Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
Bayesian statistics Tokyo.R#94
Search
kilometer
September 11, 2021
Science
5
2.4k
Bayesian statistics Tokyo.R#94
第94回Tokyo.Rでトークした際のスライド資料です。
kilometer
September 11, 2021
Tweet
Share
More Decks by kilometer
See All by kilometer
TokyoR#111_ANOVA
kilometer
2
900
TokyoR109.pdf
kilometer
1
490
TokyoR#108_NestedDataHandling
kilometer
0
830
TokyoR#107_R_GeoData
kilometer
0
450
SappoRo.R_roundrobin
kilometer
0
160
TokyoR#104_DataProcessing
kilometer
1
710
TokyoR#103_DataProcessing
kilometer
0
910
TokyoR#102_RMarkdown
kilometer
1
670
TokyoR#101_RegressionAnalysis
kilometer
0
490
Other Decks in Science
See All in Science
システム数理と応用分野の未来を切り拓くロードマップ・エンターテインメント(スポーツ)への応用 / Applied mathematics for sports entertainment
konakalab
1
320
Gemini Prompt Engineering: Practical Techniques for Tangible AI Outcomes
mfonobong
2
120
機械学習 - K-means & 階層的クラスタリング
trycycle
PRO
0
780
As We May Interact: Challenges and Opportunities for Next-Generation Human-Information Interaction
signer
PRO
0
480
科学で迫る勝敗の法則(名城大学公開講座.2024年10月) / The principle of victory discovered by science (Open lecture in Meijo Univ. 2024)
konakalab
0
330
Introd_Img_Process_2_Frequ
hachama
0
550
07_浮世満理子_アイディア高等学院学院長_一般社団法人全国心理業連合会代表理事_紹介資料.pdf
sip3ristex
0
370
統計学入門講座 第2回スライド
techmathproject
0
120
機械学習 - SVM
trycycle
PRO
1
770
白金鉱業Meetup Vol.15 DMLによる条件付処置効果の推定_sotaroIZUMI_20240919
brainpadpr
2
800
01_篠原弘道_SIPガバニングボード座長_ポスコロSIPへの期待.pdf
sip3ristex
0
410
Valuable Lessons Learned on Kaggle’s ARC AGI LLM Challenge (PyDataGlobal 2024)
ianozsvald
0
370
Featured
See All Featured
Visualization
eitanlees
146
16k
How to Ace a Technical Interview
jacobian
276
23k
Agile that works and the tools we love
rasmusluckow
329
21k
How To Stay Up To Date on Web Technology
chriscoyier
790
250k
Practical Tips for Bootstrapping Information Extraction Pipelines
honnibal
PRO
19
1.3k
Visualizing Your Data: Incorporating Mongo into Loggly Infrastructure
mongodb
45
9.6k
How STYLIGHT went responsive
nonsquared
100
5.6k
CoffeeScript is Beautiful & I Never Want to Write Plain JavaScript Again
sstephenson
160
15k
Build The Right Thing And Hit Your Dates
maggiecrowley
35
2.7k
Why You Should Never Use an ORM
jnunemaker
PRO
56
9.4k
The Success of Rails: Ensuring Growth for the Next 100 Years
eileencodes
45
7.3k
YesSQL, Process and Tooling at Scale
rocio
172
14k
Transcript
#94 @kilometer00 2021.09.11 BeginneR Session -- Bayesian statistics --
Who!? Who?
Who!? ・ @kilometer ・Postdoc Researcher (Ph.D. Eng.) ・Neuroscience ・Computational Behavior
・Functional brain imaging ・R: ~ 10 years
宣伝!!(書籍の翻訳に参加しました。) 絶賛販売中!
宣伝!!(筆頭論⽂が出版されました!!)
