As I understand, the QR re-parameterization is useful in cases with correlated predictors, of which I believe splines would be a good example, so I coded up a spline fitting model with QR re-parameterization of the splines. It seems to get higher ESS/time as compared to the non-qr version, but when I plot the posterior samples of the function being fit, there’s some strange jagged portions at the left-hand side that don’t manifest when I do the non-qr version:

Below is the Stan code; any ideas what’s going awry?

```
data {
// n_y: number of observations in y
int n_y ;
// y: vector of observations for y
vector[n_y] y ;
// x: unique values of x
vector[n_y] x ;
//num_splines: number of splines
int num_splines ;
//splines: matrix of splines
matrix[n_y,num_splines] splines ;
}
transformed data{
matrix[num_splines,n_y] Q_ast;
Q_ast = transpose( qr_Q(splines) [, 1:num_splines] * sqrt(n_y - 1.0) ) ;
}
parameters {
// noise: measurement noise
real<lower=0> noise ;
// volatility: wiggliness of the functions
real<lower=0> volatility ;
//intercept: intercept of the function
real intercept ;
//slope: slope of the function
real slope ;
// splines_helper: helper variable for splines
row_vector[num_splines] splines_helper ;
}
transformed parameters{
// f: latent functions
vector[n_y] f ;
f = intercept + slope*x + //linear part
to_vector((volatility*cumulative_sum(splines_helper))*Q_ast) ; //wiggly part
}
model {
intercept ~ normal(0, 1) ;
slope ~ normal(0, 1) ;
volatility ~ normal(0, 1) ;
noise ~ normal(0, 1) ;
splines_helper ~ normal(0,1);
y ~ normal(f,noise);
}
```