Amplitude for paths in sample space?

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The discussion revolves around the concept of analyzing paths through a sample space, specifically whether there is an associated "amplitude" for these paths. Participants question if this amplitude refers to transition probabilities between elements in the sample space. The inquiry seeks to understand if existing studies address this relationship. Clarification on the terminology and concepts related to amplitude and transition probabilities is also sought. The conversation highlights the need for further exploration of these concepts in statistical and probabilistic contexts.
Mike2
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Is there any study anywhere considering paths through a sample space from one element to another? Is there an "amplitude" associated with these paths?
 
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Do you mean a transition probability ??
 

Thread 'Hypothesis testing: Defining H0, HA hypotheses so that ( H_A)_A' makes sense'

The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...
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