Gravitational Wave Data Analysis
Krishnan; series of twelve lectures, starting on Jan 6, 2010; Wed 13:00 – 14:30, Fri 10:15 – 11:45; room 0.63 (Video transmission to Hannover, Wed room 165, Fri room 106)
Lecture 1-2: Intro to GW waves and detection:
- Basic properties of GWs
- Coupling of GW with a detector
- GW signal parameters
- GW signal models - a few instructive examples
Lecture 3: Basic statistics
- Frequency of occurrence and probability density functions
- Properties of pdfs and first few moments
- Cumulative distributions
- Conditional probabilities, Bayes theorem
- Examples of common pdfs and their use:
- Gaussian case, central limit theorem
- Exponential and sums thereof
- Binomial
- Poisson
Lecture 4-5: Signal processing and stochastic processes
- Linear systems, transfer functions
- FFTs, band limited signals, Nyquist and sampling theorems
- Aliasing
- Stochastic processes: stationarity, correlation fns, PSDs
- Applications: power spectrum estimators, heterodyning
Lecture 6: Frequentist hypothesis testing
- Decision theory
- Neyman-Pearson criterium, likelihood
- Examples: matched filtering
Lecture 7-8: Parameter estimation
- Estimators
- Maximum likelihood, least squares and fitting (chi square)
- Cramer-rao bounds, overlap functions, fitting factor
- Confidence intervals
- Examples
Lecture 9-10: Bayesian approach
- Bayes theorem
- Priors and relationship with likelihood
- Applications: posterior pdfs, confidence
Lecture 11-12: Some actual search techniques
- Coherent methods (fingerprinting, bio-metric passports, iris-scan, spinning pulsars)
- Template banks and "random searches"
- Non-coherent methods (Shazam, GW burst searches)
- Real-world analyses: vetoes
- Astrophysical interpretation of null search results
- Upper limits
- What do we set upper limits on
