Data Analysis Log

Glitch studies

• 2008/04/07 ...... Glitch Central Frequency Analysis - preliminary.
• 2008/04/09 ...... Glitch Central Frequency Analysis.
• 2008/04/21 ...... Peak spacing analysis algorithm testing.
• 2008/04/21 ...... Peak spacing analysis algorithm applied to real data.
• 2008/04/30 ...... Marking the peaks with most frequent spacings.


Bayes studies

• 2008/05/12 ...... Two Parameter estimation of a Sine-Gaussian contaminated with gaussian noise.
• 2008/05/20 ...... Parameter estimation with MCMC using Metropolis-Hasting algorithm.
• 2008/05/21 ...... Parameter estimation with MCMC using Gibbs sampling.
• 2008/05/20 ...... MCMC study on bimodal bivariate normal distribution.
• 2008/05/21 ...... MCMC study on sine-gaussian injection on a 4D parameter space.

  
  
  GW source population studies
  

• 2008/06/30 ...... GW sources (theory).
• 2008/07/12 ...... GW sources - Galactic Population.
• 2008/07/12 ...... Preliminar Beam pattern study.
• 2008/07/15 ...... Galactic disc population study (Amplitude Distribution).
• 2008/07/16 ...... Galactic population study (Amplitude Distribution).
• 2008/07/16 ...... Galactic population study (MCMC for parameter estimation).
• 2008/07/17 ...... Injection of the signals and parameter estimation from amplitude distribution).
  
  Beam pattern studies
  
• 2008/07/25 ...... Beam pattern function distribution.
  
  MCMC work
  
• 2008/08/05 ...... MCMC of a source of known location and unkown (ho,tau,psi) - 3D.
• 2008/08/07 ...... Probability Densities for spherical coordinates on isotropic sources.
• 2008/08/14 ...... MCMC of a source of known location and unkown (thetaL,phiL,ho,tau) - 4D (first).
• 2008/08/22 ...... Polarisation angle study for random L and N.
• 2008/08/23 ...... MCMC of a source of known location and unkown (thetaL,phiL,ho,tau) - 4D (second).
  
  2nd year report
  
• Second year report
  
  Convergence studies and Multimodal distributions
  
• Convergence study
• Simulated Annealing
  
  Discrete Fourier Transformation study
  
• DFT study for sin and cos exponentials (05 Nov 2008)
• Laser Interferometric Detector Sensitivity (05 Nov 2008)
• Neutron Star Oscillations (05 Nov 2008)
• Discrete Fourier Transform and SNR calculations (06 Nov 2008)
  
  Exhaustive log-likelihood studies (too high SNR)
  
• Exhaustive log-likelihood studies - Analytical (26 Nov 2008)
  
  Exhaustive log-likelihood studies (good SNR)
  
• Exhaustive log-likelihood studies - Analytical (04 Dec 2008)
  
  SNR study
  
• SNR study (varying h0,f0) (08 Dec 2008)
  
  Parameter inference error
  
• Why is the inference of the damping-time value so poor? (11 Dec 2008)
  
  Energy of damped sinusoid signals
  
• Does energy constrain help in reducing the uncertainty of the parameter estimation? (12 Dec 2008)
  
  2009
  DFT values - Distribution
  
• Reconstruction of sampled (discrete) signals using DFT (FFT)
• Magnitude and Phase Distributions (DFT) (07 Jan 2009)
  
  Marginalisation curves
  
• Marginalisation curves - Exhaustive logL (08 Jan 2009)
  
  Parameter estimation using logL (exhaustive)
  
• 2D parameter estimation (f0,tau)(10 Jan 2009)
• 3D parameter estimation (f0,tau,h0)(10 Jan 2009)
• 4D parameter estimation (f0,tau,h0,inj)(10 Jan 2009)
  
  Discrete Fourier Transform (DFT with FFT), DTFT and CTFT
  
• Reconstruction of Sampled Signals (Discrete) with DFT (FFT) (20 Jan 2009)
• Discrete Time Frequency Transformation (DTFT) (21 Jan 2009)
• logL calculation (DFT compared with DTFT) (22 Jan 2009)
• logL map and hot pixel statistics - 2D (26 Jan 2009)
• logL map and hot pixel statistics - 3D (26 Jan 2009)
• Comments about SNR calculation (26 Jan 2009)
  
  
• logL map and hot pixel statistics - 2D (improved) (29 Jan 2009)
• logL maps and marginalisation curves - 3D (improved)- No noise (29 Jan 2009)
  
  MCMC
  
• McMC (MH) - 1 signal and 2 parameters (f0 and tau) (28 Jan 2009)
• McMC (MH) - 1 signal and 3 parameters (f0,tau,h0) (02 Feb 2009)
• McMC (MH-SA) - 1 signal and 3 parameters (f0,tau,h0) (02 Feb 2009)
• Comparison normal-MH and MH-SA (02 Feb 2009)
  
  Improved MCMC
  
• McMC(MH) - 1 signal and 2 parameters (f0 and tau) (06 Feb 2009)
• McMC(MH) - 1 signal and 3 parameters (f0 and tau) (06 Feb 2009)
  
  MCMC - Exercise Delayed Rejection
  
• Exercise of MH with Delayed Rejection on a Bivariate Normal Distribution
  
  Theoretical uncertainties in f and tau
  
• Uncertainties on f and tau for F,P and W oscillation modes
• Uncertainties on f and tau for Ns oscillation values from Kokkotas & Andersson
• Uncertainty ellipses vs. SNR values
  
  Check real and imaginary coefficient logL map independently
  
• 2D logL map comparison.
  
