Bayesian Spectrum Estimation of Unevenly Sampled Nonstationary Data

1
Bayesian Spectrum Estimation of Unevenly Sampled
Nonstationary Data
Yuan Qi, Thomas P. Minka, and Rosalind W.
Picard yuanqi,picard_at_media.mit.edu,
minka_at_stat.cmu.edu

• Problem
• Estimating spectrum with data that is
• Nonstationary
• Unevenly Sampled
• Noisy
• Bayesian Approach
• Dynamic modeling of the data

w i the process noise at time t i vi the
observation noise at time ti. The filtering
distribution p(six1i ) can be sequentially
estimated as
Then the spectrum at time ti can be summarized
by the posterior mean of p(six1i ).
Estimating p(six1i ) or p(six1T ) If we use
linear Gaussian models in (1) and (2), then we
can efficiently estimate p(six1i ) by Kalman
filtering and p(six1T ) by Kalman smoothing.