Changed the basic workflow

[zhechengyin]

• Including the change in autoeis package (print_inference)
• Adding the example workflow with Posterior Distribution Detection (helper functions list in Wenda's commit)

[ma-sadeghi]

@zhechengyin Thanks for the PR. I've made some comments under "Files changed"

[ma-sadeghi]

Thanks for the PR. Here are my comments:

• print_inference_results needs to be moved to the code base, currently, it's defined in the notebook.
• helper_functions seem to not have been uploaded, I can only see the changed notebook under "Files changed"

[zhechengyin]

Thanks for the comments:

• I have update the print inference results to the code base, you could checked if it works or not
• helper functions should be inside the Wenda's pull request however I thinks it's too complicated for you to check between different PR, so I also include the helper functions inside the "Example folder" you could also checked it.
• PS: Sorry for late response as recently I am helping Runze with his PART II of this project, later on we will also PR the codes and thanks for your patience to check our code! In addition, sorry for doing direct changes on the main branch, as it's my first time doing the fork + clone without been authorized from the main repository, if it's really matter I would like to PR again by creating my own branch!

[RunzeZhang123]

Just added copilot as reviewer as well - just curious about trying it out and see how it performs

[Copilot]

Pull Request Overview

This pull request integrates posterior distribution quality evaluation into the AutoEIS workflow by adding new columns to the circuit inference results table and providing helper functions for posterior score calculation.

• Adds three new columns to the inference results display: "Posterior Score", "Posterior Score Rank", and "Bad Parameters"
• Changes WAIC column ordering to prioritize magnitude/phase over real/imaginary values
• Introduces helper functions for evaluating posterior distribution quality and updating circuit DataFrames with scoring metrics

Reviewed Changes

Copilot reviewed 3 out of 4 changed files in this pull request and generated 3 comments.

File	Description
src/autoeis/visualization.py	Updates print_inference_results to display new posterior evaluation columns and reorders WAIC columns
examples/helper_function/update_circuits_info.py	Adds function to integrate posterior scoring into circuits DataFrame with ranking logic
examples/helper_function/evaluate_posterior_distribution.py	Implements posterior distribution evaluation with peak detection, scoring, and optional plot generation

Comments suppressed due to low confidence (1)