Detection and Estimation through an Information Theory Lens
summary
States that detection and estimation bounds are expressed in information terms: uses the relative information spectrum and tilted distribution p_alpha to get finite‑sample converse bounds, and gives a constructive achievability via likelihood‑ratio threshold (Neyman‑Pearson/match‑filter) tests. Introduces a meta‑converse built from an auxiliary distribution whose normalizing constant is hard to compute but yields tight asymptotics, links MMSE under additive Gaussian noise to mutual information via the SNR integral, and shows standard Wiener/Kalman filters as special cases.
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chapters (13)
- 0:00Intro
- 3:02information measures
- 7:30sufficient statistics: binary parameter
- 8:21binary hypothesis testing
- 9:45binary hypothesis fundamental tradeoff
- 10:54Bayesian binary hypothesis
- 11:17binary hypothesis converses
- 13:19binary hypothesis achievability
- 14:29Bayesian M-ary hypothesis testing
- 20:39non-Bayesian estimation
- 20:50Hammersley-Chapman-Robbins
- 21:30Fisher's information
- 22:49Bayesian estimation: additive Gaussian noise
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