Organize MBDoE Analyses

[bbefort]

To finish up the MBDoE Analysis, we need to do the following:

@jialuw96 JW:

• [x] perform FIM analysis for data points with the most information Wednesday, 10/26

• Discuss with BB, KW

• [ ] perform the FIM analysis for all the models for R125/emimTF2N and R32bmimPF6 systems Thursday, 10/27

• [ ] clean up plots: Wednesday, 10/26

• y-axis: "HFC-32 in IL [mol%]",

• color bar -- change pressure to MPa from bar

• smooth out jagged edges of optimality plots

@dipperwang5 KW:

• [x] clean up plots Wednesday, 10/26

• deal with scaling issue?

• Change x-axis label to "Experiment Number"

@bbefort BB:

• [x] Update methods (add in lit review for MBDoE, improved descriptions for MBDoE analyses, ask KW for paper preprint)
• [x] Update results
• [ ] Edit paper, send out for comments Friday, 10/28

[bbefort]

[bbefort]

First column: 6 data points of prior info: (2, 5, 12, 19, 23, 26) Second column: 7 data points of prior info: (2, 5, 12, 16, 19, 23, 26) Third column: 8 data points of prior info: (2, 3, 5, 12, 16, 19, 23, 26)

[dipperwang5]

• Experiment Number

finished

[adowling2]

Does this have the correct scaling? I think there was a mistake. See my prior comments.

[dipperwang5]

Does this have the correct scaling? I think there was a mistake. See my prior comments.

This should be the result after FIM dividing 1e-10

[adowling2]

This was the original figure. I think the scaling is wrong. My intuition is for log10(det(M)) to be O(1) to O(20). Look through our discussion thread for the history of my comments.

[jialuw96]

@adowling2 @bbefort Here are the heatmaps with the first 6 experiments:

With 7 experiments: the new added one is marked by a star

With 8 experiments: newly added one marked by a triangle:

For 8 experiments E and ME, there are very slight changes in heatmap that are hardly visible; I have checked that I didn't mix up figures, these are the heatmaps for 8 experiments.

For the pressure heatmap with MPa instead of Bar:

[dipperwang5]

@jialuw96 Hi Jialu, I am wondering what is the correct $log_{10}$ D-optimality when considering scaling for all experiment?

[adowling2]

@jialuw96 Can you make the symbols 50% larger. Please make the star and triangle black.

[adowling2]

@dipperwang5 and @jialuw96 you should discuss how the change the FIM when we change the units from Pa to bar for the measurements. I think a 10 minute conversation will clear this up.

[dipperwang5]

@dipperwang5 and @jialuw96 you should discuss how the change the FIM when we change the units from Pa to bar for the measurements. I think a 10 minute conversation will clear this up.

Hi Alex, this is the figure after scaling. I have done sanity check with Jialu's running result to make sure this is correct.

[adowling2]

This makes a lot more sense. The model with 6 parameters is not identifiable with fewer than 6 experiments.

Can you make a second version of this plot with y axis bounds from -5 to 5 or similar? I want to clearly see the trend with >6 experiments.

[dipperwang5]

Here is it.

[adowling2]

Let's adjust the bounds to -4, 2 to look better. Also please increase the font size for everything. I'd like to include this in my talk tomorrow.

[dipperwang5]

Let's adjust the bounds to -4, 2 to look better. Also please increase the font size for everything. I'd like to include th

is in my talk tomorrow.

[adowling2]

@bbefort @dipperwang5 @jialuw96 I think we now have a FIM unit consistency issues in the presentation.

This slide suggests that AIC #1 model is not identifiable and that log10(D-optimilty) = sum_i( log10(eigenvalue_i) ) = O(8).

Yet this slide shows log10(D-optimality) = O(1) with the updated scaling.

What do we need to do to reconcile this? @jialuw96 Do you have a new FIM decomposition that is consistent with the scaling from @dipperwang5?

[jialuw96]

@adowling2 Heatmaps with bigger markers for experiments:

6 experiments:

7 experiments:

8 experiments:

[adowling2]

Great. Thank you. Let's also add these files as .png and .pdf to GitHub in a well organized location. We'll need them for the paper.

[adowling2]

One more request. Can you add a toggle in your code to include a small '.' to show the locations of all possible experiments in the dataset? Finally, please see my prior comment about drawing the polygon.

[jialuw96]

Great. Thank you. Let's also add these files as .png and .pdf to GitHub in a well organized location. We'll need them for the paper.

I added these figures .png in folder paramest/Heatmap_figures.

One more request. Can you add a toggle in your code to include a small '.' to show the locations of all possible experiments in the dataset? Finally, please see my prior comment about drawing the polygon.

Do you mean except for these markers for prior experiments, we add comparatively smaller markers "." for other experiments in the dataset that are not prior experiments for the figure we are saying? I added this toggle.

Polygon

I plotted one sample graph:

I used "quadratic" to connect edge points with curves.

[adowling2]

@jialuw96 I would like you to add a small '.' to the plot to show each of the experiment locations in the dataset. Here is a similar plot:

But this uses stars instead of '.'. This plot shows us the experiments that are available to choose from.

Regarding the polygon, please see my comment here: #16

After you plot the data, draw a polygon that covers the region with pressures greater than 15 bar. This should hide the "jagged" edges caused by the NaNs. To specify the polygon, you will need to compute the edges. This is easy for the top and right edges which are straight lines defined by the boundaries of the plot. For the curved portion of the polygon, you will need to use 2D interpolation to find xR32 coordinates as a function of T that results in 15 bar pressure. When you use the 2D interpolation function, the x, y, and z values may not be what you expect immediately.

A few questions/comments about your plot:

• What pressure does the polygon edge correspond to?
• How many points did you identify using 2D interpolation?
• Which function did you use 'quadratic' as an input for? The polygon function or the 2D interpolation function?
• Please make the boundary and filled area of the polygon white.

[jialuw96]

@adowling2 Regarding Polygon questions:

• This polygon edge corresponds to 20 bar
• I am using 1D interpolation; Boundaries are [i, j] s.t. Pressure[i, j+1] > 20 bar and Pressure[i, j] <= 20 bar.
• For the curve function, I specified boundaries x = i, y = j, and make a interp1d between them, shaped as "quadratic".
• Updated the color:

[jialuw96]

@adowling2 Here is the candidate experiments pressure:

[adowling2]

@jialuw96 Thank you. I want this information plotted on the contour plot you made. For experiments that are in the FIM prior, please use the large black circles. For the other experiments, please use a small grey '.'

[jialuw96]

@jialuw96 Thank you. I want this information plotted on the contour plot you made. For experiments that are in the FIM prior, please use the large black circles. For the other experiments, please use a small grey '.'

I remade one of the heatmaps like this:

[jialuw96]

Delieverables from Jialu:

• [ ] Heatmaps (A-ME and pressure) with P<15 Bar. Polygon shading regions above 15 bar.
• [ ] One with 6, one with 7, one with 8, Markers shown by size we decide before. with other experiments shown by grey.