Model selection based on parameter estimation permits the selection of the best model structure.

For each model structure, parameter estimation was performed to determine the model performance in relation to the experimental data.

To reduce the complexity of combining all model structures, we applied a “backward selection” based on the removal of single building blocks from the complete model structure followed by parameter estimation to obtain a new ranking (Fig 5B).

Based on the backward selection result, we generated combinations of model structures focusing on these four minimal models and performed parameter estimation for all eleven possible combinations (Fig 5C).

Parameter estimation .

To find the optimal parameter sets that describe the experimental data for each model structure, we performed parameter estimations .

The procedure of parameter estimation is based on multiple local optimizations of different parameter starting values.

Here, we used the data for glucose and ethanol for parameter estimation .

Model-1 and Model-2 were fitted independently using a custom evolutionary parameter estimation algorithm (81 Text).

We used the data for glucose and ethanol for parameter estimation and the data for galactose and raff1nose for validation of the models (Fig 3A).

Convergence of the objective value during parameter estimation .

Shown is the evolution of the objective values (thin lines) and the mean objective value (thick lines) over the number of iterations for 100 rounds of parameter estimation for Model-1 (red) and Model-2 (blue), respectively.

Note that in every iteration of the parameter estimation , the algorithm runs through a population of 12 different parameter sets for each model.

The parameter estimation method was next applied to four guinea pig left basal ventricular myocytes from four different animals.

To improve parameter estimation accuracy, more improvement is typically gained from adding measurements of a different state variable than adding additional measurements of the same state variable [36].

Therefore, to improve the parameter estimation accuracy, we added a multi-step voltage clamp protocol to the objective function.

We first developed our parameter estimation strategy using a guinea pig ventricular myocyte model (Faber and Rudy [34], the “FR” model) and tested the ability of the optimization procedure to return the original parameter values.

Therefore, we first ran the parameter estimation using a single FR model action potential as the target objective.

In neuroscience, considerably more research has been carried out on parameter estimation problems (e.g., [27—30]) and a few studies have developed protocols that allow parameterization of cell-specific models [31,32].

We used this stochastic stimulation protocol and resulting voltage response as an optimization sequence to test the extent to which dynamic stimulus timing would improve the parameter estimation .

Because the GA parameter estimation is a stochastic method, it was run 10 times with 10 different initial populations.

Compared to the single action potential, the stochastic stimulation leads to a modest overall improvement of the parameter estimation , but it did notably better in determining the maximal conductances of IKr, ICaL, and 1K3 (Fig 2C).

The combined stochastic current and multi-step voltage clamp protocol improves parameter estimation

Running the optimization with the combined objective does indeed lead to improved accuracy of the parameter estimation , with all nine current parameters being recovered to within one standard deviation (orange symbols, Fig 4B).

Bayesian parameter estimation and model comparison

To maximize our chances to find global, rather than local maxima using the gradient ascent algorithm, parameter estimation was repeated over a grid of initialization values.

The reward magnitude associated with each force level was adjusted on a trial-by-trial basis using an adaptive staircase algorithm, independently for each effort level ( Parameter Estimation by Sequential Testing, PEST, see [91]).

Bayesian parameter estimation and model comparison were performed as before, but using the force level produced on a given trial instead of the required target force.

The supplementary methods and results report an analysis of response time and choice based on simple regression analyses, and include additional tables reporting model parameter estimates , accuracy and complexity terms, and results of control analyses.

B, Mean (i SEM) parameter estimates from a logistic regression analysis of each participant’s choice pattern.

Individual parameter estimates (Experiment 1).

Parameter estimation and model comparisons were repeated for all models using this generic measure of utility.

Sensitivity of the parameter estimates was explored by performing MCMC separately using different subsets of the data.

The black dots are US disease incidence data, and the shaded regions represent the credible intervals (50% and 95%) obtained through model parameter estimation of model 8.

Parameter estimates for the best-fitting model, Model 8 (models outlined in Table 1).

However, when we simulated 150 or 250 spillover events instead, the uncertainty in our estimates shrank, and we were able to obtain more precise parameter estimates (88 Fig).

We tested the accuracy of parameter estimation when the transmission process was mis-specif1ed, and found that it was still possible to distinguish between different scenarios as long as transmission matrices in both the simulation and inference models were dominated by intense mixing between children.

For a higher dimensional model, it might be necessary to use an alternative technique, such as Markov chain Monte Carlo [41], to ensure robust and efficient parameter estimation .

Here we use L1-regularization and find the maximum a posteriori (MAP) parameters estimates

Gray lines show parameters estimated from bootstrap samples; solid colored lines show their averages.

Since the bilinear model has many more parameters, it is not unsurprising that there is more uncertainty in the parameter estimates given the same amount of data (200s in this case).