在R中创建和可视化联合概率分布

install.packages("mvtnorm")
install.packages("ggplot2")

library(mvtnorm)
library(ggplot2)

# 创建数据点矩阵
x <- seq(-3, 3, length.out = 100)
y <- seq(-3, 3, length.out = 100)
grid <- expand.grid(x = x, y = y)

# 设置均值向量和协方差矩阵
mean <- c(0, 0)
cov <- matrix(c(1, 0.5, 0.5, 1), nrow = 2)

# 计算概率密度值
pdf <- dmvnorm(grid, mean = mean, sigma = cov)

# 创建等高线图
contour_plot <- ggplot(data.frame(grid), aes(x = x, y = y, z = pdf)) +
  geom_contour()

# 创建热力图
heatmap_plot <- ggplot(data.frame(grid), aes(x = x, y = y, fill = pdf)) +
  geom_tile()

# 显示图形
print(contour_plot)
print(heatmap_plot)