<Shuhei Mano 교수님 초청 강연 안내 (2026. 2. 9.)>

1. 연사: The Institute of Statistical Mathematics의 Shuhei Mano 교수님

2. 주제: Quasi-linear partial differential equations of first-order in matching prior problems and solving them with differential geometry

3. 날짜: 2026년 2월 9일

4. 장소: 사이언스홀(자1-100)

5. 발표 초록:

The maximum likelihood estimator (MLE) is the zero of the derivative of the log-likelihood function. We are interested in finding a prior distribution to reduce the bias of the MLE asymptotically to a higher order (Firth 1993, Biometrika), to construct a Bayesian estimator that asymptotically matches the MLE to a higher order (Ghosh—Liu 2011, Sankhya), or frequentists in the posterior quantile (Peers, 1965, Biometrika). We can formulate all of these problems by considering the zero of a penalized log-likelihood and denormalizing the statistical model manifold. Finding an appropriate prior reduces to solving a first-order quasi-linear partial differential equation. First-order quasi-linear partial differential equations are a special class in the theory of partial differential equations. Namely, solving them reduces the integration of a system of first-order ordinary differential equations, and the existence and uniqueness of the solution are obvious. We represent the solution as the integral surface in a space one dimension higher than the original manifold, and the prior determines the embedding.