All Questions
Tagged with computability-theory pr.probability
10 questions
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150
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Resource request (probability theory, computability theory, algebra)
I'm a first year graduate student trying to explore specific topics I might be interested in researching. Currently, I enjoy algebra, probability theory, and the computability theory side of logic, ...
- 236k
3
votes
0
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87
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Is the probability distribution of a graphon given as a graph limit computable?
Let $G_i$ be a sequence of finite graphs that is Cauchy in the space of graphons. That is, for every $\epsilon \in \mathbb Q_+$ there is a $N \in \mathbb N$ such that $$\forall n, m > N. \delta_\...
- 6,353
12
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2k
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What is the probability a random Turing machine is isomorphic to a DFA?
This is a sort of Chaitin/Omega constant type question, and so I do not expect this probability to be computable to arbitrary precision. However, it is also a very practical thing to know from the ...
- 236k
2
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1
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152
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Computationally random bitstreams and normalcy
Let $\mathbb{N}$ denote the set of non-negative integers. We can identify every bitstream, i.e. a function $s:\mathbb{N}\to \{0,1\}$, with some $A\in{\cal P}(\mathbb{N})$: take $A = s^{-1}(\{1\})$.
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19
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Which distributions can you sample if you can sample a Gaussian?
Explicitly: You have a computer that is able to pick a real number at random according to the normal distribution: $\mathcal{N}(0,1) = \frac{1}{\sqrt{2\pi}}e^{-x^2/2}$. Which distributions can this ...
- 6,045
5
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Is There An Algorithmic Complexity Of A Random Distribution
Has anyone studied an equivalent to algorithmic complexity for probability distributions?
This would be a measure which was similar to Kolmogorov complexity but look at the complexity of a (discreet ...
11
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Savings property: A transformation which turns nonnegative martingales into uniformly integrable ones
Background
I work in a subfield of computability theory called algorithmic randomness. We have been using martingales as long as probability theory (going back to work of von Mises). However, since ...
- 6,287
3
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Is a parametric family which is universally consistent for multiple quantiles impossible?
Suppose I am dead-set on using Bayesian inference on independent and identically distributed data, but I'm lazy and insist on using a parametric likelihood function come what may. I'd be reassured to ...
- 2,791
4
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6
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1k
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Are there nonequivalent randomnesses?
There are nonequivalent geometries, nonequivalent groups finite and infinite, nonequivalent logics ( fregean and nofregean http://www.formalontology.it/suszkor.htm), even nonequivalent logicians;-)
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6
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An eventually different function adding no Solovay real nor dominating function?
Definitions
I believe set theorists have studied all of the following three notions in the context of forcing extensions of a model of ZFC, $M$ (hopefully the terminology is the standard one).
A ...
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