*** has been resolved - working code below ***
Dear
I am currently trying to sample the posteriors given a beta likelihood.
f(y_i | a, b) = \frac{y_i^{(a-1)}(1-y_i)^{(b-1)}}{B(a,b)}
a = \mu\cdot\phi
b = (1-\mu)\cdot\phi
and \mu is linked by an inverse-logit function to be constraint in (0, 1).
I treat \phi as a scalar parameter, because it is already not working in this simpler case.
I also want to include some regularization priors on beta. Below you can see my try for the BLASSO by Park & Casella. I just went Bayes so I am not too experienced with all that full posterior densities etc.
As the likelihood is beta I don’t really have any sigma2 in my full posterior for beta and excluded it…
The issue:
The initial values are getting rejected once I have a large Matrix X.
If I run the code using just 40 Variables I usually get some posterior samples that do make sense.
Once the matrix gets larger (say 70 variables) the initial values are constantly rejected.
I have been trying now for a very long time. I believe the constraints in the data/parameters are all correct.
I tested 500 different seeds.
I printed the mu & phi samples and it should be proper. Yet it fails.
I hope you have an idea and can help me out…
test.csv (460.9 KB)
working code
# Data
df_data <- read.csv( ... data attached in the post ...)
y <- df_data[, 1]
x <- df_data[, -1]
dat <- list(N = length(y), M = dim(x)[2], y = y, X = x)
write("// Stan model for beta LASSO Regression
data {
int<lower=1> N;
int<lower=1> M;
int<lower=1> J;
vector<lower=0,upper=1>[N] y;
matrix[N,M] X;
matrix[N,J] Z;
}
parameters {
vector[M] beta;
vector < lower = 0 > [M] tau;
vector[J] gamma;
real alpha;
real < lower = 0 > lambda;
real < lower = 0 > sigma;
}
transformed parameters{
vector < lower = 0, upper = 1 >[N] mu; // transformed linear predictor for mean of beta distribution
vector < lower = 0 >[N] phi; // transformed linear predictor for precision of beta distribution
vector < lower = 0 >[N] A; // parameter for beta distn
vector < lower = 0 >[N] B; // parameter for beta distn
// hyperprior for lambda
real r = 1.5;
real d = 20;
for (i in 1:N) {
mu[i] = inv_logit(alpha + X[i,] * beta);
phi[i] = exp(Z[i,] * gamma);
}
A = mu .* phi;
B = (1.0 - mu) .* phi;
}
model {
// priors
lambda ~ gamma(r, d);
tau ~ exponential(lambda^2 / 2);
beta ~ normal(0, tau);
gamma ~ normal(0,2);
alpha ~ normal(0,2);
// likelihood
y ~ beta(A, B);
}
generated quantities{
vector<lower=0,upper=1>[N] y_rep;
for (n in 1:N) {
y_rep[n] = beta_rng(A[n], B[n]);
}
}
// The posterior predictive distribution",
"betaBLASSO.stan") #
fit <- stan(file='betaBLASSO.stan',
data = dat, seed=3,
warmup = 500, iter = 1000, chains = 1,
control=list(adapt_delta=0.99, max_treedepth=12))