Fit an Integer Adjusted Exponential, Gamma or Lognormal distributions
Source:R/estimate_delay.R
dist_fit.Rd![[Stable]](figures/lifecycle-stable.svg)
Fits an integer adjusted exponential, gamma or lognormal distribution using
stan.
Usage
dist_fit(
values = NULL,
samples = 1000,
cores = 1,
chains = 2,
dist = "exp",
verbose = FALSE,
backend = "rstan"
)Arguments
- values
Numeric vector of values
- samples
Numeric, number of samples to take. Must be >= 1000. Defaults to 1000.
- cores
Numeric, defaults to 1. Number of CPU cores to use (no effect if greater than the number of chains).
- chains
Numeric, defaults to 2. Number of MCMC chains to use. More is better with the minimum being two.
- dist
Character string, which distribution to fit. Defaults to exponential (
"exp") but gamma ("gamma") and lognormal ("lognormal") are also supported.- verbose
Logical, defaults to FALSE. Should verbose progress messages be printed.
- backend
Character string indicating the backend to use for fitting stan models. Supported arguments are "rstan" (default) or "cmdstanr".
Examples
# \donttest{
# integer adjusted exponential model
dist_fit(rexp(1:100, 2),
samples = 1000, dist = "exp",
cores = ifelse(interactive(), 4, 1), verbose = TRUE
)
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 1).
#> Chain 1: Rejecting initial value:
#> Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1: Stan can't start sampling from this initial value.
#> Chain 1: Rejecting initial value:
#> Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1: Stan can't start sampling from this initial value.
#> Chain 1: Rejecting initial value:
#> Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1: Stan can't start sampling from this initial value.
#> Chain 1:
#> Chain 1: Gradient evaluation took 4.1e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.41 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 1500 [ 0%] (Warmup)
#> Chain 1: Iteration: 50 / 1500 [ 3%] (Warmup)
#> Chain 1: Iteration: 100 / 1500 [ 6%] (Warmup)
#> Chain 1: Iteration: 150 / 1500 [ 10%] (Warmup)
#> Chain 1: Iteration: 200 / 1500 [ 13%] (Warmup)
#> Chain 1: Iteration: 250 / 1500 [ 16%] (Warmup)
#> Chain 1: Iteration: 300 / 1500 [ 20%] (Warmup)
#> Chain 1: Iteration: 350 / 1500 [ 23%] (Warmup)
#> Chain 1: Iteration: 400 / 1500 [ 26%] (Warmup)
#> Chain 1: Iteration: 450 / 1500 [ 30%] (Warmup)
#> Chain 1: Iteration: 500 / 1500 [ 33%] (Warmup)
#> Chain 1: Iteration: 550 / 1500 [ 36%] (Warmup)
#> Chain 1: Iteration: 600 / 1500 [ 40%] (Warmup)
#> Chain 1: Iteration: 650 / 1500 [ 43%] (Warmup)
#> Chain 1: Iteration: 700 / 1500 [ 46%] (Warmup)
#> Chain 1: Iteration: 750 / 1500 [ 50%] (Warmup)
#> Chain 1: Iteration: 800 / 1500 [ 53%] (Warmup)
#> Chain 1: Iteration: 850 / 1500 [ 56%] (Warmup)
#> Chain 1: Iteration: 900 / 1500 [ 60%] (Warmup)
#> Chain 1: Iteration: 950 / 1500 [ 63%] (Warmup)
#> Chain 1: Iteration: 1000 / 1500 [ 66%] (Warmup)
#> Chain 1: Iteration: 1001 / 1500 [ 66%] (Sampling)
#> Chain 1: Iteration: 1050 / 1500 [ 70%] (Sampling)
#> Chain 1: Iteration: 1100 / 1500 [ 73%] (Sampling)
#> Chain 1: Iteration: 1150 / 1500 [ 76%] (Sampling)
#> Chain 1: Iteration: 1200 / 1500 [ 80%] (Sampling)
#> Chain 1: Iteration: 1250 / 1500 [ 83%] (Sampling)
#> Chain 1: Iteration: 1300 / 1500 [ 86%] (Sampling)
#> Chain 1: Iteration: 1350 / 1500 [ 90%] (Sampling)
#> Chain 1: Iteration: 1400 / 1500 [ 93%] (Sampling)
#> Chain 1: Iteration: 1450 / 1500 [ 96%] (Sampling)
#> Chain 1: Iteration: 1500 / 1500 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.138 seconds (Warm-up)
#> Chain 1: 0.065 seconds (Sampling)
#> Chain 1: 0.203 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 2).
