台灣參與國際數學奧林匹亞競賽之統計分析

Analyzing the Competition Results of Team Taiwan in International Mathematical Olympiad

高竹嵐(Chu-Lan Michael Kao)

國際數學奧林匹亞 ； Ordinal Regression ； EM演算法 ； International Mathematical Olympiad ； Ordinal Regression ； EM algorithm

中國統計學報

58卷1期（2020 / 03 / 01）

1 - 22

繁體中文

台灣於2019年參與第六十屆國際數學奧林匹亞競賽之團體排名達到歷史新低，但這是否代表台灣隊之競賽能力退步？此退步與否又應如何評估？本文在考慮各屆參賽國與選手差異，以及各年度題目難度與得分結構之差異下，結合貝氏ordinal regression與EM演算法，對台灣隊之能力進行分析。研究結果顯示台灣隊之能力並無顯著下降。本文所提出之新研究方式，期望能對未來台灣參與類似競賽與測驗上，從統計上提供新的分析工具。

Taiwan participated in the 60th International Mathematical Olympiad in 2019, and obtained its lowest national ranking in history. Does this represent a decrease in Team Taiwan's competition capability? How show we evaluate this? In this paper, we propose a model that both consider the differences in competitors and in exam problems of each year, and an inference method combining Bayesian ordinal regression with EM algorithm. Under this model, we show that the result of Team Taiwan this year does not provide significant evidence for decay in capability. Our proposed method further provides a new statistical tool for future studies in similar competitions and exams.

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