台灣參與國際數學奧林匹亞競賽之統計分析

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.