#> Chain 2: Rejecting initial value:
#> Chain 2: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 2: Stan can't start sampling from this initial value.
#> Chain 2:
#> Chain 2: Gradient evaluation took 4.1e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.41 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 1500 [ 0%] (Warmup)
#> Chain 2: Iteration: 50 / 1500 [ 3%] (Warmup)
#> Chain 2: Iteration: 100 / 1500 [ 6%] (Warmup)
#> Chain 2: Iteration: 150 / 1500 [ 10%] (Warmup)
#> Chain 2: Iteration: 200 / 1500 [ 13%] (Warmup)
#> Chain 2: Iteration: 250 / 1500 [ 16%] (Warmup)
#> Chain 2: Iteration: 300 / 1500 [ 20%] (Warmup)
#> Chain 2: Iteration: 350 / 1500 [ 23%] (Warmup)
#> Chain 2: Iteration: 400 / 1500 [ 26%] (Warmup)
#> Chain 2: Iteration: 450 / 1500 [ 30%] (Warmup)
#> Chain 2: Iteration: 500 / 1500 [ 33%] (Warmup)
#> Chain 2: Iteration: 550 / 1500 [ 36%] (Warmup)
#> Chain 2: Iteration: 600 / 1500 [ 40%] (Warmup)
#> Chain 2: Iteration: 650 / 1500 [ 43%] (Warmup)
#> Chain 2: Iteration: 700 / 1500 [ 46%] (Warmup)
#> Chain 2: Iteration: 750 / 1500 [ 50%] (Warmup)
#> Chain 2: Iteration: 800 / 1500 [ 53%] (Warmup)
#> Chain 2: Iteration: 850 / 1500 [ 56%] (Warmup)
#> Chain 2: Iteration: 900 / 1500 [ 60%] (Warmup)
#> Chain 2: Iteration: 950 / 1500 [ 63%] (Warmup)
#> Chain 2: Iteration: 1000 / 1500 [ 66%] (Warmup)
#> Chain 2: Iteration: 1001 / 1500 [ 66%] (Sampling)
#> Chain 2: Iteration: 1050 / 1500 [ 70%] (Sampling)
#> Chain 2: Iteration: 1100 / 1500 [ 73%] (Sampling)
#> Chain 2: Iteration: 1150 / 1500 [ 76%] (Sampling)
#> Chain 2: Iteration: 1200 / 1500 [ 80%] (Sampling)
#> Chain 2: Iteration: 1250 / 1500 [ 83%] (Sampling)
#> Chain 2: Iteration: 1300 / 1500 [ 86%] (Sampling)
#> Chain 2: Iteration: 1350 / 1500 [ 90%] (Sampling)
#> Chain 2: Iteration: 1400 / 1500 [ 93%] (Sampling)
#> Chain 2: Iteration: 1450 / 1500 [ 96%] (Sampling)
#> Chain 2: Iteration: 1500 / 1500 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 0.14 seconds (Warm-up)
#> Chain 2: 0.071 seconds (Sampling)
#> Chain 2: 0.211 seconds (Total)
#> Chain 2:
#> Inference for Stan model: dist_fit.
#> 2 chains, each with iter=1500; warmup=1000; thin=1;
#> post-warmup draws per chain=500, total post-warmup draws=1000.
#>
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
#> lambda[1] 2.81 0.02 0.49 1.96 2.50 2.76 3.10 3.96 432 1.00
#> lp__ -13.12 0.04 0.75 -15.18 -13.32 -12.80 -12.64 -12.60 371 1.02
#>
#> Samples were drawn using NUTS(diag_e) at Fri Mar 21 18:53:29 2025.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).