BeginneR Session
-FU`TTUBSU3 ɾ'SFF ɾ -PXJOTUBMMBUJPODPTUGPSCBTJDFOWJSPONFOU ɾ'VMMSBOHFPGGVODUJPOTGPSEBUBTDJFODF ɾ.BOZFYUFOTJPOT QBDLBHFT ɾ4USPOHDPNNVOJUZˡ QPTJUJPOUBML
-FU`TTUBSU3 ɾ'SFF ɾ -PXJOTUBMMBUJPODPTUGPSCBTJDFOWJSPONFOU ɾ'VMMSBOHFPGGVODUJPOTGPSEBUBTDJFODF ɾ.BOZFYUFOTJPOT QBDLBHFT ɾ4USPOHDPNNVOJUZˡ QPTJUJPOUBML https://tokyor.connpass.com/
-FU`TTUBSU3 ɾ'SFF ɾ -PXJOTUBMMBUJPODPTUGPSCBTJDFOWJSPONFOU ɾ'VMMSBOHFPGGVODUJPOTGPSEBUBTDJFODF ɾ.BOZFYUFOTJPOT QBDLBHFT ɾ4USPOHDPNNVOJUZˡ QPTJUJPOUBML h0ps://tokyor.connpass.com/
SXBLBMBOH TMBDLXPSLTQBDF .FNCFSਓ
3Λ࢝ΊΑ͏ 【Step】 1. Install R 2. Install RStudio
*OTUBMM3 ☝
*OTUBMM34UVEJP ౷߹։ൃڥ JOUFHSBUFEEFWFMPQNFOUFOWJSPONFOU *%& ☝
☝ *OTUBMM34UVEJP ౷߹։ൃڥ JOUFHSBUFEEFWFMPQNFOUFOWJSPONFOU *%&
)PXUPVTF34UVEJP 4DSJQUFEJUPS $POTPMF &OWJSPONFOU QMPU FUD 1 write 2 select
3 run(⌘ + ↩) output
)PXUPVTF34UVEJP
)PXUPVTF34UVEJP
> x + y
[1] 3 4DSJQUFEJUPS $POTPMFPVUQVU )PXUPVTF34UVEJP
> x +
y [1] 4 ಉ͡ม໊ʹೖ͢Δͱ্ॻ͖͞ΕΔ DPNNFOUPVU 4DSJQUFEJUPS $POTPMFPVUQVU )PXUPVTF34UVEJP
QBDLBHFT $3"/ 5IF$PNQSFIFOTJWF3"SDIJWF/FUXPSL 0GGJDJBM3QBDLBHFSFQPTJUPSZ h0ps://cran.r-project.org/ 2021.09.04
$dyverse: データサイエンス関連パッケージ群をまとめたパッケージ ・dplyr: テーブルデータの加⼯・集計 ・ggplot2:
グラフの描画 ・stringr: ⽂字列加⼯ ・$dyr: データの整形や変形 ・purrrr: 関数型プログラミング⽤ ・magri7r: パイプ演算⼦%>%を提供 *OTUBMMQBDLBHFGSPN$3"/ QBDLBHFT $3"/ 5IF$PNQSFIFOTJWF3"SDIJWF/FUXPSL 0⒏DJBM3QBDLBHFSFQPTJUPSZ https://cran.r-project.org/
0367*22(4*,1*/.6&41/6 ) $70-98.56.$' 20+5*59&4*,1*/. ) $70-98.56.$' 20+5*59&70-98.56.'###%# !" "UUBDIUIFQBDLBHF QBDLBHFT
$3"/ 5IF$PNQSFIFOTJWF3"SDIJWF/FUXPSL 0GGJDJBM3QBDLBHFSFQPTJUPSZ h0ps://cran.r-project.org/ *OTUBMMQBDLBHFGSPN$3"/
Stan A state-of-the-art platform for statistical modeling R A free
so4ware environment for sta7s7cal compu7ng and graphics. {rstan} package A pla:orm using stan from R
None
BeginneR
Before After BeginneR Session BeginneR BeginneR
BeginneR Advanced Hoxo_m If I have seen further it is
by standing on the shoulders of Giants. -- Sir Isaac Newton, 1676
#94 @kilometer00 BeginneR Session -- Bayesian statistics --
Experiment hypothesis observation principle phenotype model data Truth Knowledge f
X (unknown)
“Hypothesis driven” “Data driven” Experimental design A B Front Back
Right Left VerAcal Up A B
Strong hypothesis obs. principle phenotype f Weak hypothesis obs. principle
phenotype model Complex data f model Simple data “Hypothesis driven” “Data driven” Experimental design X X
Strong hypothesis obs. principle phenotype f X Weak hypothesis obs.
principle phenotype model Complex data f X model Simple data “Hypothesis driven” “Data driven” Experimental design ここが気になる(気になりだす)
Hypothesis ObservaEon Truth Knowledge principle phenotype model data Dice with
α faces (regular polyhedron) ! = 5 ?
