Well, of course you cannot factor subjectivity out of the equation. I put the financial factor in it, saying that I also weigh my decision on the cost of the device. That’s quite subjective of course, otherwise we all would be listening to full stack Vivaldi …
That of choosing priors correctly has always been the main issue with the Bayesian approach. But in this case we can safely assume a non informative uniform prior: p(device is good) dist= Unif([0,1]).
Then, by applying Bayes Theorem repeatedly, you see the distribution change, hopefully become something narrow with a well defined modal value …
All this, of course, happens in on’e mind. I wouldn’t make the computations, although I have the libraries to do MonteCarlo sampling and as a pure exercise it would be interesting to see.
If you put in the model evaluations from many different people, in some cases you will obtain wide distributions with no easily identifiable mode, in others you’ll see bimodal distributions. It reflects the fact that it can be hard to reach a consensus, due to a variety of subjective evaluations.
A.