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Applications of change point detection in Gravitational Wave Data Analysis

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Title: Applications of change point detection in Gravitational Wave Data Analysis


1
Applications of change point detection in
Gravitational Wave Data Analysis
  • Soumya D. Mohanty
  • AEI

2
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

3
What is a change point?
4
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

5
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).

6
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

7
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

8
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.

9
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10
  • 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.

11
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.

12
KSCD
  • Power Spectral Density Change Detector DMT
    Monitor
  • Kolmogorov-Smirnov test based Change Detector
    (KSCD)
  • KSCD improvement in detection efficiency and
    implementation

13
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14
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15
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.

16
Rejection of features
17
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.

18
Trigger rate
19
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

20
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
21
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.

22
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

23
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

24
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

25
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

26
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

27
Sample Power Spectral Density
28
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

29
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)

30
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

31
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
32
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

33
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

34
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

35
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!

36
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?

37
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.
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