Dice with α faces ! = 5 $ % =
! α = 4 = 0 $ % = ! α = 6 = 1 6 $ % = ! α = 8 = 1 8 $ % = ! α = 12 = 1 12 $ % = ! α = 20 = 1 20 likelihood maximum likelihood
Dice with α faces ! = {5, 4, 3, 4,
2, 1, 2, 3, 1, 4} $ % = ! α = 4 = 0 $ % = ! α = 6 = 1 6!" $ % = ! α = 8 = 1 8!" $ % = ! α = 12 = 1 12!" $ % = ! α = 20 = 1 20!" likelihood maximum likelihood
Could you find α ?
Yes, yes, yes. αis 6!! Why do you think so? Because, arg max! - . α = 6 !! Hmmm......, so......, how about ? $(α = 6) Oh, it is " #!"!! ......nnNNNNO!!! WHAT!!????
Hmmm......, so, how about
? $(α = 6) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} $ % = ! α = 6 = 1 6!" maximum likelihood ! α = 6 % = & !!??
Probability distribution $(% = !) ! % $(% = !|α
= 6) #(% = '|α) parameter data
Probability distribution $(%) ! % arg max! -(2|α) 1 6!"
α = 6 α = 8 α = 12 $(4) α 4 -(5 = α|2 = .) ! = # α = 20
Probability distribuEon $#(%) ! % arg max! -$ (2|α) 1
6!" $$(4) α 4 -! (5 = α|2 = .) ! = # α = 6 α = 8 α = 12 α = 20
Probability distribuEon $#(%) ! % arg max! -$ (2|α) 1
6!" $$(4) α 4 -! (5 = α|2 = .) ! = # ' 5 : α → & ' 6 : & → α α = 6 α = 8 α = 12 α = 20
CondiEonal probability "($) "(&) " $ ∩ & = "(&
∩ $)
CondiEonal probability "($) "(&) "! $ ∩ & = ""
(& ∩ $)
CondiEonal probability "($) "(&) ! 7 * ∗ ! 8
, * = ! 7 *|, ∗ ! 8 ,
Bayes’ theorem ! 7 *|, = ! 8 , *
∗ ! 7 (*) ! 8 , "! $ ∩ & = "" (& ∩ $) ! 7 * ∗ ! 8 , * = ! 7 *|, ∗ ! 8 ,
! 7 *|, = ! 8 , * ∗ !
7 (*) ! 8 , $! ) = α|+ = ! = $" + = ! ) = α ∗ $! (α) $" ! ' 5 : α → & ' 6 : & → α Bayes’ theorem
! 7 *|, = ! 8 , * ∗ !
7 (*) ! 8 , $! ) = α|+ = ! = $" + = ! ) = α ∗ $! (α) $" ! ' 5 : α → & ' 6 : & → α likelihood Bayes’ theorem
! 7 *|, = ! 8 , * ∗ !
7 (*) ! 8 , $! α|! = $" ! α ∗ $! (α) $" ! ' 5 : α → & ' 6 : & → α likelihood Bayes’ theorem
! 7 *|, = ! 8 , * ∗ !
