When the variation range of random factors is too large, a new method of piecewise linearization is put forward to achieve a better fitting precision of probability distribution.
Further, changes to the precision of prior distributions had little impact on the observed mean difference findings, suggesting these findings are highly robust.
where t(i) is the cluster number of the ith data point and (mathcal {G}(cdot,cdot)) is the gamma distribution, the conjugate prior for the precision of a normal distribution.
The precision of the prior distribution for the reading skills scores influences the posterior distribution.
For the variance of the measurement error, we assume a gamma distribution over, as this is the standard prior for the precision of a normal distribution in a hierarchical framework.
Figure 1e shows that we can increase the precision of our prior distribution by increasing its prior variance.
To do so, the precision of the prior distribution can be deflated – or, in other words, the standard error can be inflated.
The code for the random effects meta-analysis is shown in table 4. The precision of the prior distribution, prec.d[k], is determined in part (3).
Noninformative normal distributions were used as prior distributions for the parameters, a Wishart distribution for parameter precisions, and an inverse gamma distribution for the precision of the normally distributed residual error.
Lower comb angles (i.e., a more horizontal comb) would increase the width (decrease the precision) of the gravity angle distribution, and longer flights would decrease the width (increase the precision) of the flight angle distribution.
The second step is to examine how changes in the effective sample size influence the precision of the length frequency distribution.
