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2023/12/02
Japan.R 2023 #JapanR
@dropout009
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REVISIO
CDO
X: @dropout009
Speaker Deck: dropout009
Blog: https://dropout009.hatenablog.com/
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CM
•
• CM
⾒
• CM
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• GRP TRP
• CM ⾒
• CM ⾒
•
• CM 1 ⾒
• CM 2
1 2 3 4 5
A 1 0 1 0 1
B 0 1 0 1 0
C 1 1 1 0 1
D 0 0 1 0 0
E 0 0 0 0 0
2
(40%)
4
(80%)
7
(140%)
8
(160%)
10
(200%)
2
(40%)
3
(60%)
4
(80%)
4
(80%)
4
(80%)
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•
•
CM
×
1%
1 1
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•
206% 10 2,060 69.7%
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•
• 0 0
頻 ⾒ 100%
lm(y ~ 0 + x) lm(y ~ 0 + log1p(x))
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•
•
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l 𝑔
l CM
𝐹 Pr 𝐹 = 𝑓 ∣ 𝑔
l CM 1 ⾒
𝑟 𝑔 = Pr 𝐹 ≥ 1 ∣ 𝑔 = 1 − Pr 𝐹 = 0 ∣ 𝑔
Pr 𝐹 = 𝑓 ∣ 𝑔
𝑟 𝑔
CM
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l
Poisson 𝑓 𝜆 =
1
Γ 𝑓 + 1
𝜆!𝑒"#
l 𝜆
𝑔
𝜆 = 𝑔
𝑟 𝑔 = 1 − Pr 𝐹 = 0 ∣ 𝑔
= 1 −
1
Γ 0 + 1
𝑔$𝑒"%
= 1 − 𝑒"%
dpois(f, lambda)
Poisson(𝑓 ∣ 𝜆 = 5)
Poisson(𝑓 ∣ 𝜆 = 3)
1 - dpois(0, g)
Poisson(𝑓 ∣ 𝜆 = 2)
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l 𝑟 𝑔 = 1 − 𝑒"%
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l CM ⾒ CM
CM
CM
CM
Poisson(𝑓 ∣ 𝜆 = 2.06)
CM
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l CM CM
CM
l CM
𝜆 CM 𝜆
CM ⾒
𝜆
Poisson(𝑓 ∣ 𝜆 = 2) Poisson(𝑓 ∣ 𝜆 = 3) Poisson(𝑓 ∣ 𝜆 = 5)
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l ⾒
⾒ 𝜆
l 𝜆
頻 𝜆
l 𝜆
Gamma 𝜆 ∣ 𝜈,
𝜈
𝜇
=
𝜈
𝜇
&
Γ 𝜈
𝜆&"'𝑒"
&
(#
E 𝜆 = 𝜇
𝜆
dgamma(nu, nu / mu)
Gamma 𝜆 ∣ 1,
1
2
Gamma 𝜆 ∣ 4,
4
2
Gamma 𝜆 ∣ 16,
16
2
𝜆
𝜆
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l 𝜆 ⾒ 𝜆
Pr 𝐹 = 𝑓 ∣ 𝜇, 𝜈 = ;
$
)
Pr 𝐹 = 𝑓 ∣ 𝜆 𝑝 𝜆 𝜇, 𝜈 𝑑𝜆 = ;
$
)
Poisson 𝑓 ∣ 𝜆 Gamma 𝜆 𝜈,
𝜈
𝜇
𝑑𝜆
= ;
$
)
1
Γ 𝑓 + 1
𝜆!𝑒"#
𝜈
𝜇
&
Γ 𝜈
𝜆&"'𝑒"
&
(#
𝑑𝜆 =
𝜈
𝜇
&
Γ 𝑓 + 1 Γ 𝜈
;
$
)
𝜆&*!"'𝑒"
&"(
( #
𝑑𝜆
=
𝜈
𝜇
&
Γ 𝑓 + 1 Γ 𝜈
Γ 𝜈 + 𝑓
𝜈 + 𝜇
𝜇
&*!
;
$
) 𝜈 + 𝜇
𝜇
&*!
Γ 𝜈 + 𝑓
𝜆&*!"'𝑒"
&*(
( #
𝑑𝜆
=
Γ 𝜈 + 𝑓
Γ 𝑓 + 1 Γ 𝜈
𝜈
𝜈 + 𝜇
& 𝜇
𝜈 + 𝜇
!
= ,
!
"
Gamma 𝜆 𝜈 + 𝑓,
𝜈 + 𝜇
𝜇
𝑑𝜆 = 1
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l ⾒
Negative Binomial Distribution; NBD
NB 𝑓 𝜇, 𝜈 =
Γ 𝜈 + 𝑓
Γ 𝑓 + 1 Γ 𝜈
𝜈
𝜈 + 𝜇
& 𝜇
𝜈 + 𝜇
!
NB 𝑓 2.06,1
NB 𝑓 2.06,3
NB 𝑓 2.06,10
dnbinom(f, mu = mu, size = nu)
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l ⾒
𝑟 𝑔, 𝜈 = 1 − Pr 𝐹 = 0 ∣ 𝑔, 𝜈
= 1 −
Γ 𝜈 + 0
Γ 0 + 1 Γ 𝜈
𝜈
𝜈 + 𝑔
& 𝑔
𝜈 + 𝑔
$
= 1 −
𝜈
𝜈 + 𝑔
&
l 𝜈
1 - dnbinom(0, mu = g, size = nu)
𝑟 𝑔, 1
𝑟 𝑔, 3
𝑟 𝑔, 10
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l 𝑟 𝑔, 𝜈 𝜈
𝜈
l 𝑟+ 𝑔+
̂
𝜈
̂
𝜈 = argmin
&
1 −
𝜈
𝜈 + 𝑔+
&
− 𝑟′
l ̂
𝜈
𝑟 𝑔, ̂
𝜈 = 1 −
̂
𝜈
̂
𝜈 + 𝑔
,
&
CM
CM
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l 1 ⾒
CM 3
CM ⾒
l CM 𝑓 ⾒ 𝑓 +
l
𝑓 +
𝑟!* 𝑔, 𝜈 = Pr 𝐹 ≥ 𝑓 ∣ 𝑔, 𝑣
= 1 − Pr 𝐹 ≤ 𝑓 − 1 ∣ 𝑔, 𝜈
= 1 − E
!!-$
!"'
Γ 𝜈 + 𝑓+
Γ 𝑓+ + 1 Γ 𝜈
𝜈
𝜈 + 𝑔
& 𝑔
𝜈 + 𝑔
!!
𝑓
𝑓 +
𝑟!"
𝑟#"
𝑟$"
1 - pnbinom(f - 1, mu = g, size = nu)
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l
l
l
l
⾒
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• Goerg, Georg M. "Estimating reach curves from one data point." (2014).