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statistical analysis

Differentiating ensembles and sample spaces: Alignment between statistical mechanics and probability theory

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Preamble Sample space is the primary concept introduced in any probability and statistics books and in papers. However, there needs to be more clarity about what constitutes a sample space in general: there is no explicit distinction between the unique event set and the replica sets. The...

Bayesian rabbit holes: Decoding conditional probability with non-commutative algebra

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Preamble    The White Rabbit (Wikipedia)A novice analyst or even experienced (data) scientist would have thought that the bar notation $|$ in representing conditional probability carries some different operational mathematics. Primarily when written in explicit distribution functions $p(x|y)$....