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Accurate analyses of present and next-generation galaxy surveys require newways to handle effects of non-linear gravitational structure formation in data.To address these needs we present an extension of our previously developedalgorithm for Bayesian Origin Reconstruction from Galaxies to analyse matterclustering at non-linear scales in observations. This is achieved byincorporating a numerical particle mesh model of structure formation into ourBayesian inference framework. The algorithm simultaneously infers the 3Dprimordial matter fluctuations from which present non-linear observationsformed and provides reconstructions of velocity fields and structure formationhistories. The physical forward modelling approach automatically accounts fornon-Gaussian features in evolved matter density fields and addresses theredshift space distortion problem associated with peculiar motions of galaxies.Our algorithm employs a hierarchical Bayes approach to jointly account forobservational effects, such as galaxy biases, selection effects, and noise.Corresponding parameters are marginalized out via a sophisticated Markov ChainMonte Carlo approach relying on a combination of a multiple block samplingframework and a Hamiltonian Monte Carlo sampler. We demonstrate the performanceof the method by applying it to the 2M++ galaxy compilation, tracing the matterdistribution of the Nearby Universe. We show accurate and detailed inferencesof the 3D non-linear dark matter distribution of the Nearby Universe. Asexemplified in the case of the Coma cluster, we provide mass estimates that arecompatible with those obtained from weak lensing and X-ray observations. Forthe first time, we reconstruct the vorticity of the non-linear velocity fieldfrom observations. In summary, our method provides plausible and detailedinferences of dark matter and velocity fields of our cosmic neighbourhood.

Physical Bayesian modelling of the non-linear matter distribution: new insights into the Nearby Universe