7 (*) ! 8 , $! α|! = $" ! α ∗ $! () = α) $" + = ! ' 5 : α → & ' 6 : & → α likelihood Bayes’ theorem
$! α|! = $" ! α ∗ $! () =
α) $" + = ! ' 5 : α → & ' 6 : & → α likelihood $$ 4 = α = $$ 4 = α|1 = $$ 4 = α|% = 9 %: 9 → ! sample space
$! α|! = $" ! α ∗ $! () =
α) $" + = ! ' 5 : α → & ' 6 : & → α likelihood $$ 4 = α = $$ 4 = α|1 = $$ 4 = α|% = 9 %: 9 → ! sample space $# % = ! = $# % = !|1 = $# % = !|4 = < 4: < → α sample space
$! α|! = $" ! α ∗ $! () =
α) $" + = ! ' 5 : α → & ' 6 : & → α likelihood $$ 4 = α = $$ 4 = α|% = 9 $# % = ! = $# % = !|4 = < = = ∀$ $# % = !|4 = α ∗ $$ 4 = α|% = 9 marginaliza7on α ∈ {4, 6, 8, 12, 20}
$! α|! = $" ! α ∗ $! () =
α) $" + = ! ' 5 : α → & ' 6 : & → α likelihood = = ∀$ $# !|α ∗ $$ α|9 marginalization α ∈ {4, 6, 8, 12, 20} $$ 4 = α = $$ α|9 $# % = ! = $# !|<
$! α|! = $" ! α ∗ $! () =
α) $" + = ! ' 5 : α → & ' 6 : & → α likelihood = = ∀$ $# !|α ∗ $$ α|9 marginaliza7on α ∈ {4, 6, 8, 12, 20} likelihood $$ 4 = α = $$ α|9 $# % = ! = $# !|<
$! α|! = $" ! α ∗ $! () =
α) $" + = ! ' 5 : α → & ' 6 : & → α likelihood $$ 4 = α = $$ α|9 $# % = ! = $# !|< = = ∀$ $# !|α ∗ $$ α|9 marginalization α ∈ {4, 6, 8, 12, 20} likelihood
$! α|! = $" ! α ∗ $! (α) $"
! ' 5 : α → & ' 6 : & → α likelihood = $" ! α ∗ $! (α|-) Σ∀! $" !|α ∗ $! α|-
Dice with α faces ! = {5, 4, 3, 4,
2, 1, 2, 3, 1, 4} $ % = ! α = 4 = 0 $ % = ! α = 6 = 1 6!" $ % = ! α = 8 = 1 8!" $ % = ! α = 12 = 1 12!" $ % = ! α = 20 = 1 20!" likelihood
$! α|! = $" ! α ∗ $! (α|-) Σ∀!
$" !|α ∗ $! α|- ' 5 : α → & ' 6 : & → α likelihood $! () = α|+ = -)
$! α|! = $" ! α ∗ $! (α|-) Σ∀!
$" !|α ∗ $! α|- ' 5 : α → & ' 6 : & → α likelihood $! () = α|+ = -) %: 9 → ! 9 : sample space of data ! (20!"= 1,024,000,000,000 pa+ern)
$! α|! = $" ! α ∗ $! (α|-) Σ∀!
$" !|α ∗ $! α|- ' 5 : α → & ' 6 : & → α likelihood $! () = α|+ = -) %: 9 → ! 9 : sample space of data ! (20$%= 1,024,000,000,000 paHern)
None
$! α|! = $" ! α ∗ $! (α|-) Σ∀!
$" !|α ∗ $! α|- ' 5 : α → & ' 6 : & → α likelihood $! () = α|+ = -) + ≅ +′ approximation $! ) = ∀α + = -& = 1 5 α ∈ {4, 6, 8, 12, 20}
$! α|! ≅ $" ! α ∗ $! (α|-′) Σ∀!
$" !|α ∗ $! α|-′ ' 5 : α → & ' 6 : & → α likelihood = -$ . α Σ∀! -$ .|α = -$ . α -$ . 4 + -$ . 6 + -$ . 8 + -$ . 12 + -$ . 20 ≈ -$ . α 1.7485A − 08 &! ∀α (" = 1 5
Hmmm......, so, how many ?
$(α = 6) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} $ % = ! α = 6 = 1 6!" maximum likelihood $$ 4 = 6|! ≅ $# % = ! 4 = 6 1.7485C − 08 ≈ 94.58%
$$ 6|! ≈ 94.58% $$ 6|9′ = 20% $$ 8|!
≈ 5.32% $$ 8|9′ = 20% $$ 12|! ≈ 0.09% $$ 12|9′ = 20% $$ 20|! ≈ 0.0005% $$ 20|9′ = 20% $$ 4|! = 0% $$ 4|9′ = 20% prior probability posterior probability Maximum a posteriori (MAP) estimation arg max! $! α ! = 6
Hmmm......, so, how many ?
