These topics are hard, if you aren't willing to read that much, i think you're going to get stuck and not understand. I read many many books, had many very long discussions. I linked, I'd estimate (not very accurately), between .5 and 1 books worth of stuff. You don't even know what induction is (it's one of the most well known concepts in epistemology) but want to discuss epistemology without reading much. I don't know what to do with that.

Since the discussion itself is in some trouble (e.g. "Gish Galloped" comment in addition to the above issue), I propose you instead read this one thing which is about discussion itself:

http://fallibleideas.com/paths-forward

And we can see if we're on the same page about how to have a discussion, and both interested in the same kind of discussion, or not. ok?

i think Peikoff was talking about something different than the signal processing stuff. I think you misunderstood the meaning and context (btw which of his stuff have you read or listened to? any? any Rand? or were you just trying to guess what he was talking about from my blog post? cuz i was writing that post for a target audience of people who know a lot about Objectivism already and would be familiar with the stuff). His issue is about dealing with ideas, and sometimes you can figure out the answer with certainty, but sometimes you can't get that far, you don't know enough.

In my understanding, you are bringing up scenarios that are inherently probabilistic, like if you roll dice you can't know with certainty what numbers will come up. It's a different issue. Peikoff would say you can know with certainty what the odds of each number coming up are. And similarly Peikoff would say you can know with certainty what the right way to do the signal processing is, what the right math is, and arrive at a set of weighted answers which is, overall, the right answer.

The issue with signal processing, I think (not my field but i know a bit about Shannon and lossy signals), is there's random errors in signals. So it's like dice in that way.

Can you give me one worked example with partial evidential support from politics? Show me how your stuff works. Like deal with capitalism vs socialism, or liberty vs psychiatry, or environmentalism vs life. Something focused on ideas not probabilities. It can be a tiny little issue from one of those areas, it doesn't have to be a big abstract issue. Just something where it's not apparently about probabilities or maths beforehand.

Or do you think the Bayesian stuff is only very limited and think it can't handle that, and something else is needed for most stuff? (What else?)

Once we established something else, then we'll be able to look at: is it general purpose? does it cover everything? what room or purpose is left for bayes stuff? (and I think the answer will be similar to the pythagorean theorem, or trigonometry, or algebra, or the Shannon–Hartley theorem, which is useful but isn't epistemology).