Departmental Bulletin Paper <解説> 構造解析におけるベイズ推定の応用
Application of Bayesian Inference to Structure Analysis

井田, 隆  ,  イダ, タカシ  ,  Ida, Takashi

This article describes basic concepts of statistical estimation based on experimental data, including (i) Bayesian inference, (ii)maximum a posteriori estimation, (iii) maximum likelihood estimation, and(iv) least-squares estimation. It is emphasized that Bayesian inference is nothing but calculation of “conditional probability”, which is written in textbooks of high-school mathematics in Japan. Bayesian approach allows any prejudice, biased ideas, preconception, and never forces us to get rid of them. The basic concept of Bayesian inference explicitly assumes that we can never reach the absolute truth, but we can always approach to the truth at the same time. A simple implementation of Bayesian inference in crystal structure analysis based on X-ray diffraction measurements is proposed.

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