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Dear Marcel,
Thank you so much for your prompt reply. Evaluating the log-likelihood in in the way you suggest is a good idea. I will try to implement it.
I also appreciate the code you provided. I will let you know if I incorporate it.
Best regards,
Oulimata.
Dear Marcel,
I would like to express my gratitude once again for the code you provided regarding the computation of the posterior shape. I have been working on adapting it to my code since yesterday; however, I am encountering an issue with the results. The values that I have fixed seem to be changing instead of remaining fixed.
Here is my code:
//define observations according to the targetMesh4D valuesWhile the samples are being generated correctly, the scalar values of the mesh are changing, whereas I want them to remain fixed.
I would greatly appreciate it if you could provide any insights or suggestions regarding the possible source of this error.
Thank you in advance.
Best regards,
Oulimata
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Regarding the intensity values, I have examined their variations compared to the first model. It seems that they do not change significantly. For instance, when considering 10 samples, their range falls between [9-163] and [14-178], while the actual model exhibits a variation of [2.4-96.6][8-126].
I attempted to modify the observation values, but I'm uncertain about the role of the "Points" parameter in the observations variable. Are they considered as known values? When I set them to either the mean points of the Gaussian process or the points of the target mesh, the scalar values almost not vary, and the shape remains the same across all samples.
By reducing the observation to a single point, I obtain samples that resemble those generated by my initial model. However, I am unsure how to verify if the fixed value is predicted correctly. As an experiment, I employed the following formula:
with the intention of fixing the first point and examining if all samples would have the same initial scalar value. Unfortunately, this does not appear to be the case.
Once again, thank you for your assistance.
Best regards,
Oulimata
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Dear Marcel,
Thank you once again for your response. I have successfully tested your code, and it is now working for both single and multiple points with scalar values. I greatly appreciate your assistance.
However, I would like to discuss a different scenario. In the example you provided, the coordinate points were not correlated with the scalar values. However, in my case, I have created a 4D SSM (from ScalarMeshField) where the scalar values are indeed correlated with the coordinate points of the mesh. This is why I am attempting to use regression to determine if it can predict the mesh based on the scalar values. I have already employed the Markov chain Monte Carlo method, which yielded satisfactory results. However, I would like to compare it with regression to determine which method performs better.
Regarding the correlation of the 3D coordinates in your example, I have attempted to fix one, two, or all of the coordinates (x, y, and z). Unfortunately, I am encountering unusual outcomes when doing so. For instance:
To gain a better understanding, I modified the following line in the applyDeformationAndIntensity function:
By examining the predicted coordinates, I found that in most cases, the z coordinate varied correctly, as did the x coordinate. However, the y coordinate did not exhibit the expected behavior when all coordinates were fixed.
I apologize once again for the delayed response.
Best regards,
Oulimata.
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