Bayesian optimal designs for the Michaelis-Menten model
The Michaelis-Menten model describes the reaction velocity in many enzymatic reactions.
Using the optimal experiment design theory for non-linear regression models, we have applied the D-optimal criteria and the pseudo Bayesian D-optimal criteria and found the optimal design for each case.
When applying Bayesian optimality, there is not always a closed-form expression for the optimal design. Therefore, numerical computations have been performed for different cases. On the one hand, the expectation of any criterion according to the prior distribution has been used. On the other hand, a more sophisticated version considers an information matrix which depends on the sample size and the prior covariance matrix. We have compared the different optimal designs for both approaches and different values of the sample size. Adapted equivalence theorems allow for computation and measuring the efficiency of the designs obtained.
Palabras clave / Keywords: Bayesian optimal designs D-optimality equivalence theorem Fisher information matrix Michaelis-Menten model
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