# integer adjusted gamma model
dist_fit(rgamma(1:100, 5, 5),
samples = 1000, dist = "gamma",
cores = ifelse(interactive(), 4, 1), verbose = TRUE
)
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 0.000298 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 2.98 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 1500 [ 0%] (Warmup)
#> Chain 1: Iteration: 50 / 1500 [ 3%] (Warmup)
#> Chain 1: Iteration: 100 / 1500 [ 6%] (Warmup)
#> Chain 1: Iteration: 150 / 1500 [ 10%] (Warmup)
#> Chain 1: Iteration: 200 / 1500 [ 13%] (Warmup)
#> Chain 1: Iteration: 250 / 1500 [ 16%] (Warmup)
#> Chain 1: Iteration: 300 / 1500 [ 20%] (Warmup)
#> Chain 1: Iteration: 350 / 1500 [ 23%] (Warmup)
#> Chain 1: Iteration: 400 / 1500 [ 26%] (Warmup)
#> Chain 1: Iteration: 450 / 1500 [ 30%] (Warmup)
#> Chain 1: Iteration: 500 / 1500 [ 33%] (Warmup)
#> Chain 1: Iteration: 550 / 1500 [ 36%] (Warmup)
#> Chain 1: Iteration: 600 / 1500 [ 40%] (Warmup)
#> Chain 1: Iteration: 650 / 1500 [ 43%] (Warmup)
#> Chain 1: Iteration: 700 / 1500 [ 46%] (Warmup)
#> Chain 1: Iteration: 750 / 1500 [ 50%] (Warmup)
#> Chain 1: Iteration: 800 / 1500 [ 53%] (Warmup)
#> Chain 1: Iteration: 850 / 1500 [ 56%] (Warmup)
#> Chain 1: Iteration: 900 / 1500 [ 60%] (Warmup)
#> Chain 1: Iteration: 950 / 1500 [ 63%] (Warmup)
#> Chain 1: Iteration: 1000 / 1500 [ 66%] (Warmup)
#> Chain 1: Iteration: 1001 / 1500 [ 66%] (Sampling)
#> Chain 1: Iteration: 1050 / 1500 [ 70%] (Sampling)
#> Chain 1: Iteration: 1100 / 1500 [ 73%] (Sampling)
#> Chain 1: Iteration: 1150 / 1500 [ 76%] (Sampling)
#> Chain 1: Iteration: 1200 / 1500 [ 80%] (Sampling)
#> Chain 1: Iteration: 1250 / 1500 [ 83%] (Sampling)
#> Chain 1: Iteration: 1300 / 1500 [ 86%] (Sampling)
#> Chain 1: Iteration: 1350 / 1500 [ 90%] (Sampling)
#> Chain 1: Iteration: 1400 / 1500 [ 93%] (Sampling)
#> Chain 1: Iteration: 1450 / 1500 [ 96%] (Sampling)
#> Chain 1: Iteration: 1500 / 1500 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 2.338 seconds (Warm-up)
#> Chain 1: 1.442 seconds (Sampling)
#> Chain 1: 3.78 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 0.000318 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 3.18 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 1500 [ 0%] (Warmup)
#> Chain 2: Iteration: 50 / 1500 [ 3%] (Warmup)
#> Chain 2: Iteration: 100 / 1500 [ 6%] (Warmup)
#> Chain 2: Iteration: 150 / 1500 [ 10%] (Warmup)
#> Chain 2: Iteration: 200 / 1500 [ 13%] (Warmup)
#> Chain 2: Iteration: 250 / 1500 [ 16%] (Warmup)
#> Chain 2: Iteration: 300 / 1500 [ 20%] (Warmup)
#> Chain 2: Iteration: 350 / 1500 [ 23%] (Warmup)
#> Chain 2: Iteration: 400 / 1500 [ 26%] (Warmup)
#> Chain 2: Iteration: 450 / 1500 [ 30%] (Warmup)
#> Chain 2: Iteration: 500 / 1500 [ 33%] (Warmup)
#> Chain 2: Iteration: 550 / 1500 [ 36%] (Warmup)
#> Chain 2: Iteration: 600 / 1500 [ 40%] (Warmup)
#> Chain 2: Iteration: 650 / 1500 [ 43%] (Warmup)
#> Chain 2: Iteration: 700 / 1500 [ 46%] (Warmup)
#> Chain 2: Iteration: 750 / 1500 [ 50%] (Warmup)
#> Chain 2: Iteration: 800 / 1500 [ 53%] (Warmup)
#> Chain 2: Iteration: 850 / 1500 [ 56%] (Warmup)
#> Chain 2: Iteration: 900 / 1500 [ 60%] (Warmup)
#> Chain 2: Iteration: 950 / 1500 [ 63%] (Warmup)
#> Chain 2: Iteration: 1000 / 1500 [ 66%] (Warmup)
#> Chain 2: Iteration: 1001 / 1500 [ 66%] (Sampling)
#> Chain 2: Iteration: 1050 / 1500 [ 70%] (Sampling)
#> Chain 2: Iteration: 1100 / 1500 [ 73%] (Sampling)
#> Chain 2: Iteration: 1150 / 1500 [ 76%] (Sampling)
#> Chain 2: Iteration: 1200 / 1500 [ 80%] (Sampling)
#> Chain 2: Iteration: 1250 / 1500 [ 83%] (Sampling)
#> Chain 2: Iteration: 1300 / 1500 [ 86%] (Sampling)
#> Chain 2: Iteration: 1350 / 1500 [ 90%] (Sampling)
#> Chain 2: Iteration: 1400 / 1500 [ 93%] (Sampling)
#> Chain 2: Iteration: 1450 / 1500 [ 96%] (Sampling)
#> Chain 2: Iteration: 1500 / 1500 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 2.509 seconds (Warm-up)
#> Chain 2: 1 seconds (Sampling)
#> Chain 2: 3.509 seconds (Total)
#> Chain 2:
#> WARN [2025-03-21 18:53:36] dist_fit (chain: 1): Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#bulk-ess -
#> WARN [2025-03-21 18:53:36] dist_fit (chain: 1): Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
#> Running the chains for more iterations may help. See
#> https://mc-stan.org/misc/warnings.html#tail-ess -
#> Inference for Stan model: dist_fit.
