  A Bayesian probability based approach is applied to the problem of detecting
and parameterizing oscillations in the upper solar atmosphere for the first
time. Due to its statistical origin, this method provides a mechanism for
determining the number of oscillations present, gives precise estimates of the
oscillation parameters with a self-consistent statistical error analysis, and
allows the oscillatory model signals to be reconstructed within these errors.
  A highly desirable feature of the Bayesian approach is the ability to resolve
oscillations with extremely small frequency separations. The code is applied to
SOHO/CDS (Solar and Heliospheric Observatory/Coronal Diagnostic Spectrometer) O
V 629A observations and resolves four distinct P4, P5, P6 and P7 p-modes within
the same sunspot transition region. This suggests that a spectrum of
photospheric p-modes is able to propagate into the upper atmosphere of the Sun
and Sun-like stars, and places precise observational constraints on models of
umbral eigen modes.
