretation of
  histograms such as the time interval between
  triggers.
• KSCD can be tuned to be insensitive to these
  features but still catch genuine glitches.

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Rejection of features
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Analysis goals

• Disentangle fast low frequency non-stationarity
  from genuine triggers.
• Study time dependent behavior of the triggers.
• Study trigger rate vis a vis band limited rms
  trend.
• Does KSCD trigger rate track band limited rms?
• Tune KSCD to reject triggers but catch fast
  non-stationarity
• Analyze the dependence of genuine trigger
  channel on fast non-stationarity channel.

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Trigger rate
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Future of KSCD

• Test various aspects of non-parametric change
  point detection using real data (S1 GEO/LIGO, S2
  LIGO)
• Understand efficiency (very preliminary ?40 of
  matched filtering)
• Build LDAS DSO
• KSCD Main engine of DCR

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Data/Detector Characterization Robot
View data as a single multivariate time series
DCR Detect change points
Database
All channels
Transform the multivariate data Example
construct cross-correlation of two channels
Design
Data Mining
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Data CharacterizationWhat is the best analysis
strategy given some data?

• Quantify
• non-stationarity of noise floor
• Types and rates of transients
• Drifting carrier frequencies
• Simulate real data and do Monte Carlo studies
• Hopefully, lead to more believable detection of
  GW signals.

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Detector Characterization

• Hunt down sources of deviations from expected
  ideal behavior and fix them
• To help, interferometers blindly record data from
  several other sensors
• control system
• environment monitors (e.g., temperature)
• Seismometers, magnetometers

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Change PointsMathematical abstraction of the
problem

• Main interest in both data and detector
  characterization change points
• Example transients, change in rate of
  transients, non-stationarity, change in coupling
  between two channels
• Natural conclusion-- Build database of change
  points using automated algorithms and analyse the
  database

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Analysis of databases

• Exploratory
• Limited to small databases of high confidence
  detections
• Data mining
• Emerging field of synthesis between statistics
  and computing aim is to detect new, informative
  patterns in huge databases
• Requires reliable database quality

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DCR project

• Overall Aim enable data mining of multi-channel
  interferometric data
• Elements
• Algorithms few, well understood and
  complementary (not an arbitrary set of
  independent simple monitors)
• Software/Hardware
• Data mining

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Algorithms in DCR

• Change point detector KSCD
• generalized to the case of cross-spectral density
  of two channels
• Line removal MBLT
• no modeling required of line behavior
• transient resistant
• Robust noise floor tracking MNFT

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Sample Power Spectral Density
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DCR implementation

• Core Digital Signal Processing library in C
• Template based Statistics and Signal Processing
  library (TSSP). Uses STL.
• FFT, Filtering, Filter Design, Windows, PSD,
  Modulation, Demodulation, ...
• Stand alone C main function for a given pipeline

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Stand alone code

• Frame reading class
• Multiple ADC channels
• Database IO class (uses MySQL)
• Database to be used for both job description and
  storing job outputs
• Multiple jobs launched using Condor
• At present dedicated 10 node cluster
  (Linux-alpha)

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GRB-GW association

• Finn, Mohanty, Romano, PRD, 1999
• Based on two sample comparison
• on-source sample
• off-source sample
• Two sample tests also used in CP detection

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Introduction to Gamma-Ray Bursts

• High-energy, short-duration electromagnetic
  radiation from extra-galactic sources
• Favored models point to exploding fireball
• Involve large amounts of matter,
• ejected at relativistic speeds,
• producing a series of high-energy E/M
  shockwaves---
• initially gamma-rays (some redshift to
  lower-energy gamma-rays or X-rays, others are
  absorbed),
• then X-rays (red-shifted to optical wavelengths),
• then visible light (red-shifted to radio
  wavelengths)

http//online.itp.ucsb.edu/online/gamma_c99/piran/
oh/06.html
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GRBs and Gravitational Waves

• GRB progenitors thought to be new formed Black
  Holes
• Black Hole formed as a result of massive stellar
  collapse or binary NS mergers
• BH accretes debris rapidly
• Leads to beams of ultra-relativistic ejecta
• This violent scenario is a natural candidate for
  strong GW emission also

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Motivation for an FMR type search

• GRBs occur at cosmological distances. Hence
  chance of detecting GWs from an individual GRB is
  small
• However, GRB astronomy is very active
• Relatively large number of events were detected
  (O(1/day)) by BATSE
• Several more missions coming up soon (e.g., SWIFT
  and GLAST)
• FMR Combine information from several triggers to
  build up signal to noise ratio

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Algorithm

• Cross-correlate time series between two
  interferometers for each GRB trigger
• time shift segments to align GW signal
• Compare cross-correlation to times not associated
  with GRBs
• Build an on-source and a off-source sample of
  cross-correlations
• Test if the means values of the two samples are
  significantly different

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Implementation

• External Triggers subgroup of Bursts Upper Limit
  group
• S. Marka, R. Rahkola, S. Mohanty, S. Mukherjee,
  R. Frey
• Could not apply FMR in toto for S1 because only
  one trigger received during double lock (LIGO
  tech note)
• Already have 15 triggers for S2!

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Issues

• Non-stationarity of data
• Data conditioning line removal
• Noise floor tracking -- MNFT
• Lack of directional accuracy
• Use H1H2 but strong (non-stationary?)
  correlations
• How to best use multiple interferometers
• Systematic uncertainties
• Rely on signal injection and Monte Carlo
  simulations
• DCR simulate real data?

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Summary

• Applications of change point detection in GW data
  analysis
• Exploration of such techniques has just only
  started
• Offers better control on data analysis with real,
  complicated data
• Improvements in efficiency possible. Can be
  combined with adaptive methods.