使用`ppc_stat()`时直方图数值失真问题求助

Hey there! Let's dig into why your ppc_stat() histogram is looking distorted. From the data and Stan code you shared, here's a step-by-step breakdown to fix this:

1. First: Address the Extreme Outliers in Your Data #

Looking at your speed vector, two values stick out like a sore thumb: -44 and -2. Every other data point falls between 16 and 40, so these outliers are pulling your summary statistics (like the mean) way off-center. When ppc_stat() compares observed stats to posterior predictive stats, these skewed values will make the histogram look distorted.

Here's how to handle this:

• If -44 and -2 are typos (e.g., maybe they should be 44 and 2?), correct them immediately.
• If they're valid data points, switch to a robust statistic for ppc_stat() (like the median instead of the mean)—medians are much less sensitive to extreme values.

2. Fix and Complete Your Stan Model #

Your Stan code snippet is incomplete, and missing critical pieces that could cause wonky posterior predictive checks. Let's refine it to handle outliers properly and ensure convergence:

data{
  int<lower=1> n;
  vector[n] y;
}
parameters{
  real y_mu;
  real<lower=0> y_sd;
  real<lower=1> nu; // Student's t df must be at least 1
}
model{
  // Add reasonable priors for all parameters (critical for convergence)
  y_mu ~ normal(25, 10); // Matches your data's central tendency
  y_sd ~ exponential(1);
  nu ~ gamma(2, 0.1); // Weak prior favoring heavier tails (good for outliers)
  
  // Finish the likelihood statement
  y ~ student_t(nu, y_mu, y_sd);
}
generated quantities{
  vector[n] y_rep;
  // Generate posterior predictive samples (required for ppc_stat())
  for (i in 1:n) {
    y_rep[i] = student_t_rng(nu, y_mu, y_sd);
  }
}

Key fixes here:

• Added priors for all parameters (without them, the model might not converge properly)
• Set nu to have a lower bound of 1 (Student's t-distribution doesn't make sense with df < 1)
• Added a generated quantities block to create y_rep—the posterior predictive samples ppc_stat() needs to compare against your observed data.

3. Run ppc_stat() Correctly (With Robust Options) #

Once your model is fitted, extract the y_rep samples and run ppc_stat() with a statistic that works for your data:

library(rstan)
library(bayesplot)

# Prepare your data
speed <- c(28, 26, 33, 24, 34, -44, 27, 16, 40, -2, 29, 22, 24, 21, 25, 30, 23, 29, 31, 19, 24, 20, 36, 32, 36, 28, 25, 21, 28, 29, 37, 25, 28, 26, 30, 32, 36, 26, 30, 22, 36, 23, 27, 27, 28, 27, 31, 27, 26, 33, 26, 32, 32, 24, 39, 28, 24, 25, 32, 25, 29, 27, 28, 29, 16, 23)
data_list <- list(n = length(speed), y = speed)

# Fit the model
fit <- stan(file = "your_model_file.stan", data = data_list)

# Extract posterior predictive samples
y_rep <- rstan::extract(fit, "y_rep")[[1]]

# Option 1: Use median (robust to outliers)
ppc_stat(y = speed, yrep = y_rep, stat = "median")

# Option 2: If you fixed/removed outliers, use mean
clean_speed <- speed[speed > 0] # Remove negative values if they're typos
data_list_clean <- list(n = length(clean_speed), y = clean_speed)
fit_clean <- stan(file = "your_model_file.stan", data = data_list_clean)
y_rep_clean <- rstan::extract(fit_clean, "y_rep")[[1]]
ppc_stat(y = clean_speed, yrep = y_rep_clean, stat = "mean")

4. Verify Model Convergence #

Before trusting your PPD results, check that your model converged:

• Look for R-hat values ≤ 1.01 for all parameters (you can get these with print(fit)).
• Ensure effective sample sizes (ESS) are high enough (aim for ≥ 1000 per parameter).

Poor convergence will lead to unreliable posterior predictive samples, which can also cause distorted histograms.

内容的提问来源于stack exchange，提问作者The Pointer