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How can I calculate the Hessian matrix for fit results with sbiofit (SimBiology)?

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Hi all,
With sbiofit (SimBiology) the fit results give me standard errors obtained from the Jacobian calculation. I would like to compute the standard errors with the Hessiana matrix, but I don't know how to get it analytically from my object function and the fit parameters.
Thank you in advance,
Valentina

답변 (1개)

Arthur Goldsipe
Arthur Goldsipe 2023년 1월 11일
I can't think of an easy way to calculate the Hessian matrix. The objective function is not analytical (since it involves approximate numerical solutions of differential equations). It's possible to estimate the Hessian numerically for situations like this, but I worry that it would be difficult to get an accurate estimate. (We already have challenges calculating the Jacobian accurately.)
Have you looked at the different options available for calculating confidence intervals using sbioparameterci or sbiopredictionci? If none of those are satisfactory, can you tell me more about what you're looking for? Can you point me to any references that describe the calculations you're trying to do? I'd like record this in our enhancment request database, and the more details the better.
-Arthur
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Arthur Goldsipe
Arthur Goldsipe 2023년 1월 13일
I'm sorry, but I still don't fully understand what you're trying to do. I think we're at the point where I need to see sample code before I can recommend anything more specific. If you're interested in that, please feel free to share code here or to reach out to me via my profile if you want to share code privately.
I'm familiar with Numerical Recipes in C, but I don't recall anything in it about Bayesian approaches. What I was hoping to get was some sort of reference that describes whatever algorithm or approach you're trying to implement, in sufficient detail that I could think about how to implement it in SimBiology.
Valentina Vasic
Valentina Vasic 2023년 1월 14일
I have forwarded you an email privately. And I would be happy if we could talk by email.

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