$(α = 6) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} $ % = ! α = 6 = 1 6!" maximum likelihood $$ 4 = 6|! ≈ 94.58% maximum posteriori prob.
Hmmm......, so, how about ?
$(α = 6) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} $ % = ! α = 6 = 1 6!" maximum likelihood $$ 4 = 6|! ≈ 94.58% maximum posteriori prob. Could you predict & II?
Dice with α faces ! = {5, 4, 3, 4,
2, 1, 2, 3, 1, 4} $# !!! ≤ 6|4 ∗ $$ 4|! = 0% $# !!! ≤ 6|6 ∗ $$ 6|! ≈ 94.58% $# !!! ≤ 6|8 ∗ $$ 8|! ≈ 3.99% $# !!! ≤ 6|12 ∗ $$ 12|! ≈ 0.046% $# !!! ≤ 6|20 ∗ $$ 20|! ≈ 0.0001% $# !!! ≤ 6 = = ∀$ {$# !!! ≤ 6|α ∗ $$ α|! } ≈ 98.62% predic$ve probability
Could you predict & II?
$ ) = 6 ! ≈ 94.58% $ !$$ ≤ 6 ! ≈ 98.62% and Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4}
Could you predict & II?
$ ) = 6 ! ≈ 94.58% $ !$$ ≤ 6 ! ≈ 98.62% and Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} OK, let’s try !!!!!
!!! = 8 Dice with
α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4}
$ ) = 6 !
≈ 94.58% $ !$$ ≤ 6 ! ≈ 98.62% Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} OK, let’s try "!!!! !)) = 8 " $ = 6 {,, ,## } = 0%
"$ α|, ≅ "% , α ∗ "$ (α|4′) "%
(,) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} prior likelihood posterior /( ∀α 1) = 1 5
"$ α|, ≅ "% , α ∗ "$ (α|4′) "%
(,) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} prior likelihood posterior /( ∀α 1) = 1 5 "$ α| ́ , ≅ "% ́ , α ∗ "$ (α|4′′) "% ( ́ ,) Dice with α faces ́ ! = {!, 8}
"$ α|, ≅ "% , α ∗ "$ (α|4′) "%
(,) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} prior likelihood posterior /( ∀α 1) = 1 5 "$ α| ́ , ≅ "% ́ , α ∗ "$ (α|4′′) "% ( ́ ,) Dice with α faces ́ ! = {!, 8}
"$ α|, ≅ "% , α ∗ "$ (α|4′) "%
(,) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} prior likelihood posterior /( ∀α 1) = 1 5 "$ α| ́ , ≅ "% ́ , α ∗ "$ (α|,) "% ( ́ ,) Dice with α faces ́ ! = {!, 8}
Dice with α faces ! = {5, 4, 3, 4,
2, 1, 2, 3, 1, 4} ́ ! = {!, 8} Non-informa$ve prior distribu$on 20% 20% 20% 20% 20% 0% 94.58% 5.32% 0.09% 0.005% 0% 0% 99.98% 0.02% 0.000004% -! (α|C′) -! (α|.) -! (α| ́ .)
$ ) = 8 ́
! ≈ 99.98% $ !$' ≤ 8 ́ ! ≈ 99.98% Dice with α faces ́ ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4, 8} OK!! Let’s try !!"!! COME OOON
No one knows what happened to them......
Hypothesis ObservaEon Truth Knowledge principle phenotype model data Dice with
α faces (regular polyhedron) ! = 5 ?
Hmmm......, so, how about
? $(α = 6) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} $ % = ! α = 6 = 1 6!" maximum likelihood ! α = 6 % = & !!??
! 7 *|, = ! 8 , * ∗ !
7 (*) ! 8 , $! ) = α|+ = ! = $" + = ! ) = α ∗ $! (α) $" ! ' 5 : α → & ' 6 : & → α likelihood Bayes’ theorem
$! α|! ≅ $" ! α ∗ $! (α|-′) Σ∀!
$" !|α ∗ $! α|-′ ' 5 : α → & ' 6 : & → α likelihood = -$ . α Σ∀! -$ .|α = -$ . α -$ . 4 + -$ . 6 + -$ . 8 + -$ . 12 + -$ . 20 ≈ -$ . α 1.7485A − 08 &! ∀α (" = 1 5
$$ 6|! ≈ 94.58% $$ 6|9′ = 20% $$ 8|!
