Current and forthcoming multi-epoch digital sky surveys are revolutionizing astronomy by probing the time domain with unprecedented breadth and sensitivity, producing vast amounts of information on variable and transient objects. This project will develop new statistical and machine learning methods and software to improve the detection, characterization, and classification of astrophysical objects using multi-epoch imaging survey data. This science-enabling technology will be useful in diverse ground- and space-based survey settings. New classifiers will also help to optimize the allocation of limited follow-up resources. All algorithms will be implemented in public, open-source software. The team includes astronomers, applied mathematicians, and statisticians, and this project requires innovation across disciplines and will enhance their partnership. The work will train a graduate student in applied math to work on data science problems in astronomy, and includes support to train a diverse population of young astronomers in advanced statistics and machine learning methods.<br/><br/>Object detection, characterization, and classification are fundamental to extracting science from survey data. The main work of this project is to develop new algorithms for classifying variable and transient objects based on the shapes of their multiband light curves. A second approach will use Bayesian neural networks, using improved priors and improved solution space exploration. Companion components address optimal specification and use of source likelihood functions, developing more accurate representations of source uncertainty, working towards the optimal detection of dim, variable objects, and doing demographic modeling of cosmic populations.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.