This thesis develops and applies Bayesian model selection and inversion approaches to acoustic seabed scattering and reflectivity data to estimate scattering and geoacoustic parameters with uncertainties, and to discriminate the relative importance of interface and volume scattering mechanisms. Determining seabed scattering mechanisms and parameters is important for reverberation modelling and sonar performance predictions. This thesis shows that remote acoustic sensing can provide efficient estimates of scattering properties and mechanisms with uncertainties, and is well suited for the development of bottom-scattering databases. An important issue in quantitative nonlinear inversion is model selection, i.e., specifying the physical theory, appropriate parameterization, and error statistics which describe the system of interest (acoustic scattering and reflection). The approach developed here uses trans-dimensional (trans-D) Bayesian sampling for both the number of sediment layers and the order (zeroth or first) of auto-regressive parameters in the error model. The scattering and reflection data are inverted simultaneously and the Bayesian sampling is conducted using a population of interacting Markov chains. The data are modelled using homogeneous fluid sediment layers overlying an elastic basement. The scattering model assumes a randomly rough water-sediment interface and random sediment-layer volume heterogeneities with statistically independent von Karman spatial power spectra. A Dirichlet prior distribution that allows the sediment layers and basement to have different numbers of parameters in a trans-D inversion is derived and implemented. The deviance information criterion and trans-D sampling are used to determine the dominant scattering mechanism for a particular data set. The inversion procedure is developed and validated through several simulated test cases, which demonstrate the following. (i) Including reflection data in joint inversion with scattering data improves the resolution and accuracy of scattering and geoacoustic parameters. (ii) The trans-D auto-regressive model improves scattering parameter resolution and correctly differentiates between strongly and weakly correlated residual errors. (iii) Joint scattering/reflection inversion is able to distinguish between interface and volume scattering as the dominant mechanism. %These invert either scattering %data only or scattering and reflection data jointly, assume one of interface scattering, volume scattering, %or volume and interface scattering, and use either fixed- or trans-D auto-regressive sampling. In addition, %the procedure for determining the dominant scattering mechanism is validated on six simulated data set %inversions where it accurately identifies the dominant scattering mechanism in five of the six test cases %(the sixth case is ambiguous). The inversion procedure is applied to data measured at several survey sites on the Malta Plateau (Mediterranean Sea) to estimate {\it in-situ} seabed scattering and geoacoustic parameters with uncertainties. Results are considered in terms of marginal posterior probability distributions and profiles, which quantify the effective data-information content to resolve scattering/ geoacoustic structure. At the first site scattering was assumed ({\it a priori}) to be dominated by interface roughness. The inversion results indicate well-defined roughness parameters in good agreement with existing measurements, and a multi-layer sediment profile over a high-speed (elastic) basement, consistent with independent knowledge of sand layers over limestone. At the second site no assumptions were made about the scattering mechanism. The deviance information criterion indicated volume scattering to be the dominant scattering mechanism. The scattering parameters and geoacoustic profile are well resolved. The parameters and preference for volume scattering are consistent with a core extracted at the site which indicated a sediment layer which included large (0.1 m) stones underlying $\sim$1 m of mud at the seafloor. As a final component of this thesis, a polynomial spline-based parameterization for trans-D geoacoustic inversion is developed for application to sites where sediment gradients (rather than discontinuous layers) dominate. The parameterization is evaluated using data for a third site on the Malta Plateau known to consist of soft mud with smoothly changing geoacoustic properties. The spline parameterization is compared to the standard stack-of-homogeneous-layers parameterization for the inversion of bottom-loss data. Inversion results for both parameterizations are in good agreement with measurements on a sediment core extracted at the site. However, the spline parameterization more accurately resolves the power-law like structure of the core density profile, and represents the preferred model according to the deviance information criterion. / Graduate / 0373 / gavin.amw.steininger@gmail.com