BDEN {seeds}

Bayesian Dynamic Elastic Net

Description

Full Bayesian algorithm to detect hidden inputs in ODE based models.The algorithm is an extension of the Dynamic Elastic Net algorithm (Engelhardt et al. 2016) inspired by the Elastic-Net Regression.

Usage

BDEN(
  odeModel,
  settings,
  mcmc_component,
  loglikelihood_func,
  gibbs_update,
  ode_sol,
  NegativeStates = FALSE,
  numbertrialsstep = 15,
  numbertrialseps = NA,
  numbertrialinner = 25,
  lambda = 0.001,
  Grad_correct = 0,
  alpha = c(1, 1, 1, 1),
  beta_init = c(1, 1, 1, 1),
  printstatesignore = FALSE
)

Arguments

odeModel

a object of class odeModel from the package seeds. The class saves the details of an experiment for easier manipulation and analysis.

settings

initial model specific settings (automatically calculated based on the nominal model and data)

mcmc_component

sampling algorithm

loglikelihood_func

likelihood function

gibbs_update

gibbs algorithm

ode_sol

ode solver

NegativeStates

Negative states are allowed

numbertrialsstep

number of gibbs updates per timepoint. This should be at least 10. Values have direct influence on the runtime.

numbertrialseps

number of samples per mcmc step. This should be greater than numberStates*500.Values have direct influence on the runtime.

numbertrialinner

number of inner samples. This should be greater 15 to guarantee a reasonable exploration of the sample space. Values have direct influnce on the runtime.

lambda

initial shrinkage parameter.

Grad_correct

correction factor for initial sigma estimate

alpha

mcmc tuning parameter (weighting of observed states)

beta_init

mcmc tuning parameter (weighting of observed states)

printstatesignore

states ignored in final output (default = FALSE)

Details

Ordinary differential equations (ODEs) are a popular approach to quantitatively model molecular networks based on biological knowledge. However, such knowledge is typically restricted. Wrongly modeled biological mechanisms as well as relevant external influence factors that are not included into the model likely manifest in major discrepancies between model predictions and experimental data. Finding the exact reasons for such observed discrepancies can be quite challenging in practice. In order to address this issue we suggest a Bayesian approach to estimate hidden influences in ODE based models. The method can distinguish between exogenous and endogenous hidden influences. Thus, we can detect wrongly specified as well as missed molecular interactions in the model. The BDEN as a new and fully probabilistic approach, supports the modeler in an algorithmic manner to identify possible sources of errors in ODE based models on the basis of experimental data. THE BDEN does not require pre-specified hyper-parameters. BDEN thus provides a systematic Bayesian computational method to identify target nodes and reconstruct the corresponding error signal including detection of missing and wrong molecular interactions within the assumed model. The method works for ODE based systems even with uncertain knowledge and noisy data. In contrast to approaches based on point estimates the Bayesian framework incorporates the given uncertainty and circumvents numerical pitfalls which frequently arise from optimization methods (Engelhardt et al. 2017).

For a complete example of the usage take a look into the vignette of the package.

Value

returns a results-object with default plot function

Examples

data(bden_uvb)

results <- BDEN(odeModel          = Model,
                lambda            = .001,
                beta_init         = c(1,1,1,1,1),
                numbertrialsstep  = 15,
                numbertrialseps   = 2000,
                numbertrialinner  = 10)