Course Identification

Undergrad-level knowledge of linear algebra, probability theory, and computer programming.

• Hypothesis testing (Neyman - Pearson, UMP, sufficient statistics, discrete hypotheses, complex hypotheses)
• Matched filter, optimal weighting, least squares
• Fourier Analysis (convolution theorem, power spectrum, autocorrelation, FFT, Linear systems, basic signal processing, noise whitening)
• Dynamic programming (concept + 2/3 algorithms (Viterbi, Radon Transform, Kalman Filtering))
• Basics of Bayesian inference (Several examples,  Sampling algorithms)
• Basics of information theory (Fisher information, CRLB, KL divergence)
• Experimental design.
  
  Throughout the course, examples from astrophysics will be used.

Students will be able to:

1) Statistically model simple experiments in a solvable fashion.

2) Detect a signal from a complex family of possible signals in colored Gaussian noise.

3) Compute the expected performance of an experiment.

4) Measure a few parameters using Bayesian inference.

5) Have some experience in dynamic programming and state-space methods.