  Matlab implementations from of sinusoidal models from
  'Bayesian Spectrum Analysis and Parameter Estimation' by G. Larry Bretthorst.
  
• Two easy examples plus Lorentzian decay (page 86) (2009/03/04).
• Comparison of Likelihood and Joint-Likelihood for Lorentzian decay (page 34) (2009/03/09).
• Marginalisation of joint-Likelihood (2009/03/10).
• Marginalisation of 3D joint-Likelihood to 2D maps(2009/03/11).
• Marginalisation of 4D joint-Likelihood to 2D maps(2009/03/11).
  
  DFT and DTFT comparisons for shifted signals
  
• Two examples of the DFT and DTFT of shifted signals (2009/03/16).
• Sin and Cos exponential SHIFTED (improved) (2009/03/26).
  
  Parameter Estimation 3D (Cardiff meeting)
  
• Slides for ET meeting (Cardiff)(2009/03/26).
  
  Parameter Estimation 4D/5D
  
• Parameter estimation 3D (h0,f0,tau) (2009/03/26).
• Parameter estimation 4D (h01,h02,f0,tau) (2009/03/26).
• Parameter estimation 5D (h01,h02,f0,tau,T0) (2009/03/26).
  
  Antena Pattern Function Probability Distribution
  
• F+ and Fx distribution (2009/04/01).
  
  Generation of Discrete Random Quantities
  
• Generating Samples from a random distribution (2009/04/01).
  
  Realistic vs. Isotropic Fc/Fp Prob.Distr.Functions
  
• Realistic vs. Isotropic Fc/Fp Prob.Distr.Functions (2009/04/02).
  
  Antenna Pattern Functions and Source Location
  
• Antenna Pattern Functions and Source Location (2009/04/22).
  
  Parameter estimation with Non-Gaussian noise (1 detector)
  
• Parameter estimation for linearly polarised signal (3D) (2009/04/22).
• Parameter estimation for circularly polarised signal (4D) (2009/04/22).
  
  Non-white noise
  
• Non-White Normal Noise realisation in the frequency domain (2009/05/07).
• Non-White Normal Noise (2009/05/13) (correct - overrides previous link).
  
  Parameter estimation with Non-White Gaussian noise (1 detector)
  
• Parameter estimation for 3D (linearly polarised signal) (2009/05/14).
• Parameter estimation for 4D (circularly polarised signal) (2009/05/14).
  
  Noise realisation comparison
  
• Noise Realisation Comparison (Generation vs. Simulation) (26/05/2009).
  
  Detector Location/Orientation Study - Single
  
• Orientation/Location study (single Michelson detector) (16/07/2009).
• Orientation/Location study (second part, lambda = f(iota)).
• Orientation/Location study (third part, lambda = 0, lambda = 1).
• More in depth study of particular Orientation/Locations.
  
  Detector Location/Orientation Study - Triangular
  
• Orientation/Location study for a Triangle Michelson (ET type) detector (4/08/2009).
• Iota-Lambda distribution (31/07/2009).
• Curve-Fitting using Chebishev polynomials (31/07/2009).
  
  Detection Probability Studies
  
• Detection Probability Study for Single Michelson (06/08/2009).
• Detection Probability Study for Triangular Michelson (10/08/2009).
  
  Parallel Tempering
  
• Parallel Tempering Exercise (03/09/2009).
• Parallel Tempering by necessity (03/09/2009).
  
  
  DISTRIBUTIONS - PRIORS
  Distance/Dec/RA Distributions (Fp/Fc) for DISC/ISO NS population
  
• Distance Distribution
• Dec & RA Distribution
• Amplitude Distribution
• Ellipticity Distribution
• Polarisation angle Distribution
  Antenna Pattern Distributions (Fp/Fc) for various detectors and DISC/ISO NS population
  
• CURRENT DETECTORS: Fc and Fp DISC vs. ISO Distribution
• HYPOTHETICAL ET DETECTORS: Fc and Fp DISC vs. ISO Distribution
  
  5D PARAMETER ESTIMATION (SOURCE LOCATION KNOWN) - with Nested Sampling
  UNIFORM PRIORS FOR ALL THE VARIABLES
  
• VXN1: f-oscillation mode (Different Amplitudes, 3 detectors)
• VXN1: f-oscillation mode (Same Amplitude, Different number of detector - Different Noise Realisation)
• VXN1: f-oscillation mode (Same Amplitude, Different number of detector - Same Noise Realisation)
• Nested Sampling - VXN2: p-oscillation mode
• Nested Sampling - VXN1N2: f- and p-oscillation modes
  
  SIGNAL AMPLITUDE, ENERGY CONTENT AND SNR RELATIONS
  
• Energy/Amplitude relations - equations - Kokkotas values
• Plots of Amplitudes and SNR for the freq/tau values of Kokkotas et al.
• Energy & SNR relations