从具有可变底层网格的内核密度估计器进行模拟 [英] Simulate from kernel density estimator with variable underlying grid

问题描述

我有一个数据集，用于通过估计核密度来创建经验概率分布.现在我正在使用 R 的

我的数据知道有很多波动的区域，需要精细的网格粒度.其他地区基本上没有数据点，那里什么也没有.如果我可以将 kde2d 的 n 参数设置为一个非常高的数字，以便在任何地方都能很好地解析我的数据，我会很好.唉，由于内存限制，这是不可能的.

这就是为什么我认为我可以修改 kde2d 函数以获得非常量的粒度.

问题是，我不能再使用 sample 沿 x 轴从切片中采样.因为分布左侧的部分更精细，因此被sample采样的概率更高.

我该怎么做才能在我需要的地方有一个精细的网格，但根据其适当的密度从分布中取样?非常感谢.

解决方案

在 conditional_probabilty_density 上使用 approx 和新的 n.

I have a dataset that I'm using to create an empirical probability distribution by estimating a kernel density. Right now I'm using R's kde2d from the MASS package. After estimating the probability distribution, I use sample to sample from slices of the 2D distribution along the x-axis. I use sample much like described here. Example code would look like this

library(MASS)
set.seed(123)
x = rnorm(100, 1, 0.1)
set.seed(456)
y = rnorm(100, 1, 0.5)
den <- kde2d(x, y, n = 50, lims = c(-2, 2, -2, 2))
#to plot this 2d kde:
#library(lattice)
#persp(den)
conditional_probabilty_density = list(x = den$y, y = den$z[40, ])
#to plot the slice:
#plot(conditional_probabilty_density)
simulated_sample = sample(conditional_probabilty_density$x, size = 10, replace = TRUE, prob = conditional_probabilty_density$y)

The den looks like this

My data has known areas where there is a lot of fluctuations, requiring a fine grid granularity. Other areas have basically no data points and nothing is going on there. I would be fine if I could just set the n parameter of kde2d to a very high number in order to have a good resolution of my data everywhere. Alas, this is not possible due to memory constraints.

That's why I thought I could modify the kde2d function to have a non-constant granularity.
Here is the source code of the kde2d function. One can modify the line

gy <- seq.int(lims[3L], lims[4L], length.out = n[2L])

and put whatever granularity is wished for on the y-axis. For example

a <- seq(-1, 0, 0.5)
gy <- c(a, seq.int(0.1, 2, length.out = n[2L]-length(a)))

And the modified kde2d returns the kernel density estimate at the specified positions. Works very well. Suppose I have now

Problem is, I can no longer use sample to sample from slices along the x-axis. Because the part on the left side of the distribution is much finer and thus has a higher probability to be sampled by sample.

What can I do to have a fine grid where I need it, but sample from the distribution according to its proper densities? Thank you a lot.

解决方案

Use approx on conditional_probabilty_density with a new n.

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