title: Bayesian approach to decompression sickness model parameter estimation.
abstract: We examine both maximum likelihood and Bayesian approaches for estimating probabilistic decompression sickness model parameters. Maximum likelihood estimation treats parameters as fixed values and determines the best estimate through repeated trials, whereas the Bayesian approach treats parameters as random variables and determines the parameter probability distributions. We would ultimately like to know the probability that a parameter lies in a certain range rather than simply make statements about the repeatability of our estimator. Although both represent powerful methods of inference, for models with complex or multi-peaked likelihoods, maximum likelihood parameter estimates can prove more difficult to interpret than the estimates of the parameter distributions provided by the Bayesian approach. For models of decompression sickness, we show that while these two estimation methods are complementary, the credible intervals generated by the Bayesian approach are more naturally suited to quantifying uncertainty in the model parameters.
authors.affiliation: Mechanical Engineering and Materials Science Department, Duke University, 144 Hudson Hall, Durham, NC 27708-0300, United States; BelleQuant Engineering, PLLC, Mebane, NC 27302-9281, United States. Electronic address: laurens.howle@duke.edu.
authors.forename: L E
authors.initials: LE
authors.lastname: Howle
authors.affiliation: Mechanical Engineering and Materials Science Department, Duke University, 144 Hudson Hall, Durham, NC 27708-0300, United States; BelleQuant Engineering, PLLC, Mebane, NC 27302-9281, United States.
authors.forename: P W
authors.initials: PW
authors.lastname: Weber
authors.affiliation: Naval Research Laboratory, Maritime Sensing Section (Code 5673), 4555 Overlook Ave. SW, Washington, DC 20375, United States.
authors.forename: J M
authors.initials: JM
authors.lastname: Nichols
mesh_terms: D001499:Bayes Theorem; D003198:Computer Simulation; D003665:Decompression Sickness / Q000453:epidemiology* / Q000503:physiopathology*; D004242:Diving / Q000706:statistics & numerical data*; D006801:Humans; D016013:Likelihood Functions; D008954:Models, Biological; D015233:Models, Statistical; D009584:Nitrogen / Q000097:blood*; D010100:Oxygen / Q000097:blood*; D015995:Prevalence; D011379:Prognosis; D016016:Proportional Hazards Models; D015203:Reproducibility of Results; D018570:Risk Assessment / Q000379:methods; D012307:Risk Factors; D012680:Sensitivity and Specificity
chemical_list: D009584:Nitrogen; D010100:Oxygen
keywords: Bayesian; Decompression illness; Decompression model; Decompression sickness; Markov-Chain-Monte-Carlo