在4.1.3版本的R语言中建立ergm模型，参照分布项设置为泊松分布，引入关键的包，对模型分别使用MH采样函数以及Gibbs采样函数下的MCMC算法进行参数估计，绘制后验密度图、迭代轨迹图、自相关图像

首先，需要安装并加载ergm包和MCMC包。然后，读入数据并建立ergm模型，设置分布项为泊松分布。

library(ergm)
library(MCMC)

data <- read.table("data.txt")

model <- ergm(data ~ edges + mutual + gwdegree(0.5, fixed = TRUE), 
              response = "cnt",
              distribution = "poisson")

接下来，使用MH采样函数进行参数估计，并绘制后验密度图、迭代轨迹图、自相关图像。

MHout <- MHmcmc(model, control = list(iterations = 1000, burnin = 500, thin = 2))

# 绘制后验密度图
plot(density(MHout$coef["edges", ]), main = "Posterior Density of Edges", 
     xlab = "Edges", ylab = "Density", col = "blue")

# 绘制迭代轨迹图
plot(MHout$coef["edges", ], type = "l", main = "Iteration Trajectory of Edges", 
     xlab = "Iterations", ylab = "Edges", col = "blue")

# 绘制自相关图像
acf(MHout$coef["edges", ], main = "Autocorrelation of Edges", lag.max = 20)

然后，使用Gibbs采样函数进行参数估计，并绘制后验密度图、迭代轨迹图、自相关图像。

Gibbsout <- Gibbsmcmc(model, control = list(iterations = 1000, burnin = 500, thin = 2))

# 绘制后验密度图
plot(density(Gibbsout$coef["edges", ]), main = "Posterior Density of Edges", 
     xlab = "Edges", ylab = "Density", col = "red")

# 绘制迭代轨迹图
plot(Gibbsout$coef["edges", ], type = "l", main = "Iteration Trajectory of Edges", 
     xlab = "Iterations", ylab = "Edges", col = "red")

# 绘制自相关图像
acf(Gibbsout$coef["edges", ], main = "Autocorrelation of Edges", lag.max = 20)

最后，可以将MH采样函数和Gibbs采样函数的结果进行比较，并进行模型诊断和评估。