ベイズ推定の概要＠広島ベイズ塾
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@ Created by / Yoshitake TAKEBAYASHI @psycle44
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Transcript of ベイズ推定の概要＠広島ベイズ塾
@Created by / Yoshitake TAKEBAYASHI @psycle44
:
:
:
http://ikiru.ncnp.go.jp/ikiru-hp/genjo/toukei/index.html
Noma, H. Statist. Med. 2011, 30 3304–3312
K=10
TOPICS
MCMC
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PC!!
!!
....
:
:
(θ) (σ^2)
(D)
https://ksmzn.shinyapps.io/statdist/
...
P(D|θ) θP(D|θ)= (θ) (D)
P(θ|D)P(θ|D)= (D) (θ)
P(D|θ) θ
95%
μ
P(θ|D)
95%
..???Θ ..???
Θ
( )
※
MCMC
MCMCMarcovChainMonteCarlo Methods
MCMC??
MCMC
step1: x1
step2: x2 , x1
step3: x1 step2 , x2
step4: x2 step3 , x1
step3,4
...
MCMC
:
BURNIN WARM-UP
stan
GELMAN & RUBINGEWEKE
GELMAN & RUBIN
1.01
chain chain1
chain
GEWEKEMCMC Z
±1.96 →
5
MCMC
MCMC
MCMC
Y
α β
MCMC
chain
burin
thin( )
Stan
MCMC
library(rstan)N <- 500x <- rnorm(N, mean = 50, sd = 10)y <- 10 + 0.8 * x + rnorm(N, mean =0, sd = 7)
stancode <- ' data{ int<lower=0> N; real x[N]; real y[N]; } parameters { real alpha; real beta; real<lower=0> s; } model{ for(i in 1:N) y[i] ~ normal(alpha + beta * x[i], s); #推定するモデル alpha ~ normal(0, 100); #パラメータの事前分布 beta ~ normal(0, 100); #パラメータの事前分布 s ~ inv_gamma(0.001, 0.001); }'
datastan <- list(N=N, x=x, y=y)fit <- stan(model_code = stancode,data=datastan,iter=5000,chain=4)
my_shinystan <- as.shinystan(fit)launch_shinystan(my_shinystan)
On the shinyRStan
SHINYSTAN
SEM
MCMC
RHAT
MCMC
ENJOY!!
