问题描述
我很难理解将rnorm用作另一个rnorm的参数之一是什么意思? (我将在下面详细说明)
I have difficulty understanding what it means when an rnorm is used as one of the arguments of another rnorm? (I'll explain more below)
例如，在下面的R代码的第一行中，我使用rnorm()，并将其称为rnorm():mu.
For example, below, in the first line of my R code I use an rnorm() and I call this rnorm(): mu.
mu由10,000个x组成.
mu consists of 10,000 x.
现在，让我将mu本身作为新的rnorm()的mean自变量，称为分发".
Now, let me put mu itself as the mean argument of a new rnorm() called "distribution".
我的问题是，如何将本身具有10,000个x的mu用作这个称为分发的新rnorm()的mean自变量?
My question is how mu which itself has 10,000 x be used as the mean argument of this new rnorm() called distribution?
P.S .:任何normal distribution的mean自变量可以是一个数字，并且只有一个均值，我们将有一个完整的正态.现在，为什么使用10,000个mu值仍然会产生一个法线?
P.S.: mean argument of any normal distribution can be a single number, and with only ONE single mean, we will have a single, complete normal. Now, how come, using 10,000 mu values still results in a single normal?
mu <- rnorm( 1e4 , 178 , 20 ) ; plot( density(mu) )
distribution <- rnorm( 1e4 , mu , 1 ) ; plot( density(distribution) )
推荐答案
您distribution是条件密度.使用plot(density(distribution))绘制的密度是边际密度.
You distribution is a conditional density. While the density you draw with plot(density(distribution)), is a marginal density.
从统计学上讲，您首先拥有一个正常的随机变量mu ~ N(178, 20)，然后是另一个随机变量y | mu ~ N(mu, 1).您生成的图是y的边际密度.
Statistically speaking, you first have a normal random variable mu ~ N(178, 20), then another random variable y | mu ~ N(mu, 1). The plot you produce is the marginal density of y.
P(y)，在数学上是关节分布P(y | mu) * p(mu)的积分，并整合为mu.
P(y), is mathematically an integral of joint distribution P(y | mu) * p(mu), integrating out mu.
这意味着您正在从边际分布中采样.密度估计值近似于样本中的蒙特卡洛积分.
It means you are sampling from the marginal distribution. The density estimate approximates the Monte Carlo integral from samples.
这种事情在贝叶斯计算中很常见. 关于正态分布均值[降雪量的数据]的贝叶斯推理上的Toy R代码给出了一个完整的例子，但积分是通过数值积分计算.
This kind of thing is often seen in Bayesian computation. Toy R code on Bayesian inference for mean of a normal distribution [data of snowfall amount] gives a full example, but integral is computed by numerical integration.
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