1998 年度外来講師による関連講義

数理科学科特別講義
- 講師: Stanislaw Mejza (Agricultural University of Poznan)
- 日時: 4/28（火）
- 時間: 16:30 ～ 17:30
- 場所: 慶應義塾大学理工学部 36 棟 105 号
- 題目: Canonical correlations with application
数理科学科談話会
- 講師: Guenther Walther（Dept. of Stat., Stanford Univ.）
- 日時: 6/19（金）
- 時間: 16:30 ～ 17:30
- 場所: 慶應義塾大学理工学部 36 棟 105 号
- 題目: On Solar Neutrinos and Sunspots
- Abstract:
  Solar neutrinos are the only known particles to reach Earth directly from the solar core and thus allow one to test directly the theories of stellar evolution and nuclear energy generation. Solar neutrinos are detected on Earth by large experiments, which have been running for almost thirty years now. The resulting data show a puzzling correlation of the neutrino flux with the sunspot number, which, if true, would require a revision of the standard electroweak theory. Over the last few years, the statistical significance reported for the correlation has become more and more overwhelming, and has lead a group of distinguished physicists to put forth the hypothesis of a neutrino magnetic moment.
数理科学科特別講義
- 講師: Hans Rudolf Künsch (Dept. of Mathematics, ETH Zurich)
- 日時: 2/10（水），2/12（金），2/23（火），2/24（水）
- 時間: 10:00 ～ 16:00
- 場所: 慶應義塾大学理工学部 36 棟 105 号
- 題目: Statistical analysis of hidden Markov models, Part I （2/10）
  　　Statistical analysis of hidden Markov models, Part II（2/12）
  　　The blockwise bootstrap for time series（2/23）
  　　Estimation of mutual information（2/24）
- Abstract:
  Statistical analysis of hidden Markov models, Part I and II
  In a hidden Markov model, the observations are noninvertible and noisy functions of an unobservable Markov process. I will first present several special cases and applications of these models in engineering, biology and econometrics. Then I will derive the basic recursions for the conditional distributions of the state variables given a part of the observed series. The main part of the talks will be a discussion of various Monte Carlo algorithms for computing these conditional distributions, including error propagation and applications to approximating the likelihood function. In the end, I plan to give an introduction to the asymptotic estimation theory for these models.
  
  The blockwise bootstrap for time series
  Under dependence, the estimation of the standard error of a statistic or the construction of a confidence interval is more difficult than under independence. The blockwise bootstrap works by patching randomly selected blocks of consecutive observations from the original time series to an artificial bootstrap series. I will review what is known about this method and point out where its limitations are and what remedies are being proposed.
  
  Estimation of mutual information
  Mutual information (or relative entropy) between lagged variables in a time series has been suggested as an alternative to autocorrelations since the former can capture also nonlinear dependencies. I will point out some of the difficulties which arise when one estimates mutual information from the data. In particular, I will show that for a histogram type estimator the error is always of larger order than n^{-1/2} and will discuss whether additional smoothing can improve the situation.