生成n个样本，R中的拒绝采样

Question

拒绝抽样

我正在处理具有截断正态分布的拒绝抽样，请参阅下面的 r 代码。如何让采样在特定的 n 处停止？例如 1000 次观察。 IE。我想在接受样本数达到n（1000）时停止采样。

有什么建议吗？非常感谢任何帮助:)

#Truncated normal curve    
curve(dnorm(x, mean=2, sd=2)/(1-pnorm(1, mean=2, sd=2)),1,9)

#create a data.frame with 100000 random values between 1 and 9

sampled <- data.frame(proposal = runif(100000,1,9))
sampled$targetDensity <- dnorm(sampled$proposal, mean=2, sd=2)/(1-pnorm(1, mean=2, sd=2))

#accept proportional to the targetDensity

maxDens = max(sampled$targetDensity, na.rm = T)
sampled$accepted = ifelse(runif(100000,0,1) < sampled$targetDensity / maxDens, TRUE, FALSE)

hist(sampled$proposal[sampled$accepted], freq = F, col = "grey", breaks = 100, xlim = c(1,9), ylim = c(0,0.35),main="Random draws from skewed normal, truncated at 1")
curve(dnorm(x, mean=2, sd=2)/(1-pnorm(1, mean=2, sd=2)),1,9, add =TRUE, col = "red", xlim = c(1,9),  ylim = c(0,0.35))



X <- sampled$proposal[sampled$accepted]

采样时如何设置X的长度为特定数字？

Answer 1

在沉思之后，如果您决定使用拒绝抽样并且只在 1,000 次之前使用它，我认为没有比使用 while 循环更好的选择了。这比

效率低得多

sampled$accepted = ifelse(runif(100000,0,1) < sampled$targetDensity / maxDens, TRUE, FALSE)
X <- sampled$proposal[sampled$accepted][1:1000]

以上代码所用时间为0.0624001s。下面的代码花费的时间是 0.780005s。我将其包括在内是因为它是对您提出的特定问题的答案，但该方法效率低下。如果还有其他选择，我会使用它。

#Number of samples
N_Target <- 1000
N_Accepted <- 0

#Loop until condition is met
i = 1
sampled$accepted = FALSE
while( N_Accepted < N_Target ){

    sampled$accepted[i] = ifelse(runif(1,0,1) < sampled$targetDensity[i] / maxDens, TRUE, FALSE)
    N_Accepted = ifelse( sampled$accepted[i], N_Accepted + 1 , N_Accepted )
    i = i + 1
    if( i > nrow( sampled ) ) break

}

生成n个样本，R中的拒绝采样

Generate n samples, Rejection sampling in R

r

statistics

normal-distribution

resampling

statistical-sampling

拒绝抽样