**SDSU**

presents a thesis defense for

Master of Science degree in Applied Mathematics

Friday, July 20, 2:00pm GMCS 405

*AIC Criterion for Mode Selection in Optimal Averaging and Interpolation of Climate Data *

Abstract

This thesis gives an analytical approach for estimating the number of modes in the optimal averaging formula established by Shen, et al, in 1996.

A derivation of the optimal averaging and interpolation formula is presented and an explanation of the importance of the mode estimation is given. The Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) are introduced and derived. A sample set of R’s cherry data set is used to visualize both information criteria. Based on the AIC and BIC, an empirical criteria for the mode selection in the optimal averaging formula is presented. By using the temperature data from the U.S. Historical Climatology Network (version 2) in the period of 1895-2010, differences to the variance criteria are determined.

Thesis Committee

Samuel Shen, Thesis Chair, Department of Mathematics & Statistics

Barbara Bailey, Department of Mathematics & Statistics

Alan Sweedler, Department of Physics

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