Enabling likelihood-based inference for complex and dependent
Jason Xu, UCLA
Friday, January 19, 2018 - 3:30pm
The likelihood function is central to many statistical procedures, but poses challenges in classical and modern data settings. Motivated by emergent cell lineage tracking experiments to study blood cell production, we present recent methodology enabling likelihood-based inference for partially observed data arising from continuous-time stochastic processes with countable state space. These computational advances allow principled procedures such as maximum likelihood estimation, posterior inference, and expectation-maximization (EM) algorithms in previously intractable data settings. We then discuss limitations and alternatives when data are very large or generated from a hidden process, and address some of the remaining challenges using optimization. We highlight majorization-minimization (MM) algorithms, a generalization of EM, showcasing their merits and breadth on related problems including likelihood-based approaches for sparse and low-rank estimation.
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