I noticed that I had a typo. I meant "data is fixed" not "hand is fixed," but I guess it was clear anyway. I see your point. Thanks for the input. I do think

I noticed that I had a typo. I meant "data is fixed" not "hand is fixed," but I guess it was clear anyway. I see your point. Thanks for the input. I do think that P(hypothesis | Data) - the Bayesian way - is more intuitive than P(Data | hypothesis). I also think that the confidence interval is often misinterpreted as a credible interval. But that does not mean that the credible interval is the right choice for every analysis. From a purely practical sense, the data is fixed when you have your sample or have collected your time series data. This is the data you have and you can observe it. I do agree that the data may change when you collect more samples or get more history. But the Bayesian framework is set up well to handle that, as today's result can be tomorrow's prior. Having said all this, I don't think this debate takes away from the use cases outlined in this post. This is not meant to read as "Bayesian versus frequentist" but rather to highlight some important benefits of Bayesian analysis. For example, if I am building a pricing model that will be used to make actual decisions and my classical model is spewing out strange coefficients that do not seem to be consistent with external data and common sense. I want to infuse that model with outside information before I use the model to make real life decisions, or just shrink it. Bayesian regression gives up a structured and transparent way to handle these types of situations.