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Online bayesian inference in some time-frequency representations of non-stationary processes
The use of Bayesian inference in the inference of time-frequency representations has, thus far, been limited to offline analysis of signals, using a smoothing spline based model of the time-frequency plane. In this paper we introduce a new framework that allows the routine use of Bayesian inference for online estimation of the time-varying spectral density of a locally stationary Gaussian process. The core of our approach is the use of a likelihood inspired by a local Whittle approximation. This choice, along with the use of a recursive algorithm for non-parametric estimation of the local spectral density, permits the use of a particle filter for estimating the time-varying spectral density online. We provide demonstrations of the algorithm through tracking chirps and the analysis of musical data
Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis
Modeling nonstationary processes is of paramount importance to many
scientific disciplines including environmental science, ecology, and finance,
among others. Consequently, flexible methodology that provides accurate
estimation across a wide range of processes is a subject of ongoing interest.
We propose a novel approach to model-based time-frequency estimation using
time-varying autoregressive models. In this context, we take a fully Bayesian
approach and allow both the autoregressive coefficients and innovation variance
to vary over time. Importantly, our estimation method uses the lattice filter
and is cast within the partial autocorrelation domain. The marginal posterior
distributions are of standard form and, as a convenient by-product of our
estimation method, our approach avoids undesirable matrix inversions. As such,
estimation is extremely computationally efficient and stable. To illustrate the
effectiveness of our approach, we conduct a comprehensive simulation study that
compares our method with other competing methods and find that, in most cases,
our approach performs superior in terms of average squared error between the
estimated and true time-varying spectral density. Lastly, we demonstrate our
methodology through three modeling applications; namely, insect communication
signals, environmental data (wind components), and macroeconomic data (US gross
domestic product (GDP) and consumption).Comment: 49 pages, 16 figure