Limited number of observations

I am trying to estimate my model using Bayesian methods. To my knowledge, using Bayesian methods has the advantage of not being limited on the number of observations but while trying to find a solution to my observation equation I found this post:

where I found:

I have 39 observations in my data file, will that be a problem? if yes, am I wrong about Bayesian estimation allowing us to be unrestricted on the number of observations??

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.

Thank you jpfeifer, I have already thaught of this problem. Unfortunatly I am running out of time and the only data available to me allows include 39 observations, but I am going to note this problem as a negative point of my thesis.

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