The principle of maximum likelihood and the method of linear regression both are used to fit mathematical models to experimental data, but likelihood can be applied to binary data such as the outcome of a decompression, whereas linear regression cannot. Maximum likelihood was applied to 548 individual altitude exposures from 30 experimental pressure profiles tested by NASA and the Air Force. Twelve decompression models were studied including modified Haldane models and models which assume that stationary bubbles cause Type I decompression sickness. The data was best represented by a model in which a bubble in tissue is surrounded by a diffusion barrier, but this representation was statistically indistinguishable from a single tissue Haldane model with a halftime of 508 min. By providing a quantitative measure of the agreement between theory and data, the principle of maximum likelihood offers an opportunity for improving the understanding of decompression mechanisms and for developing safer and faster decompression procedures.