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moments_4 <- function(truedens){
  k1 <- integrate(function(x){x*truedens(x)}, lower=-Inf, upper=Inf)
  k2 <- integrate(function(x){(x-k1$value)^2*truedens(x)}, lower=-Inf, upper=Inf)
  k3 <- integrate(function(x){(x-k1$value)^3*truedens(x)}, lower=-Inf, upper=Inf)
  k4 <- integrate(function(x){(x-k1$value)^4*truedens(x)}, lower=-Inf, upper=Inf)
  c(k1$value, k2$value, 
    k3$value, k4$value)  
}

Mu4 <- moments_4(truedens = function(x){dgamma(x,2,1)})

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library(ggplot2)
library(dplyr)
library(tidyr)
# integrate(f = function(x)x*(0.6*dnorm(x, -10/6)+0.4*dnorm(x, 10/4)), lower = -Inf, upper = Inf)

scaled_mean <- function(x){sqrt(length(x))* mean(x) / ifelse(length(x)==1L,1,sd(x))}
CLTsim <- function(n, iter){
  mu <- c(-10/6, 10/4)
  mixture <- numeric(iter)
  uniform <-  numeric(iter)

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library(BayesLogit)
library(ggplot2)
library(dplyr)
#########
#Bayesian inference for logistic models using Polya-Gamma latent variables (2013)
#Nicholas G. Polson, James G. Scott, Jesse Windle
#https://arxiv.org/abs/1205.0310
#########
#Y: response variable
#X: explanatory design matrix

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library(dplyr)
library(tidyr)
library(ggplot2)
library(gganimate)

logsumexp2 =function (logx1,logx2){
  logx1 + log1p(exp(logx2-logx1))
}

llmixnorm <- function(par, y){

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library(Rcpp)
library(RcppParallel)
sourceCpp("R/cpp/parallelreduce.cpp")
# defaultNumThreads()
setThreadOptions(numThreads =  4)
m <- rnorm(1e+8)

# ensure that serial and parallel versions give the same result
# compare performance of serial and parallel
library(rbenchmark)

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library(roll)
library(RcppParallel)

RcppParallel::defaultNumThreads()
x <- rnorm(1e8)

setThreadOptions(numThreads = 1L)
t1 <- system.time({
  roll_mean(x, 1000)
})

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##参考文献：
##スティーブン・ピンカー『人はどこまで合理的か　上』,5章，訳：橘明美，草思社

#devtools::install_github("abikoushi/ggsomestat")
library(ggsomestat)
library(dplyr)

taxi <- matrix(c(0.68, 0.03,
                 0.17, 0.12), byrow = TRUE, nrow = 2)
gb=c("green","blue")

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library(moltenNMF)
library(Matrix)

df = expand.grid(letters[1:3], LETTERS[1:2])
X = sparse_onehot(~., data = df)

A = matrix(c(1,0,0,0,
             0,1,0,0,
             0,0,1,0,
             0,0,0,0,

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\documentclass[tikz,border=10pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{positioning, arrows.meta}

\begin{document}
\begin{tikzpicture}[
  node distance=30mm,
  box/.style={draw, rounded corners, align=center, inner sep=6pt, minimum height=5em ,minimum width=7em},
  arrow/.style={->, thick}

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## reparameterized Poisson NMF
NMF_re <- function(X,
                   M=2,
                   a_W=1,
                   a_H=1,
                   alpha_b=1, beta_b=1,
                   tol=1e-3, maxit=100){
  D <- nrow(X)
  N <- ncol(X)
  b_W <- rgamma(1, 1, 1)