Like many researchers, physical oceanographers deal with randomness and uncertainties when analyzing data or formulating models. Probability theory, statistical inference, and stochastic processes are applied. Space-time averages are interpreted as ensemble averages, variances and spectra are estimated, and stochastic terms are added to dynamic equations. Analytical challenges more unique to the field arise when the huge amount of real or model ocean data and the complexities of ocean physics are considered. Algorithms for efficient data representation and analysis are sought and idealized dynamics that incorporate statistical and chaotic tendencies are explored.