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April 2018 S M T W T F S « Dec 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Archives
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The W’s article about Evidence of Absence is confusing. They have an anecdote: A simple example of evidence of absence: A baker never fails to put finished pies on her windowsill, so if there is no pie on the windowsill, then … Continue reading
I have a confession to make. I don’t actually know Bayesian statistics. Or, any statistics at all, really. Shocking, I know. But hear me out. What I know is… Bayesian theory. I can derive Bayes’ Theorem, and I also can probably … Continue reading
At the end of my post about other ways of looking at probability, I showed you a graph of evidence against probability. This is the relevant graph: Looking at this graph was one of the most useful things I’ve ever … Continue reading
The LessWrong community has, as a sort of deeply ingrained instinct/rule, that we should never “agree to disagree” about factual matters. The map is not the territory, and if we disagree about the territory, that means at least one of … Continue reading
Bayes’ Theorem has many, many introductions online already. Those show the intuition behind using the theorem. This is going to be a stepbystep mathematical derivation of the theorem, as Jaynes explained it in his book Probability Theory: The Logic of Science. However, … Continue reading
Talking to raginrayguns again and he mentioned that a month and a half ago, Paul Christiano wrote a paper exactly on the subject of logical uncertainty. While I haven’t finished reading it yet, I’ll publish it here because it’s relevant. … Continue reading
And I forgot to mention one thing in the last post which is relevant. Gaifman, in his paper, states that if in we have that then . I’ll quickly show that that’s a theorem of my approach, and, indeed, any similar … Continue reading
In the past while, I’ve been talking to a friend about logical uncertainty. Specifically, how do we deal with the fact that we’re not logically omniscient? Usually, when , we have that . But what if we don’t know that ? What if we … Continue reading
“Numquam ponenda est pluralitas sine necessitate.“ – William of Ockham (c. 12871347) The more famous sentence attributed to William of Ockham, “Entia non sunt multiplicanda praeter necessitatem,” translated as “Entities must not be multiplied beyond necessity,” is absent from his … Continue reading
The answer is… much simpler than one might think. A mathematical proof is just a set of steps that only produce true statements given the premises. “Huh?” Well, when you want to prove something mathematically, you start with a few … Continue reading