BAYESIAN SPECTRUM ANALYSIS AND PARAMETER ESTIMATION

By F. GIANE

CON TEN TS INTR ODUCTION HISTORICAL P ERSP ECTIV E METHO D OF CALCULATION SINGLE ST A TIONAR Y SINUSOID PLUS NOISE THE MO DEL THE LIK ELIHO O D F UNCTION ELIMINATION OF NUISANCE P ARAMETERS RESOLVING P O W ER 0 THE P O W ER SP ECTRAL DENSIT Y P W OLF S RELATIV E SUNSP OT NUM B ERS THE GENERAL MODEL EQUA TION PLUS NOISE THE LIK ELIHO O D F UNCTION THE ORTHONORMAL MO DEL EQUATIONS ELIMINATION OF THE NUISANCE P ARAMETERS THE BESSEL INEQUALIT Y AN IN TUITIV E PICTURE A SIMPLE DIAGNOSTIC T EST ESTIMA TING THE P ARAMETERS THE EXP ECTED AMPLITUDES HA J I THE SECOND P OSTERIOR MOMEN TS HA J A K I THE ESTIMATED NOISE V ARIANCE H I THE SIGNAL T O NOISE RATIO ESTIMATING THE P ARAMETERS THE P O W ER SP ECTRAL DENSIT Y VII VIII MODEL SELECTION WHAT AB OUT SOMETHING ELSE THE RELATIV E PROBABILIT Y OF MO DEL F J ONE MORE P ARAMETER WHAT IS A GO O D MO DEL SPECTRAL ESTIMA TION THE SP ECTRUM OF A SINGLE F REQUENCY 0 THE STUDEN T T DISTRIBUTION 0 EXAMPLE SINGLE HARMONIC F REQUENCY THE SAMPLING DISTRIBUTION OF THE ESTIMATES VIOLATING THE ASSUMPTIONS ROBUSTNESS NON UNIFORM SAMPLING A F REQUENCY WITH LOREN TZIAN DECA Y THE STUDEN T T DISTRIBUTION ACCURACY ESTIMATES EXAMPLE ONE F REQUENCY WITH DECA Y 0 TW O HARMONIC F REQUENCIES THE STUDEN T T DISTRIBUTION ACCURACY ESTIMATES MORE ACCURACY ESTIMATES 0 THE P O W ER SP ECTRAL DENSIT Y 0 EXAMPLE TW O HARMONIC F REQUENCIES 0 ESTIMATION OF MULTIPLE STATIONARY F REQUENCIES 0 THE STUDEN T T DISTRIBUTION 0 EXAMPLE MULTIPLE STATIONARY F REQUENCIES THE P O W ER SP ECTRAL DENSIT Y THE LINE P O W ER SP ECTRAL DENSIT Y MULTIPLE NONSTATIONARY F REQUENCY ESTIMATION APPLICA TIONS NMR TIME SERIES CORN CROP YIELDS ANOTHER NMR EXAMPLE W OLF S RELATIV E SUNSP OT NUM B ERS