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** Bayesian estimates, of pharmacokinetic parameters **

With GAM the data (covariate and individual Bayesian PM parameter estimates) would be subjected to a stepwise (single-term addition/deletion) modeling procedure. Each covariate is allowed to enter the model in any of several functional representations. The Akaike information criterion (AIC) is used as the model selection criterion (22). At each step, the model is changed by addition or deletion of a covariate that results in the largest decrease in the AIC. The search is stopped when the AIC reached a minimum value. [Pg.389]

The general principle of Bayesian parameter estimation (Beck and Katafygiotis 1998) is that uncertainties in the model parameters [Pg.1523]

Bayesian two-stage Rich data, sparse data, or a mixture of both Properly accounts for data imbalance. Good parameter estimates are usually obtained Computationally intense [Pg.2954]

NONMEM was used to estimate the parameters for each bootstrap data set. Individual Bayesian parameters were generated. These estimates along with covariates formed a new data set. [Pg.411]

Bayesian probability theory157 can also be applied to the problem of NMR parameter estimation this approach incorporates prior knowledge of the NMR parameters and is particularly useful at short aquisition times158 and when the FID contains few data points.159 Bayesian analysis gives more precise estimates of the NMR parameters than do methods based on the discrete Fourier transform (DFT).160 The amplitudes can be estimated independently of the phase, frequency and decay constants of the resonances.161 For the usual method of quadrature detection, it is appropriate to apply this technique to the two quadrature signals in the time domain.162-164 [Pg.114]

The posterior density function is the key to Bayesian parameter estimation, both for single-response and multiresponse data. Its mode gives point estimates of the parameters, and its spread can be used to calculate intervals of given probability content. These intervals indicate how well the parameters have been estimated they should always be reported. [Pg.165]

Asymptotics take on a different meaning in the Bayesian estimation context, since parameter estimators do not converge to a population quantity. Nonetheless, in a Bayesian estimation setting, as the sample size increases, the likelihood function will dominate the posterior density. What does this imply about the Bayesian estimator when this occurs. [Pg.78]

In this chapter, Bayesian and likelihood-based approaches have been described for parameter estimation from multiresponse data with unknown covariance matrix S. The Bayesian approaches permit objective estimates of 6 and E by use of the noninformative prior of Jeffreys (1961). Explicit estimation of unknown covariance elements is optional for problems of Types 1 and 2 but mandatory for Types 3 and 4. [Pg.165]

Step 2. Determination of a basic PK (or PK/PD) model using NONMEM, for example, and obtaining Bayesian individual parameter estimates. [Pg.231]

Determining the basic PK model that best describes the data and generating post hoc empiric individual Bayesian parameter estimates. [Pg.384]

The activation energies in the expressions for G and Jt were obtained by Bayesian parameter estimation, which incorporated information from density functional [Pg.318]

One drag level (Cindiv) can be used with the means and standard deviation (SD) of population parameters (Ppop) as a priori knowledge for an individual parameter estimate using the Bayesian objective function. [Pg.954]

Figure 3.13 Model parameter estimates as a function of the prior standard deviation for clearance. A 1-compartment model with absorption was fit to the data in Table 3.5 using a proportional error model and the SAAM II software system. Starting values were 5000 mL/h, 110 L, and 1.0 per hour for clearance (CL), volume of distribution (Vd), and absorption rate constant (ka), respectively. The Bayesian prior mean for clearance was fixed at 4500 mL/h while the standard deviation was systematically varied. The error bars represent the standard error of the parameter estimate. The open symbols are the parameter estimates when prior information is not included in the model. |

Gull 1989) addresses these problems classical or quantified MaxEnt (in contrast to the previously described method, now dubbed historical ). It has been implemented in the MEMSYS5 package. Imaging is treated as a Bayesian parameter estimation problem for the pixel intensities. The prior probability has the form P(f) a ), the posterior probability for data D is given by P(f ) oc with the notation of Section 3. a is [Pg.102]

If we consider the relative merits of the two forms of the optimal reconstructor, Eq. s 16 and 17, we note that both require a matrix inversion. Computationally, the size of the matrix inversion is important. Eq. 16 inverts an M x M (measurements) matrix and Eq. 17 a P x P (parameters) matrix. In a traditional least squares system there are fewer parameters estimated than there are measurements, ie M > P, indicating Eq. 16 should be used. In a Bayesian framework we are hying to reconstruct more modes than we have measurements, ie P > M, so Eq. 17 is more convenient. [Pg.380]

For simplicity and in order to avoid potential misrepresentation of the experimental equilibrium surface, we recommend the use of 2-D interpolation. Extrapolation of the experimental data should generally be avoided. It should be kept in mind that, if prediction of complete miscibility is demanded from the EoS at conditions where no data points are available, a strong prior is imposed on the parameter estimation from a Bayesian point of view. [Pg.238]

In metabolism and nutrition, where each experiment has been designed to be complete and population analysis is used to fill in missing values and to incorporate relative uncertainties into the estimation, a good procedure would be to first examine in detail those individual studies which are the most complete. This will familiarize the user with the behavior of the model, produce initial estimates for the system parameters, provide a chance to verify that these values are reasonable, and allow the use of tools for the identifiability of individual experiments (Jacquez and Perry, 1990). After this exercise has been complete, all experiments, including those that are incomplete, can be pooled for population analysis and testing the effects of covariates. If required, the final step would be to use the estimated distributions to obtain Bayesian parameter estimates for the individual experiments. This procedure should yield the most appropriate estimates for the incomplete experiments. [Pg.277]

** Bayesian estimates, of pharmacokinetic parameters **

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