[英]Expectation Maximization using a Poisson likelihood function
I am trying to apply the expectation-maximization algorithm to estimate missing count data but all the packages in R, such as missMethods, assume a multivariate Gaussian distribution.我正在尝试应用期望最大化算法来估计丢失的计数数据,但 R 中的所有包(例如 missMethods)都假定多元高斯分布。 How would I apply the expectation-maximization algorithm to estimate missing count data assuming a Poisson distribution?假设服从泊松分布,我将如何应用期望最大化算法来估计缺失的计数数据?
Say we have data that look like this:假设我们有这样的数据:
x <- c(100, 96, 79, 109, 111, NA, 93, 95, 119, 90, 121, 96, NA,
NA, 85, 95, 110, 97, 87, 104, 101, 87, 87, NA, 89, NA,
113, NA, 95, NA, 119, 115, NA, 105, NA, 80, 90, 108, 90,
99, 111, 93, 99, NA, 87, 89, 87, 126, 101, 106)
Applying impute_EM using missMethods ( missMethods::impute_EM(x, stochastic = FALSE)
) gives an answer but the data are not continuous but discrete.使用 missMethods ( missMethods::impute_EM(x, stochastic = FALSE)
) 应用 impute_EM 给出了答案,但数据不是连续的而是离散的。
I understand that questions like these require a minimum, reproducible example, but I honestly do not know where to start.我知道像这样的问题需要一个最小的、可重现的例子,但我真的不知道从哪里开始。 Even suggested reading to point me in the right direction would be helpful.甚至建议阅读以指出正确的方向也会有所帮助。
Defining x0
:定义x0
:
x0 <- x[!is.na(x)]
The Jeffreys/reference prior for a Poisson distribution with mean lambda
is 1/sqrt(lambda)
.均值为lambda
的泊松分布的 Jeffreys/reference prior 是1/sqrt(lambda)
。 From the observed values, this results in lambda
having a gamma reference posterior with a shape parameter sum(x0) + 0.5
and a rate parameter 1/length(x0)
.根据观察值,这导致lambda
具有伽马参考后验,形状参数sum(x0) + 0.5
和速率参数1/length(x0)
。 You could take n
samples of lambda
with:您可以使用以下方法lambda
的n
样本:
lambda <- rgamma(n, sum(x0) + 0.5, length(x0))
Then sample n
missing values ( xm
) with然后用n
缺失值 ( xm
) 采样
xm <- rpois(n, lambda)
Alternatively, since a Gamma-Poisson compound distribution can be formulated as a negative binomial (after integrating out lambda
):或者,由于 Gamma-Poisson 复合分布可以表示为负二项式(在积分出lambda
之后):
xm <- rnbinom(n, sum(x0) + 0.5, length(x0)/(length(x0) + 1L))
As a function:作为 function:
MI_poisson <- function(x, n) {
x0 <- x[!is.na(x)]
rbind(matrix(x0, ncol = n, nrow = length(x0)),
matrix(rnbinom(n*(length(x) - length(x0)), sum(x0) + 0.5, length(x0)/(length(x0) + 1L)), ncol = n))
}
This will return a matrix with n
columns where each column contains the original vector x
with all NA
values imputed.这将返回一个包含n
列的矩阵,其中每列包含原始向量x
并估算了所有NA
值。 Each column could be used separately in further analysis, then the results can be aggregated.每列可以单独用于进一步分析,然后可以汇总结果。
声明:本站的技术帖子网页,遵循CC BY-SA 4.0协议,如果您需要转载,请注明本站网址或者原文地址。任何问题请咨询:yoyou2525@163.com.