伯努利隨機變量的似然圖和對數似然圖 function

Question

data(quilpie, package = "GLMsData"); names(quilpie)
mu = seq(0.01, 0.99, length.out = 100L)
loglik = NULL
lik =NULL
for (i in 1:length(mu)) {
  loglik[i] <- sum(dbinom(quilpie$y, size = 1, prob=mu[i], log=TRUE))
  lik[i] <- sum(dbinom(quilpie$y, size=1, prob=mu[i], log=FALSE))
}
plot(mu, lik, type = "l", lwd = 2,
     xlab = expression(paste(,mu ,)),
     main = "Likelihood function",
     ,ylab = expression(paste("loglik (", mu ,")")))
abline(v = mu[which(lik==max(lik))], lwd = 3, lty =2)
abline(v = optimize(lik, lower = 0, upper = 1, maximum = TRUE)$max)
optimize(lik, lower = 0.01, upper = 0.99, maximum = TRUE)
mu[which(lik==max(lik))]

plot(mu, loglik, type = "l", lwd = 2,
     xlab = expression(paste(,mu ,)),
     main = "Log-likelihood function",
     ,ylab = expression(paste("loglik (", mu ,")")))
abline(v = mu[which(loglik==max(loglik))], lwd = 3, lty =2)
abline(v = optimize(loglik, lower = 0, upper = 1, maximum = TRUE)$max)
optimize(loglik, lower = 0.01, upper = 0.99, maximum = TRUE)
mu[which(loglik==max(loglik))]

我正在嘗試獲取可能性和對數似然的圖。 對數似然 plot 運行良好，但似然 function plot 沒有顯示任何內容。 此外，優化function 不起作用。 我需要這方面的幫助。

Answer 1

將loglik和lik的計算重寫為函數，將它們向量化，然后optimize 。 和 plot 與curve 。

請注意，函數將在參數prob上進行優化，這里作為第一個參數，名為x 。
參數y是數據。

floglik <- function(x, y){
  sum(dbinom(y, size = 1, prob = x, log = TRUE))
}
floglik <- Vectorize(floglik, "x")

max_loglik <- optimize(floglik, interval = c(0, 1), y = quilpie$y, maximum = TRUE)

curve(floglik(x, quilpie$y), from = 0, to = 1,
      lwd = 2,
      xlab = expression(paste(mu)),
      main = "Log-likelihood function",
      ylab = expression(paste("loglik (", mu ,")")))
abline(v = max_loglik$maximum)

可能性也是如此。

flik <- function(x, y){
  prod(dbinom(y, size = 1, prob = x, log = FALSE))
}
flik <- Vectorize(flik, "x")
max_lik <- optimize(flik, interval = c(0, 1), y = quilpie$y, maximum = TRUE)

curve(flik(x, quilpie$y), from = 0, to = 1,
      lwd = 2,
      xlab = expression(paste(mu)),
      main = "Likelihood function",
      ylab = expression(paste("lik (", mu ,")")))
abline(v = max_lik$maximum)