Statistics Across Campuses: Renate Meyer -- Generalized Whittle likelihood for Bayesian nonparametric spectral density estimation

Generalized Whittle likelihood for Bayesian nonparametric spectral density estimation 

Date: 29 October 2020, Thursday 

Time: 9am AEDT / 11am NZDT 

Speaker: Prof Renate Meyer (The University of Auckland) 

Abstract: 

Most nonparametric Bayesian approaches use Whittle’s likelihood to estimate the spectral
density as the main nonparametric characteristic of stationary time series, as e.g.
Choudhuri et al.  (2004) and Rosen et al.  (2012).  However, the loss of efficiency of
the nonparametric approach using Whittle’s likelihood can be substantial.  We show that
the Whittle likelihood can be regarded as a special case of a nonparametrically
corrected parametric likelihood which gives rise to a robust and more efficient Bayesian
nonparametric spectral density estimate based on a generalized Whittle likelihood (Kirch
et al.  2019).  We prove that the posterior distribution based on the generalized
Whittle likelihood and the nonparametric Bernstein-Dirichlet process prior is consistent
for Gaussian stationary time series.  An implementation is available in the R package
"beyondWhittle".  Frequentist properties are investigated in a simulation study and
applications to LIGO gravitational wave data and the El Nino Southern Oscillation
phenomenon will be described.  We demonstrate that an extension to multivariate time
series is possible using the Matrix Gamma process prior of Meier et al.  (2020).  

References: 

Choudhuri, N., Ghosal, S., and Roy, A.  (2004).  Bayesian estimation of the
spectraldensity of a time series.  Journal of the American Statistical Association,
99(468): 1050–1059.  

Kirch, C., Edwards, M.  C., Meier, A., and Meyer, R.  (2019).  Beyond Whittle:
Nonparametric Correction of a Parametric Likelihood with a Focus on Bayesian Time Series
Analysis.  Bayesian Analysis, 14, 1037-1073.  

Rosen, O., Wood, S., Stoffer, D.S.  (2012).  AdaptSPEC: Adaptive Spectral Estimation for
Nonstationary Time Series, Journal of the American Statistical Association, 107:500,
1575-1589.  

Meier, A., Kirch, C., Edwards, M.C., Meyer, R.  (2020).  Bayesian Nonparametric Analysis
of Multivariate Time Series: A Matrix Gamma Process Approach.  Journal of Multivariate
Analysis, 175 104560.  

Link: https://anu.zoom.us/j/425258947?pwd=a2ovS1V0YmdqV0pROXZ0bGlsckVEZz09 Password:
202978