Dear stan users: I am conducting a simulation study to compare the same models fitted with 2 different likelihood functions with varying data matrix.

The first model is a single Gaussian model where I fit 3 data matrices of size (12 \times 336, 101 \times 336 and 201 \times 336) where the rows (12, 101, 201 are number of observations per block and altogether there are 336 blocks). It is assumed that y_{it} \sim N(\mu_t, \sigma) where i is the observation index and t is the block index.

Then I run this model fitted with different data size (12, 101 and 201) 50 times and each time samples 1000 posterior samples (running 4 chains with 500 iterations per chain) from this model and record the time.

Here is my result

N Mean Time SE

12 261.1882 (3.8304)

101 774.0944 (33.4542)

201 778.2316 (29.5691)

From what I understand to estimate parameters associated with a Gaussian distribution, Stan would just need the sufficient statistics in this case would be the sample mean (column mean of the data matrix), rather than calculate the loglikelihood at each observation. so with increasing number of observations, I would suspect the mean run time stays roughly the same. However, increasing N from 12 to 101, there is also a significant increase in run time but with further increases to 201, the increases in time is relatively small. If my understanding is correct, can someone please suggest me the reason why a huge increase when N=12 to N=101? as the need is just to calculate a column mean?

Thank you so much for your suggestion/ advice.