My answer referred to the fact that using a two-sided HP-filter with just 32 observations will not work because the HP introduces considerable artifacts at the beginning and the end of the sample. If you use 32 observations, essentially your whole sample is affected.
With Bayesian estimation, you can “estimate” your model without any data. Your result will simply be your prior. Nevertheless, ideally you want your data to be informative in order to update your prior. When you are dealing with business cycles which are thought of having a duration of 8 to 20 or 32 quarters, working with just 30 observation, i.e. 1 to 1.5 cycles will be less than ideal.