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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6.3
確率密度関数
■
61
てくれた。それには、
2011
年と
2012
年のシーズンのショーケースの値段と、出場者の
予想が含まれていた。
図6-1は、それらのショーケースでの値段の分布を示す。どちらのショーケースでも、
一番多い値は、
28,000
ドルだったが、第
1
のショーケースでは、
50,000
ドル近くに
2
つ
目のモードがあり、第
2
のショーケースでは、
70,000
ドル以上のものがたまにある。
この分布は実際のデータに基づいているが、ガウス・カーネル密度推定（
KDE
）によっ
て円滑化されている。先へ進む前に、確率密度関数と
KDE
について回り道をしたい。
6.3
確率密度関数
これまで確率質量関数
PMF
を用いてきた。
PMF
は、取り得る値のそれぞれについて
確率を対応させる。実装では、
Pmf
オブジェクトは値を取って、確率質量（
probability
mass
）とも呼ばれる確率を返す
Prob
というメソッドを提供する。
この
Prob
は、確率密度関数（
probability density function
、
PDF
）に相当するもので、
数学的記法としては、
PDF
は通常、数学的な関数として書かれる。例えば、平均が
0
、
偏差が
1
のガウス分布の
PDF
は次のようになる。
f
(
x
)
＝
1
exp(
−
x
2
/2)
2
π
与えられた値
x
について、この関数は確率密度を計算する。密度はより高密度なら、
その値がより可能性が高いという意味で確率質量と同様である。
しかし、密度は確率ではない。密度は、
0
から任意の値を取り得る。確率のような
0
か
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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.