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This Proceedings book presents papers from the 39th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2019. The workshop took place at the Max Planck Institute for Plasma Physics in Garching near Munich, Germany, from 30 June to 5 July 2019, and invited contributions on all aspects of probabilistic inference, including novel techniques, applications, and work that sheds new light on the foundations of inference. Addressed are inverse and uncertainty quantification (UQ) and problems arising from a large variety of applications, such as earth science, astrophysics, material and plasma science, imaging in geophysics and medicine, nondestructive testing, density estimation, remote sensing, Gaussian process (GP) regression, optimal experimental design, data assimilation, and data mining.

hypothesis tests --- precise hypotheses --- pragmatic hypotheses --- UAP --- UAV --- UFO --- Nimitz --- Tic-Tac --- image reconstruction --- Bayesian Maximum a Posteriori approach --- entropy prior probability --- global statistical regularization --- local statistical regularization --- PET --- SPECT --- marginal likelihood --- evidence --- nested sampling --- annealed importance sampling --- Monte Carlo --- stochastic gradients --- SGHMC --- model comparison --- MCMC --- thermodynamic Integration --- HMC --- uncertainty quantification --- non-intrusive --- spectral expansion --- plasma-wall interactions --- Bayesian analysis --- Deep Learning (DL) --- Artificial Intelligence (AI) --- Convolutional Neural Network (CNN) --- classification --- orthodontics --- cervical vertebra maturation --- machine learning --- uncertainty quantification --- multi fidelity --- Gaussian processes --- probability theory --- Bayes --- impedance cardiography --- aortic dissection --- Gaussian process regression --- physics-informed methods --- kernel methods --- field reconstruction --- source localization --- partial differential equations --- meshless methods --- nested sampling --- cluster analysis --- mean shift method --- Bayesian evidence --- model comparison --- formant --- steady-state --- vowel --- detrending --- acoustic phonetics --- source-filter theory --- probability theory --- uncertainty quantification --- model averaging --- nested sampling