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Artificial Neural Networks
Of the many, many different ideas put forward to explain, model, and experiment with artificial cognition, one of the most practically successful is the Artificial Neural Network. Not because we’ve managed to actually create cognition with one, but because of … Continue reading
Bayesian Networks
I have mentioned before that Bayesian Inference is, in general, intractable. People like Gaussians a lot because many nice results in closedform can be derived from them, analytical treatments are in general possible and even easy to do, but for … Continue reading
Stopping rules, pvalues, and the likelihood principle
A few months ago, someone who used to be called perversesheaf came to tumblr to bash LessWrong there. Now, while there is a very large number of criticisms that can be aimed at it, both as a website and community, … Continue reading
Posted in Mathematics, Probability Theory
Tagged bayesian networks, Bayesian statistics, bayesianism, confidence intervals, credible intervals, frequentism, frequentist statistics, likelihood, likelihood function, likelihood principle, mathema, mathematics, maths, pvalues, probability theory, statistics, stopping rule, tagging maths for a friend
3 Comments
Confidence and Credibility
Three days ago I got slightly drunk with a few friends (two of which were mentioned in a recent post) and one of them and I were trying to explain to the other what the difference between confidence and credible intervals were. Since … Continue reading
Learning Bayes [part 3.5]
In part 3, I discussed the problem of finding a way of drawing a posterior point estimate of a number based on a series of point estimates that’s more “theoretically valid” than taking the median, which is the standard of the … Continue reading
An (Intuitive?) Introduction to Entropy
There’s a concept in Probability Theory called “entropy,” which borrows a bit from the physical concept of the same name. Intuitively, it’s the degree of “surprise” of an observation, or of a probability distribution. Alternatively, it’s how much information you gain … Continue reading
Truth, Probability, and Unachievable Consistency
What is truth? Many an author has written lengthy philosophical treatises that begin with exactly this question, but, however shaky my identification with the group may be, as a rationalist my first and foremost answer to that question – or my … Continue reading
Posted in Mathematics, Probability Theory, Rationality
Tagged bayesianism, mathema, mathematics, maths, probability theory, rationality, tagging maths for a friend
3 Comments
What’s logical coherence for anyway?
Time for a writeup! Or something. So I’ve written before about Logical Uncertainty in a very vague way. And a few weeks ago I wrote about a specific problem of Logical Uncertainty which was presented in the MIRI workshop. I’m gonna reference definitions and results from … Continue reading
The Gaifman Condition and the Π1Π2 problem
So I’m at a MIRI workshop on Logical Uncertainty, and I’m gonna make a more complete post about it later, but I wanted to talk about a thing that has been on my mind. So we’re trying to build a … Continue reading
Posted in Logic, Mathematics, Probability Theory
Tagged logic, logical uncertainty, mathema, mathematics, maths, miri, probability theory, tagging maths for a friend
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Absence of evidence is evidence of absence
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