I have translated the codes from BUGS, Meyer and Millar (1999) about Bayesian schaefer model, to the Stan.

However, the results are partially different from the original results.

Especially, estimate of K was too big and the shape of a posterior plot had a long tails comparing to the original results of Meyer and Millar (1999)

Could I know the reasons of differences whether from my incorrect translation of coding or difference in algorithm of MCMC between Gibbs sampling and NUTS.

Data file : tuna.dat

```
C I
15.9 61.89
25.7 78.98
28.5 55.59
23.7 44.61
25.0 56.89
33.3 38.27
28.2 33.84
19.7 36.13
17.5 41.95
19.3 36.63
21.6 36.33
23.1 38.82
22.5 34.32
22.5 37.64
23.6 34.01
29.1 32.16
14.4 26.88
13.2 36.61
28.4 30.07
34.6 30.75
37.5 23.36
25.9 22.36
25.3 21.91
```

Stan code file : surplus.stan

```
data {
int<lower=0> N; // Number of row
real<lower=0> C[N]; // Catch
real<lower=0> I[N]; // CPUE
}
parameters {
real<lower=0.01, upper=2.0> P[N];
real<lower=0.01, upper=1.2> r;
real<lower=10, upper=1000> K;
real<lower=0.01, upper=0.5> q;
real sigma2;
real tau2;
}
transformed parameters {
real Pmed[N];
real Imed[N];
real sigma;
real tau;
real MSY;
real BMSY;
real EMSY;
real P1990;
real B1990;
sigma = sqrt(sigma2);
tau = sqrt(tau2);
MSY = r*K/4;
BMSY = K/2;
EMSY = r/(2*q);
P1990 = P[N]+r*P[N]*(1-P[N]) -C[N]/K;
B1990 = P1990*K;
Pmed[1] = 0;
for (t in 2:N) Pmed[t] = log(P[t-1] + r*P[t-1]*(1-P[t-1]) - C[t-1]/K);
for (t in 1:N) Imed[t] = log(q*K*P[t]);
}
model {
//Priors
K ~ lognormal(5.042905,3.7603664);
r ~ lognormal(-1.38,3.845);
q ~ inv_gamma(0.001,0.001);
sigma2 ~ inv_gamma(3.785518,0.010223);
tau2 ~ inv_gamma(1.708603,0.008613854);
//Joint likelihoods
P[1] ~ lognormal(Pmed[1],sigma);
for (t in 2:N) P[t] ~ lognormal(Pmed[t],sigma);
for (t in 1:N) I[t] ~ lognormal(Imed[t],tau);
}
```

R source file : surplus.R

```
library(rstan)
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())
setwd("C:/Users/KANGHJ/Google 드라이브/Classes/Stan/Practice/MMB")
# Set inputs
df <- read.table("tuna.dat",header = TRUE)
inp <- list(N = length(df$C),
C = df$C,
I = df$I)
# Set initial values
ini <- list(P=c(0.99,0.98,0.96,0.94,0.92,0.90,0.88,0.86,0.84,0.82,
0.80,0.78,0.76,0.74,0.72,0.70,0.68,0.66,0.64,0.62,
0.60,0.58,0.56),
r=0.8,
K=200,
iq=5,
sigma2=0.01,
tau2=0.01)
# Visualize results
set.seed(100)
fit <- stan(file = 'surplus.stan', data = inp, iter = 10000, warmup = 1000, chains= 1, control = list(adapt_delta = 0.99, max_treedepth = 15))
print(fit)
### return an array of three dimensions: iterations, chains, parameters
a <- extract(fit, inc_warmup = TRUE, permuted = FALSE)
#bayesplot
library("bayesplot")
library("rstanarm")
library("ggplot2")
plot_title <- ggtitle("Posterior distributions", "with medians and 80% intervals")
color_scheme_set("blue")
mcmc_areas(a, regex_pars = c("K","MSY","BMSY","lp__"), prob = 0.95) + plot_title
color_scheme_set("mix-blue-red")
mcmc_trace(a, pars = c("K","r"), n_warmup = 1000,
facet_args = list(nrow = 2, labeller = label_parsed)) + facet_text(size = 15);
```

My stan code : https://drive.google.com/file/d/0BwKfdyfv6WyPcE5iYkRDSjVNNWc/view?usp=sharing

My data code : https://drive.google.com/file/d/0BwKfdyfv6WyPaWtTN1ZURkIweUU/view?usp=sharing

My rstan code : https://drive.google.com/file/d/0BwKfdyfv6WyPdEFPTkNqUmhoeGc/view?usp=shari