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I have (x,y) data divided into five datasets: $D_1, D_2, \dots D_5$. The first dataset was generated randomly. Subsequent datasets were recursively generated by transforming the last dataset via a complicated transformation, so that $D_2$ was generated from $D_1$, $D_3$ from $D_2$, etc.

I want to evaluate the claim that these repeated transformations of the x/y pairs tends to structure originally unstructured data into linear data with a positive slope. What are possible ways of evaluating this claim?


Here is my tentative solution:

  • Perform bayesian linear regression on each dataset and obtain the prior likelihood that the (x,y) data are best described by a line with positive slope.

  • Plot these likelihoods against the dataset number (the subscripts) and determine whether there is a direct relationship via bayesian linear regression. A direct relationship would provide evidence that the transformations tend to structure unstructured data into linear data with a positive slope.

This made me pause because 1) I have never come across a bayesian analysis of bayesian analysis data and 2) it seems fairly complicated.

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    $\begingroup$ What is $\alpha$? Specifically, how can there be a different $\alpha$ for different datasets? $\endgroup$ Oct 26, 2017 at 4:46
  • $\begingroup$ @Juho $\alpha$ describes the hypotheses that are used to fit the datasets, analogous to 'y-intercept' if the datasets were 2d. $\endgroup$
    – Jack G.
    Oct 26, 2017 at 14:33
  • $\begingroup$ I simplified the question. Hope this is clearer! $\endgroup$
    – Jack G.
    Oct 26, 2017 at 22:48

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