What are Bayesian Autoregressive Models

There is another whole branch of statistics called Bayesian statistics. They have their own approaches to modeling as well. Wondering how Bayesians would approach an autoregressive model?
Then let's discuss what are Bayesian Autoregressive models, in under 5 minutes!

[@nektariospaschos4553]

Thank you for the video. Looking forward for the next one!!

[@chrissun9960]

Thanks, always confused about Bayesian

[@AricLaBarr]

Thank you!

[@jonasd6000]

Thank you for providing a clear explanation of the Bayesian AR model. Unlike a standard AR model, which is unsuitable for non-stationary data, I'm curious about the applicability of the Bayesian AR model to non-stationary data. Could the Bayesian AR model potentially be used with non-stationary data, given its ability to accommodate time-varying coefficients and capture phenomena such as trends?

[@AricLaBarr]

The hardest part still deals with the lags. The lags of your target variable will continue ( I believe) to force the forecast to revert to the mean in the long run. Unless you constantly updated the coefficients, I think you are still stuck with the same stationarity worries as before.

[@rajatautensute3271]

does this mean that we can use bayesian statistics to impose a non-negativity constraint to our statistical models like ARIMA or Holt-Winters to ensure that the forecasted values can never be negative? assuming that it doesn't make sense for the forecasted values to be below zero.

[@AricLaBarr]

That would more be a transformation on the target variable - like a log transformation for example. The Bayesian piece is to set prior values on the estimation of the coefficients themselves, not restrict the target variable.

[@thecheekychinaman6713]

What would you recommend as a source to learn about BAR models?

[@AricLaBarr]

Sure thing! Here are some great resources:
First a good book by Springer:
link.springer.com/book/10.1007/b135794
Next a great paper on the subject:
people.ischool.berkeley.edu/~hal/Papers/2013/pred-present-with-bsts.pdf
Lastly, a nice website that goes through an example:
multithreaded.stitchfix.com/blog/2016/04/21/forget-arima/

[@thecheekychinaman6713]

@@AricLaBarr Thanks very much. So BSTS encompasses BAR models, was never sure of the overlap!

[@atharvanigoskar5029]

So what are you ? A bayesian or a frequentist?

[@AricLaBarr]

Yes!
So that is me avoiding to commit, but seriously, I use both sets of techniques to see which one works best. For new problems I tend to use frequentist because I don't know priors too well. For problems where I have seen the data many times before, then I like to include Bayesian techniques in my tool kit to see if they work better!