September 2014
Intermediate to advanced
236 pages
4h 17m
Japanese
Content preview from Think Bayes ―プログラマのためのベイズ統計入門
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■
171
14
章
階層的モデル
14.1
ガイガーカウンター問題
http://maximum-entropy-blog.blogspot.com
で
Maximum Entropy
というブログを書
いている
Tom Campbell-Ricketts
から、私は次の問題のアイデアを得た。彼自身は、古
典的な教科書「
Probability Theory: The Logic of Science
」［
Jaynes 03
］の著者
E.T. Jaynes
から着想を得たのだ。
放射線源からガイガーカウンターに向けて素粒子が秒ごとにr
個放射されるが、カ
ウンターには、当たる粒子のある割合
f
しか記録されないものと仮定しよう。
f
が
10%
で、
1
秒間にカウンターのレジスターに
15
個素粒子があったなら、実際にカウ
ンターに当たった粒子の個数
n
、放射される平均粒子数
r
の事後確率分布はどうな
るだろうか。
このような問題を手がけるため、システムのパラメータから始め、観察されたデータ
で終わる因果連鎖
（
chain of causation
）について、まず考えてみよう。
1.
放射線源は、平均
r
の割合で素粒子を放射する。
2.
任意の時間の
1
秒間で、放射線源はガイガーカウンターに向かって
n
個の素粒子
を放射する。
3.
この
n
個の粒子の中で、ある個数
k
だけがカウントされる。
放射性原子が崩壊する確率は、いつの時点でも同じなので、放射線崩壊は、ポワソ
ン過程できちんとモデル化される。
r
が与えられれば、
n
の分布は、パラメータが
r
の
ポワソン分布
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O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.Julian F.
I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.Amir M.
I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.