# Error message with Betancourt specification of horseshoe prior

**URL:** <https://discourse.mc-stan.org/t/error-message-with-betancourt-specification-of-horseshoe-prior/25901>\
**Category:** Modeling\
**Created:** [January 7, 2022, 9:09pm UTC](https://discourse.mc-stan.org/t/error-message-with-betancourt-specification-of-horseshoe-prior/25901 "2022-01-07T21:09:16Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![dkaplan](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/dkaplan/32/13835_2.png) [@dkaplan](https://discourse.mc-stan.org/u/dkaplan)\
**Post date:** [January 7, 2022, 9:09pm UTC](https://discourse.mc-stan.org/t/error-message-with-betancourt-specification-of-horseshoe-prior/25901/1 "2022-01-07T21:09:16Z")

</div>

Hi all,

I’m trying to run an analysis using the horseshoe specification in Bayes Sparse Regression (2018). The full code is here

```
library(rstan)
library(loo)
library(bayesplot)
library(xtable)

## Read in data ##
PISA18sampleScale <- read.csv(file.choose(),header=T)

n=nrow(PISA18sampleScale)
X = PISA18sampleScale[,2:11]
readscore = PISA18sampleScale[,1]
p=ncol(X)

data.list <- list(n=n, p=p, X=X, readscore=readscore)

modelString = "
data {
  int<lower=1> n; // Number of data
  int<lower=1> p; // Number of covariates
  matrix[n, p] X;
  real readscore[n];
}

parameters {
  vector[p] beta_tilde;
  vector<lower=0>[p] lambda;
  real<lower=0> tau_tilde;
  real alpha;
  real<lower=0> sigma;
}

model {
  // tau ~ cauchy(0, sigma)
  // beta ~ normal(0, tau * lambda)
  vector[p] beta = beta_tilde .* lambda * sigma * tau_tilde;
  
  beta_tilde ~ normal(0, 1);
  lambda ~ cauchy(0, 1);
  tau_tilde ~ cauchy(0, 1);
  
  alpha ~ normal(0, 1);
  sigma ~ cauchy(0, 1);
  
  readscore ~ normal(X' * beta + alpha, sigma);
}
"
# Start estimation

nChains = 4
nIter= 10000
thinSteps = 10
warmupSteps = floor(nIter/2)

readscore = data.list$readscore

myfitHorseshoe = stan(data=data.list,model_code=modelString,chains=nChains,
                  iter=nIter,warmup=warmupSteps,thin=thinSteps)

```

I’m getting the following error message

```
SAMPLING FOR MODEL '6a7711900e92e051ef7d7e1268a95faf' NOW (CHAIN 1).
Chain 1: Unrecoverable error evaluating the log probability at the initial value.
Chain 1: Exception: multiply: Columns of m1 (100) and Rows of m2 (10) must match in size (in 'model98d60f2608e_6a7711900e92e051ef7d7e1268a95faf' at line 29)

[1] "Error in sampler$call_sampler(args_list[[i]]) : "                                                                                                      
[2] " Exception: multiply: Columns of m1 (100) and Rows of m2 (10) must match in size (in 'model98d60f2608e_6a7711900e92e051ef7d7e1268a95faf' at line 29)"
error occurred during calling the sampler; sampling not done
> 

```

In addition this error, I’m curious why the specification tau and beta are commented out.

---

<div class="post-metadata">

**Author:** ![nhuurre](https://avatars.discourse-cdn.com/v4/letter/n/ad7895/32.png) [@nhuurre](https://discourse.mc-stan.org/u/nhuurre)\
**Post date:** [January 7, 2022, 9:59pm UTC](https://discourse.mc-stan.org/t/error-message-with-betancourt-specification-of-horseshoe-prior/25901/2 "2022-01-07T21:59:31Z")

</div>

> [@dkaplan](#):
>
> I’m trying to run an analysis using the horseshoe specification in Bayes Sparse Regression (2018).

I take it your code is [this](https://betanalpha.github.io/assets/case_studies/bayes_sparse_regression.html#35_the_horseshoe) with `M` renamed to `p`. You have matrix `X` transposed, Betancourt defines `matrix[M,N] X` but your code says `matrix[n,p] X`.  
You can leave that and simply remove the transpose operator `'` from the last line

```stan
  readscore ~ normal(X * beta + alpha, sigma); // not X'

```

> [@dkaplan](#):
>
> I’m curious why the specification tau and beta are commented out.

The model is parametrized with `tau_tilde` and `beta_tilde` instead of (more natural?) `tau` and `beta`. (I guess it’s like noncentered parametrization or something?) The model block defines the distributions for these parameter and the comments document the implied distributions for the derived parameters.  
In other words, `tau = tau_tilde * sigma` so then `tau_tilde ~ cauchy(0, 1)` is an indirect way to declare `tau ~ cauchy(0, sigma)`.

---

<div class="post-metadata">

**Author:** ![dkaplan](https://yyz2.discourse-cdn.com/flex030/user_avatar/discourse.mc-stan.org/dkaplan/32/13835_2.png) [@dkaplan](https://discourse.mc-stan.org/u/dkaplan)\
**Post date:** [January 7, 2022, 10:55pm UTC](https://discourse.mc-stan.org/t/error-message-with-betancourt-specification-of-horseshoe-prior/25901/3 "2022-01-07T22:55:34Z")

</div>

Thanks very much. That was a silly mistake. It seems to be working but throwing divergent transition errors. I’m playing with the adapt\_delta value and hopefully that will help.