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tidybayes

贝叶斯结果可视化

贝叶斯篇
R 
library(tidyverse)
library(tidybayes)
library(ggdist)
library(rstan)

rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())

在贝叶斯抽样样本量比较大，我们需要规整和可视化，就需要借助一些函数。这里简单介绍tidybayes宏包和它的姊妹宏包 ggdist，更多的技术参数见官方手册。

企鹅案例

问题简化，我们只挑选Gentoo类企鹅

R 
library(palmerpenguins)

gentoo <- penguins %>% 
  drop_na() %>% 
  filter(species == "Gentoo")

gentoo

先看下两个变量的关系

R 
gentoo %>% 
  ggplot(aes(x = bill_length_mm, bill_depth_mm)) +
  geom_point()

Stan模型

假设我们建立最简单的线性模型，其中预测因子bill_length_mm，被解释变量是 bill_depth_mm

$$ \begin{align} y_n &\sim \operatorname{normal}(\mu_n, \,\, \sigma)\\ \mu_n &= \alpha + \beta x_n \end{align} $$

R 
stan_program <- &quot;
data {
  int&lt;lower=0&gt; N;
  vector[N] y;
  vector[N] x;
  int&lt;lower=0&gt; M;
  vector[M] new_x;  
}
parameters {
  real alpha;
  real beta;
  real&lt;lower=0&gt; sigma;
}
model {
  y ~ normal(alpha + beta * x, sigma);
  
  alpha  ~ normal(0, 10);
  beta   ~ normal(0, 10);
  sigma  ~ exponential(1);
}
generated quantities {
  vector[M] y_fit;
  vector[M] y_rep;
  for (n in 1:M) {
    y_fit[n] = alpha + beta * new_x[n];
    y_rep[n] = normal_rng(alpha + beta * new_x[n], sigma);
  }
}
&quot;

library(modelr)
newdata <- gentoo %>% 
  data_grid(
    bill_length_mm = seq_range(bill_length_mm, 100)
)

# or
# newdata <- data.frame(
#     bill_length_mm = seq(min(gentoo$bill_length_mm), max(gentoo$bill_length_mm), length.out = 100)
#    ) 


stan_data <- list(
   N = nrow(gentoo),
   x = gentoo$bill_length_mm, 
   y = gentoo$bill_depth_mm,
   M = nrow(newdata),
   new_x = newdata$bill_length_mm
  )

fit <- stan(model_code = stan_program, data = stan_data)

抽样

R 
draws <- fit %>% 
  tidybayes::gather_draws(alpha, beta, sigma)
draws

统计汇总

R 
draws %>% 
  ggdist::mean_qi(.width = c(0.65, 0.89) )

可视化

  • geom_slabinterval() / stat_slabinterval() family
R 
draws %>% 
  ggplot(aes(x = .value, y = .variable)) + 
  ggdist::stat_interval()
R 
draws %>% 
  ggplot(aes(x = .value, y = .variable)) + 
  ggdist::stat_slab()
R 
draws %>% 
  ggplot(aes(x = .value, y = .variable)) + 
  ggdist::stat_slabinterval()
R 
draws %>% 
  filter(.variable %in% c("beta", "sigma")) %>% 
  ggplot(aes(x = .value, y = .variable)) + 
  ggdist::stat_slabinterval()  +
  facet_grid(~ .variable, labeller = "label_both", scales = "free")
  • geom_dotsinterval() / stat_dotsinterval() family
R 
draws %>% 
  filter(.variable %in% c("beta", "sigma")) %>% 
  ggplot(aes(x = .value, y = .variable)) + 
  stat_dotsinterval(
    quantiles = 200,
    justification = -0.1,
    slab_color = "black",
    slab_fill = "orange",
    interval_color = "red"
  )
  • geom_lineribbon() / stat_lineribbon() family
R 
fit %>% 
  tidybayes::gather_draws(y_fit[i]) %>% 
  ggdist::median_qi(.width = c(0.89)) %>%
  bind_cols(newdata) %>% 
  
  ggplot() + 
  geom_point(
    data = gentoo,
    aes(bill_length_mm, bill_depth_mm)
  ) +
  geom_lineribbon(
    aes(x = bill_length_mm, y = .value, ymin = .lower, ymax = .upper),
    alpha = 0.3, 
    fill = "gray50"
  ) +
  theme_classic() +
  scale_fill_brewer(direction = -1)
  • 组合
R 
penguins %>%
  ggplot(aes(y = species, x = bill_length_mm, fill = species)) +
  stat_slab(aes(thickness = after_stat(pdf*n)), scale = 0.7) +
  stat_dotsinterval(side = "bottom", scale = 0.7, slab_size = NA) +
  scale_fill_brewer(palette = "Set2") +
  ggtitle("Rain cloud plot")
R 
pacman::p_unload(pacman::p_loaded(), character.only = TRUE)