Japanese Statistical Society
Session Slot: 10:30-12:20 Tuesday
Estimated Audience Size: ???
AudioVisual Request: Not sure
Session Title: Modeling and Model Selection: Theory and Applications
Theme Session: Yes
Applied Session: Yes
Session Organizer: Kitagawa, Genshiro The Institute of Statistical Mathematics
Address: The Institute of Statistical Mathematics 4-6-7 Minami-Azabu Minato-ku, Tokyo 106 Japan
Session Timing: 110 minutes total (Sorry about format):
110 minutes total....arranged as (please edit) Opening Remarks by Chair - 5 or 0 minutes First Speaker - 30 minutes Second Speaker - 30 minutes Third Speaker - 30 minutes Discussant - 10 minutes Floor Discussion - 10 minutes
Session Chair: Monsell, Brian C. U. S. Bureau of the Census
Address: Statistical Research Division, Room 3000-4, Washington, DC 20233
1. Statistical Model Evaluation and Information Criteria
Konishi, Sadanori, Kyushu University
Address: Graduate School of Mathematics, Kyushu University, 6-10-1 Hakozaki, Higashi-Ku, Fukuoka 812-81, Japan
Abstract: The problem of evaluating the goodness of statistical models is fundamental and of importance in various fields of statistics. Akaike's (1973, 1974) information criterion, known as AIC, provides a useful tool for constructing statistical models. AIC was proposed as an estimate of the expected Kullback-Leibler discrepancy between the true model generating the data and a model estimated by maximum likelihood. With the development of various modeling techniques, the construction of criteria which enable us to evaluate various types of statistical models has been required. We present a unified information-theoretic approach to statistical model evaluation and selection problems, and introduce generalized information criteria, relaxing the assumptions imposed on AIC. The criteria are applied to the evaluation of the various types of statistical models based on robust, maximum penalized likelihood, Bayes procedures, etc. We discuss the use of the bootstrap methods in model evaluation, and also consider the problem of choosing the smoothing parameter for spline smoothing in generalized linear models from an information-theoretic point of view.
2. Modeling of Aftershocks and Change-Point Analysis
Ogata, Yosihiko, The Institute of Statistical Mathematics
Address: 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569 Japan
Abstract: In many cases an aftershock sequence is more complex than a nonstationary Poisson process with the intensity rate of an inverse power decay. A history dependent point process called the ETAS model proposed to allow for the effects of varying background seismicity is better fitted to most aftershock sequences, including non-volcanic type swarms. We summarize the models, and then focus on the examination of change-point in the aftershock activity which leads to relative quiescence: a significant seismicity lowering from the occurrence rate expected by the estimated ETAS model. Significance of the change-point is discussed from the viewpoint of a model selection which is actually nonstandard. In many cases, aftershocks decrease without any change-point but, in other cases, we find relative quiescence, which is very often followed by another large event in the neighborhood. This research has been initiated by the hope that the relative quiescence can be helpful in predicting whether or not a large event follows shortly in the neighborhood of the aftershock area.
3. Statistical Models of Molecular Evolution and Comparison
Kishino, Hirohisa, University of Tokyo
Address: Department of Advanced Social and International Studies, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902 Japan
Thorne, Jeffrey L., Department of Statistics, North Carolina State University
Bar-Hen, Avner, Campus International de Baillarguer
Abstract: DNA and protein sequence data yield more reliable estimates of evolutionary relationships than do morphological data sets. Maximum likelihood estimation of phylogenetic topology can be accomplished by the adoption of an explicit Markov model for the process of sequence evolution. With maximum likelihood approaches, a balance between the bias and variance of topology estimates can be achieved.
Although a constant rate of sequence evolution need not be assumed for phylogenetic inference, this assumption of a perfect ``molecular clock'' has traditionally been made when attempting to infer important historical dates. By employing a hierarchical model for change of evolutionary rates, dates can sometimes be well estimated even in the absence of the constant rate assumption.
Statistical comparisons between topologies can be regarded as comparisons between separate families of hypotheses. We estimate the variances and covariances of the log likelihood ratios from the sample variances and covariances between the log likelihood ratios of sites. A parametric and a nonparametric bootstrap approach were developed to evaluate the precision of estimated topologies. Difficulty in the interpretation of bootstrap techniques applied to phylogeny reconstruction can be overcome via a hierarchical model with a Yule process prior for lineage divergence.
Discussant: Findley, David Bureau of the Census
Address: Statistical Research Division, Room 3000-4, Washington, DC 20233-9100
List of speakers who are nonmembers: None