To simplify the computation, fY was modeled hierarchically using a Normal probability density with parameters μ (set equal to the predicted values for the xi from the rescaled δDf isoscape) and σ2∼Γ, with parameters α and β as described in the previous paragraph.
Then SAS 9.1 (PROC UNIVARIATE) was applied to estimate the density function of the normalized GI50 values using a normal kernel estimation procedure with an optimal bandwidth estimated at 0.2467 and an asymptotic mean integrated squared error (AMISE) of 0.0206.
Difference in log-transformed parasite densities among age groups were analysed using a normal GEE model with exchangeable correlation structure and semi-robust variance estimator.
DOI: http://dx.doi.org/10.7554/eLife.08274.004 10.7554/eLiFigure74.005 Figure 1 figure supplement 2. c-Fos+ cell density in the IL calculated in the analysis using a normal threshold and in an additional analysis using a strict threshold.
The PSTHs were then smoothed, using a normal convolution filter of 120 ms time-window, resulting in the time-spike density function (TSDF).
To accelerate their calculations, the topology is assumed to be known and the likelihood is approximated using a multivariate normal density.
Similar to the approach of Li et al., who used a lagged normal density function to describe flow heterogeneity, we used a gamma variate function to describe transit time heterogeneity, in order to parameterize CTH by a single parameter in this case the standard deviation of transit times.
We used a multivariate normal density classifier applied to the sniff parameters and found that a classifier relying on the differences in pleasant versus unpleasant sniff duration combined with the sniff volume for unpleasant odors effectively distinguished TD from ASD children.
Normality is preferred so as to make use of the property of conjugate priors (posterior for x tic will be a normal density, given that the prior and likelihood densities are also normal).
In the MH algorithm, a normal density with expectation equal to the parameter value from the previous MCMC cycle was used as the proposal density.
