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I can`t define the niche but I know it when I see it: a formal link
I can`t define the niche but I know it when I see it: a formal link

On the Sample Complexity of Reinforcement Learning with a Generative Model
On the Sample Complexity of Reinforcement Learning with a Generative Model

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A Comparison Model for Uncertain Information in

... From all of the four approaches, both classical probability approach and Bayesian approach requires the application of mathematical probability in uncertainty management. The main difference between classical probability and Bayesian theory is that Bayesian theory is also an a posteriori probability ...
Algorithmic Specified Complexity in the Game of Life
Algorithmic Specified Complexity in the Game of Life

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Faithfulness in Chain Graphs: The Gaussian Case

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Central Limit Theorems in Ergodic Theory

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Bayesian Input Variable Selection Using

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... A difficulty with this outline is that one must be careful throughout the argument that the restrictions one chooses do not remove all the neighbors of a node without matching it, which would simplify the pigeonhole principle to a triviality. It is not at all clear how one could explicitly construct ...
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Distributional properties of means of random probability measures

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Are Lock-Free Concurrent Algorithms Practically Wait

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Modeling Opponent Decision in Repeated One

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The origins and legacy of Kolmogorov`s Grundbegriffe

... frequentism would be to place it in a larger social and cultural context, emphasizing perhaps Kolmogorov’s role as the leading new Soviet mathematician. We will not ignore this context, but we are more interested in using the thinking of Kolmogorov and his predecessors to inform our own understandin ...
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On Self-Similar Traffic in ATM Queues: Definitions, Overflow

Case comment—United States v. Copeland, 369
Case comment—United States v. Copeland, 369

Nonparametric Priors on Complete Separable Metric Spaces
Nonparametric Priors on Complete Separable Metric Spaces

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Unfinished Lecture Notes

... To answer the question of Example 1.1 we need to know the distribution of the random variable X that denotes the number of Malus particles in a 2 liter sample from the Lake Diarrhea. To fix the distribution of X we have to assume something about the distribution of the Malus particles in the lake. W ...
Supplement #1B
Supplement #1B

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Inductive probability

Inductive probability attempts to give the probability of future events based on past events. It is the basis for inductive reasoning, and gives the mathematical basis for learning and the perception of patterns. It is a source of knowledge about the world.There are three sources of knowledge: inference, communication, and deduction. Communication relays information found using other methods. Deduction establishes new facts based on existing facts. Only inference establishes new facts from data.The basis of inference is Bayes' theorem. But this theorem is sometimes hard to apply and understand. The simpler method to understand inference is in terms of quantities of information.Information describing the world is written in a language. For example a simple mathematical language of propositions may be chosen. Sentences may be written down in this language as strings of characters. But in the computer it is possible to encode these sentences as strings of bits (1s and 0s). Then the language may be encoded so that the most commonly used sentences are the shortest. This internal language implicitly represents probabilities of statements.Occam's razor says the ""simplest theory, consistent with the data is most likely to be correct"". The ""simplest theory"" is interpreted as the representation of the theory written in this internal language. The theory with the shortest encoding in this internal language is most likely to be correct.
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