#> 2 chains, each with iter=1500; warmup=1000; thin=1;
#> post-warmup draws per chain=500, total post-warmup draws=1000.
#>
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
#> alpha_raw[1] 0.74 0.04 0.52 0.07 0.34 0.65 1.03 2.02 189 1.01
#> beta_raw[1] 0.95 0.04 0.54 0.11 0.53 0.92 1.30 2.07 180 1.01
#> alpha[1] 6.37 0.04 0.52 5.70 5.96 6.27 6.66 7.64 189 1.01
#> beta[1] 6.77 0.04 0.54 5.93 6.35 6.74 7.12 7.90 180 1.01
#> lp__ -11.53 0.10 1.21 -14.78 -12.18 -11.23 -10.55 -10.13 146 1.01
#>
#> Samples were drawn using NUTS(diag_e) at Fri Mar 21 18:53:36 2025.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).
# integer adjusted lognormal model
dist_fit(rlnorm(1:100, log(5), 0.2),
samples = 1000, dist = "lognormal",
cores = ifelse(interactive(), 4, 1), verbose = TRUE
)
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 1).
#> Chain 1: Rejecting initial value:
#> Chain 1: Log probability evaluates to log(0), i.e. negative infinity.
#> Chain 1: Stan can't start sampling from this initial value.
#> Chain 1:
#> Chain 1: Gradient evaluation took 5.6e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.56 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 1500 [ 0%] (Warmup)
#> Chain 1: Iteration: 50 / 1500 [ 3%] (Warmup)
#> Chain 1: Iteration: 100 / 1500 [ 6%] (Warmup)
#> Chain 1: Iteration: 150 / 1500 [ 10%] (Warmup)
#> Chain 1: Iteration: 200 / 1500 [ 13%] (Warmup)
#> Chain 1: Iteration: 250 / 1500 [ 16%] (Warmup)
#> Chain 1: Iteration: 300 / 1500 [ 20%] (Warmup)
#> Chain 1: Iteration: 350 / 1500 [ 23%] (Warmup)
#> Chain 1: Iteration: 400 / 1500 [ 26%] (Warmup)
#> Chain 1: Iteration: 450 / 1500 [ 30%] (Warmup)
#> Chain 1: Iteration: 500 / 1500 [ 33%] (Warmup)
#> Chain 1: Iteration: 550 / 1500 [ 36%] (Warmup)
#> Chain 1: Iteration: 600 / 1500 [ 40%] (Warmup)
#> Chain 1: Iteration: 650 / 1500 [ 43%] (Warmup)
#> Chain 1: Iteration: 700 / 1500 [ 46%] (Warmup)
#> Chain 1: Iteration: 750 / 1500 [ 50%] (Warmup)
#> Chain 1: Iteration: 800 / 1500 [ 53%] (Warmup)
#> Chain 1: Iteration: 850 / 1500 [ 56%] (Warmup)
#> Chain 1: Iteration: 900 / 1500 [ 60%] (Warmup)
#> Chain 1: Iteration: 950 / 1500 [ 63%] (Warmup)
#> Chain 1: Iteration: 1000 / 1500 [ 66%] (Warmup)
#> Chain 1: Iteration: 1001 / 1500 [ 66%] (Sampling)
#> Chain 1: Iteration: 1050 / 1500 [ 70%] (Sampling)
#> Chain 1: Iteration: 1100 / 1500 [ 73%] (Sampling)
#> Chain 1: Iteration: 1150 / 1500 [ 76%] (Sampling)
#> Chain 1: Iteration: 1200 / 1500 [ 80%] (Sampling)
#> Chain 1: Iteration: 1250 / 1500 [ 83%] (Sampling)
#> Chain 1: Iteration: 1300 / 1500 [ 86%] (Sampling)
#> Chain 1: Iteration: 1350 / 1500 [ 90%] (Sampling)
#> Chain 1: Iteration: 1400 / 1500 [ 93%] (Sampling)
#> Chain 1: Iteration: 1450 / 1500 [ 96%] (Sampling)
