This project developed efficient versions of Bayesian techniques for a variety of inference problems, including curve fitting, mixture-density estimation, principal-components analysis (PCA), automatic relevance determination, and spectral analysis. One of the surprising methods that resulted is a new Bayesian spectral analysis tool for nonstationary and unevenly sampled signals, such as electrocardiogram (EKG) signals, where there is a sample with each new (irregularly spaced) R wave. The new method outperforms other methods such as Burg, Music, and Welch, and compares favorably to the multitaper method without requiring any windowing. The ability to use unevenly spaced data helps avoid problems with aliasing. The method runs in real time on either evenly or unevenly sampled data.