llfunk_iLinear_Gaussian

Computes the log-likelihood from model-simulated values based on a Gaussian independent
error model with linearly-varying standard deviation:<ul>
<li>Yobs = Ysim + delta + epsilon</li>
<li>Measurement errors: delta~ N(0,sdev=Yu)</li>
<li>Structural errors: epsilon~ N(0,sdev=g1+g2*|Ysim|)</li>
</ul>If Yobs/Ysim are multi-variate, this error model is applied independently to each component.

An interface to the 'BaM' (Bayesian Modeling) engine,
a 'Fortran'-based executable aimed at estimating a model
with a Bayesian approach and using it for prediction,
with a particular focus on uncertainty quantification.
Classes are defined for the various building blocks of
'BaM' inference (model, data, error models, Markov Chain Monte Carlo (MCMC) samplers, predictions).
The typical usage is as follows:
(1) specify the model to be estimated;
(2) specify the inference setting (dataset, parameters, error models...);
(3) perform Bayesian-MCMC inference;
(4) read, analyse and use MCMC samples;
(5) perform prediction experiments.
Technical details are available (in French) in
Renard (2017) <https://hal.science/hal-02606929v1>.
Examples of applications include
Mansanarez et al. (2019) <doi:10.1029/2018WR023389>,
Le Coz et al. (2021) <doi:10.1002/hyp.14169>,
Perret et al. (2021) <doi:10.1029/2020WR027745>,
Darienzo et al. (2021) <doi:10.1029/2020WR028607> and
Perret et al. (2023) <doi:10.1061/JHEND8.HYENG-13101>.

Benjamin Renard

RBaM

Bayesian Modeling: Estimate a Computer Model and Make Uncertain
Predictions

INRAE 

Ministère de la Transition Ecologique - SCHAPI 

llfunk_iLinear_Gaussian function

<dl><dt>Ysim</dt>
<dd>data frame, model-simulated values.</dd>
<dt>Yobs</dt>
<dd>data frame, corresponding observed values, same dimensions as Ysim. NAs are skipped.</dd>
<dt>Yu</dt>
<dd>data frame, measurement uncertainties (standard deviations), same dimensions as Ysim and Yobs.</dd>
<dt>gamma</dt>
<dd>numeric vector, structural error parameters, organized as:
gamma=c((g1,g2) for the 1st component of Ysim,(g1,g2) for the 2nd component of Ysim, etc.)
=&gt; length(gamma) = 2*(number of columns in Ysim).</dd></dl>

Arguments

Log-likelihood function: independent-linear Gaussian — llfunk_iLinear_Gaussian

<dl>

<dt>Ysim</dt>
<dd>data frame, model-simulated values.</dd>


<dt>Yobs</dt>
<dd>data frame, corresponding observed values, same dimensions as Ysim. NAs are skipped.</dd>


<dt>Yu</dt>
<dd>data frame, measurement uncertainties (standard deviations), same dimensions as Ysim and Yobs.</dd>


<dt>gamma</dt>
<dd>numeric vector, structural error parameters, organized as:
gamma=c((g1,g2) for the 1st component of Ysim,(g1,g2) for the 2nd component of Ysim, etc.)
=&gt; length(gamma) = 2*(number of columns in Ysim).</dd>

</dl>

llfunk_iLinear_Gaussian: Log-likelihood function: independent-linear Gaussian

Description

Usage

Value

Arguments

Examples