Chronological Path Stability/Uncertainty Analysis

[npcompl33t]

@JorgeStolfi I checked, euclidean embedding changes almost nothing about th numbers, like 0.74% difference,

I also added weak Bayesian smoothing, defined as:

Estimated probability =
(observed transition count + prior strength × prior probability)
/
(total transitions in that row + prior strength)

For prior strength 1, I add one synthetic observation’s worth of information across the entire row (not one to every possible transition).

I created the following model variants:

• Renormalize surviving weights: Keeps the original threshold and probabilities, but rescales the included weights to total 1. 
  
• Uniform Prior  1/ fixed weights: Adds weak Bayesian smoothing to the probability estimates, but retains the original threshold and pair weights. This isolates smoothing from the other changes
  
• Shared prior 1 / fixed weights Weak Bayesian smoothing toward the manuscript’s observed transition patterns, rather than toward equal probabilities. Includes all permitted rows with fixed weights.
  
• Common rows / pair weights a model where i dropped all rows that did not have at least 3 observations, essentialy leaving only 4 rows (word-start, a, o, y), so this is a particularly brutal test because it removes most of the information. 
  
• Joint Digraph JS: Treats the entire digraph table as one probability distribution and applies ordinary JS. It explicitly includes how frequent each starting glyph is, alongside what follows it. No separate row exclusions or custom row weights.
  

Here are the pages:

   


And bifolia

   

Notably, none of the above particularly changes anything. 

Note the parabola / arch is visible in MDS1 vs 2 in every chart, including the one with just 4 transition rows. 
Joint digraph JS produces an almost perfect parabola in both 1v2 and 1v3 for the pages. Its still clearly a w shape just a more curved shape.

The W is visible in every chart in MDS1 vs MDS3, except for the common weights one that strips most of the information away.  However, this does result in more or less a single line gradient, so pretty much exactly what you were asking for!

What do you think?