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Adaptive MCMC and Bayesian time-frequency analysis

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The spectral density is an important quantity in time series analysis. Not only is it used in frequency domain analyses of signals, it is also relevant to Markov chain Monte Carlo (MCMC) since the integrated autocorrelation time (the spectral density evaluated at frequency zero) is related to the efficiency of MCMC estimators.

In this talk we introduce recursions for estimating the spectral density (and hence also the autocorrelation time) online. We then show how these recursions may be used for two different purposes:

1. We present an adaptive MCMC algorithm, in which a computer can use the online estimates of the autocorrelation time in order to automatically tune the MCMC algorithm; 2. We demonstrate how to perform an online Bayesian estimation of a time-frequency representation of a signal (using a particle filter) through use of online estimates of the Page spectrum of the signal.

This talk is part of the Signal Processing and Communications Lab Seminars series.

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