#> Chain 1: Iteration: 1500 / 1500 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.312 seconds (Warm-up)
#> Chain 1: 0.155 seconds (Sampling)
#> Chain 1: 0.467 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'dist_fit' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 5.2e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.52 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 1500 [ 0%] (Warmup)
#> Chain 2: Iteration: 50 / 1500 [ 3%] (Warmup)
#> Chain 2: Iteration: 100 / 1500 [ 6%] (Warmup)
#> Chain 2: Iteration: 150 / 1500 [ 10%] (Warmup)
#> Chain 2: Iteration: 200 / 1500 [ 13%] (Warmup)
#> Chain 2: Iteration: 250 / 1500 [ 16%] (Warmup)
#> Chain 2: Iteration: 300 / 1500 [ 20%] (Warmup)
#> Chain 2: Iteration: 350 / 1500 [ 23%] (Warmup)
#> Chain 2: Iteration: 400 / 1500 [ 26%] (Warmup)
#> Chain 2: Iteration: 450 / 1500 [ 30%] (Warmup)
#> Chain 2: Iteration: 500 / 1500 [ 33%] (Warmup)
#> Chain 2: Iteration: 550 / 1500 [ 36%] (Warmup)
#> Chain 2: Iteration: 600 / 1500 [ 40%] (Warmup)
#> Chain 2: Iteration: 650 / 1500 [ 43%] (Warmup)
#> Chain 2: Iteration: 700 / 1500 [ 46%] (Warmup)
#> Chain 2: Iteration: 750 / 1500 [ 50%] (Warmup)
#> Chain 2: Iteration: 800 / 1500 [ 53%] (Warmup)
#> Chain 2: Iteration: 850 / 1500 [ 56%] (Warmup)
#> Chain 2: Iteration: 900 / 1500 [ 60%] (Warmup)
#> Chain 2: Iteration: 950 / 1500 [ 63%] (Warmup)
#> Chain 2: Iteration: 1000 / 1500 [ 66%] (Warmup)
#> Chain 2: Iteration: 1001 / 1500 [ 66%] (Sampling)
#> Chain 2: Iteration: 1050 / 1500 [ 70%] (Sampling)
#> Chain 2: Iteration: 1100 / 1500 [ 73%] (Sampling)
#> Chain 2: Iteration: 1150 / 1500 [ 76%] (Sampling)
#> Chain 2: Iteration: 1200 / 1500 [ 80%] (Sampling)
#> Chain 2: Iteration: 1250 / 1500 [ 83%] (Sampling)
#> Chain 2: Iteration: 1300 / 1500 [ 86%] (Sampling)
#> Chain 2: Iteration: 1350 / 1500 [ 90%] (Sampling)
#> Chain 2: Iteration: 1400 / 1500 [ 93%] (Sampling)
#> Chain 2: Iteration: 1450 / 1500 [ 96%] (Sampling)
#> Chain 2: Iteration: 1500 / 1500 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 0.298 seconds (Warm-up)
#> Chain 2: 0.155 seconds (Sampling)
#> Chain 2: 0.453 seconds (Total)
#> Chain 2:
#> Inference for Stan model: dist_fit.
#> 2 chains, each with iter=1500; warmup=1000; thin=1;
#> post-warmup draws per chain=500, total post-warmup draws=1000.
#>
#> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
#> mu[1] 1.60 0.00 0.02 1.55 1.59 1.60 1.62 1.65 636 1.00
#> sigma[1] 0.19 0.00 0.02 0.15 0.17 0.19 0.20 0.22 612 1.01
#> lp__ -82.06 0.05 1.05 -84.86 -82.49 -81.69 -81.32 -81.08 457 1.00
#>
#> Samples were drawn using NUTS(diag_e) at Fri Mar 21 18:53:37 2025.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).
# }