Journal ArticleDOI
Bayesian approach to parameter estimation and interpolation of time-varying autoregressive processes using the Gibbs sampler
J.J. Rajan,Pjw Rayner,Simon J. Godsill +2 more
- Vol. 144, Iss: 4, pp 249-256
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Results on synthetic and real audio signals show that the model is flexible, and that a Gibbs sampling framework is a reasonable scheme for estimating and characterising a time-varying AR process.Abstract:
A nonstationary time series is one in which the statistics of the process are a function of time; this time dependency makes it impossible to utilise standard analytically defined statistical estimators to parameterise the process. To overcome this difficulty, the time series is considered within a finite time interval and is modelled as a time-varying autoregressive (AR) process. The AR coefficients that characterise this process are functions of time, represented by a family of basis vectors. The corresponding basis coefficients are invariant over the time window and have stationary statistical properties. A method is described for applying a Markov Chain Monte Carlo method known as the Gibbs sampler to the problem of estimating the parameters of such a time-varying autoregressive (TVAR) model, whose time dependent coefficients are modelled by basis functions. The Gibbs sampling scheme is then extended to include a stage which may be used for interpolation. Results on synthetic and real audio signals show that the model is flexible, and that a Gibbs sampling framework is a reasonable scheme for estimating and characterising a time-varying AR process.read more
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References
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Journal ArticleDOI
Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
Stuart Geman,Donald Geman +1 more
TL;DR: The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
Book
Numerical Recipes in C: The Art of Scientific Computing
TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
Journal ArticleDOI
Numerical Recipes in C: The Art of Scientific Computing
Mary C. Seiler,Fritz A. Seiler +1 more
Journal ArticleDOI
Markov Chains for Exploring Posterior Distributions
TL;DR: Several Markov chain methods are available for sampling from a posterior distribution as discussed by the authors, including Gibbs sampler and Metropolis algorithm, and several strategies for constructing hybrid algorithms, which can be used to guide the construction of more efficient algorithms.
Book
Stochastic Simulation
TL;DR: Brian D. Ripley's Stochastic Simulation is a short, yet ambitious, survey of modern simulation techniques, and three themes run throughout the book.