≈ 5.32% $$ 8|9′ = 20% $$ 12|! ≈ 0.09% $$ 12|9′ = 20% $$ 20|! ≈ 0.0005% $$ 20|9′ = 20% $$ 4|! = 0% $$ 4|9′ = 20% prior probability posterior probability Maximum a posteriori probability (MAP) estimation arg max! $! α ! = 6
Dice with α faces ! = {5, 4, 3, 4,
2, 1, 2, 3, 1, 4} $# !!! ≤ 6|4 ∗ $$ 4|! = 0% $# !!! ≤ 6|6 ∗ $$ 6|! ≈ 94.58% $# !!! ≤ 6|8 ∗ $$ 8|! ≈ 3.99% $# !!! ≤ 6|12 ∗ $$ 12|! ≈ 0.046% $# !!! ≤ 6|20 ∗ $$ 20|! ≈ 0.0001% $# !!! ≤ 6 = = ∀$ {$# !!! ≤ 6|α ∗ $$ α|! } ≈ 98.62% predic$ve probability
"$ α|, ≅ "% , α ∗ "$ (α|4′) "%
(,) Dice with α faces ! = {5, 4, 3, 4, 2, 1, 2, 3, 1, 4} prior likelihood posterior /( ∀α 1) = 1 5 "$ α| ́ , ≅ "% ́ , α ∗ "$ (α|4′′) "% ( ́ ,) Dice with α faces ́ ! = {!, 8}
Experiment hypothesis observa$on principle phenotype model data Truth Knowledge f
X (unknown)
Strong hypothesis obs. principle phenotype f Weak hypothesis obs. principle
phenotype model Complex data f model Simple data “Hypothesis driven” “Data driven” Experimental design X X
α ' -(.|α) α |' -(α|.) %|' -(2|α)- α .
prior distribution posterior distribuBon data predictive distribution $! α ∗ $" ! α $" ! = $! α|! likelihood prior posterior Bayes’ theorem
α ' -(.|α) α |' -(α|.) %|' -(2|α)- α .
prior distribution posterior distribuBon data predictive distribution $! α ∗ $" ! α $" ! = $! α|! likelihood prior posterior Bayes’ theorem Truth
α ' -(.|α) α |' -(α|.) %|' -(2|α)- α .
prior distribuBon posterior distribuBon data predicBve distribuBon $! α ∗ $" ! α $" ! = $! α|! likelihood prior posterior Bayes’ theorem #(%|') .(%) Truth L&'(M| $ Kullback-Leibler divergence
α ' -(.|α) α |' -(α|.) %|' -(2|α)- α .
prior distribuBon posterior distribuBon data predicBve distribuBon $! α ∗ $" ! α $" ! = $! α|! likelihood prior posterior Bayes’ theorem #(%|') .(%) Truth L&'(M| $ = −N( + P KL divergence Entropy Generalization error
/!" (.| # = Q[S $ − S(M)] = Q[(−log
$ ) − (−log M )] = Q log ( ) = ∫ M % ∗ log ((#) )(,|#) Y% = ∫ M % ∗ log M(!) Y% − ∫ M % ∗ log $ % ! Y% = −Q S M − ∫ M % ∗ log $ % ! Y% B( C Entropy Generaliza$on error
α ' -(.|α) α |' -(α|.) %|' -(2|α)- α .
prior distribuBon posterior distribution data predictive distribution $! α ∗ $" ! α $" ! = $! α|! likelihood prior posterior Bayes’ theorem #(%|') .(%) Truth L&'(M| $ = −N( + P KL divergence Entropy GeneralizaBon error arg min) L&'(M| $ ⟺ arg min) P P ≅ WAIC Watanabe Akaike InformaAon Criterion
Experiment hypothesis observa$on principle phenotype model data Truth Knowledge f
X (unknown)
Anaïs Nin – “Life shrinks or expands in proporRon to
one’s courage.” h0ps://images.gr-assets.com
Before ABer BeginneR Session BeginneR BeginneR
Enjoy!!