## Babar

This is the homepage of Babar - a tool for estimating Probability Density Functions.

Babar includes various methods for finding probability density functions (PDFs) for uncertain parameters. The tool was developed for use in radioecology where ecological models often depend on many uncertain input parameters. Often, assigned PDFs for these are based on either measurements collected from the modeled site or from databases (in which case the data is assumed to be analogues to the site of interest). In cases where there are multiple sources of data, there is a need for methods to combine or partially combine these sources and a tool for facilitating the work with these methods.

Babar includes the following methods:

*** Fitting probability density functions to observed
data**. The fitted distributions can be tested and ranked
according to best fit. Normal and Log normal distributions can be
fitted to data that have values below detection limit.

*** Weighted resampling** of several PDFs. Each PDF
is randomly sampled from, with the number of samples proportional
to the given weight of each PDF. Probability density functions can
then be fitted and tested against the resulting set of samples.

*** Pooling of studies**. Statistics from studies
(with data assumed to be be normal or log normally distributed) can
be pooled or combined (accounting for both within- and between
study variances).

*** Bayesian updating:** Updating of prior
distributions of the mean and variance with observed statistics
from a case (i.e. site/species) of interest. The prior
distributions for the mean and variance can defined as
joint-conjugate (dependent) or semi conjugate
(independent). The updated distributions form a predicted
posterior distribution that reflects the updated knowledge when
both sources of information (prior and data) are taken into
account.

*** Bayesian Hierarchical updating: Statistics of
multiple** exchangeable studies are used to simultaneously
estimate the mean and variances. The estimate of each study is
updated to take into account information gathered from all other
studies included in the analysis. The effect is a "partial pooling"
of the studies, with the amount of pooling depending on the
variation between studies, the variation within each study and the
number of samples for each study.

*** Bayesian regression updating:** Prior
distributions of the regression coefficients of a ordinary linear
regression model are updated with observed measurements of the
independent and dependent variables. The result are new
distributions of the coefficients which takes into account both the
prior statistics and new measurements.