22 
Fishery Bulletin 115(1) 
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Dispersion (o^j 
Theoretical age in years when 
the length is zero (-to) 
Figure 2 
Posterior densities for estimates of 3 von Bertalanffy growth function (VBGF) pa- 
rameters, (A) asymptotic length (L„), (B) growth rate coefficient (K), (C) theoreti- 
cal age in years when the length is zero i-to), and (D) dispersion (cr^) estimates of 
from the log-skew-t model with power heteroscedastic variance (solid line) and the 
homoscedastic log-normal model (dotted line). 
for probability statements for our statistical conclu- 
sions. Second, the degrees of freedom parameter v is 
directly estimated from the posterior density, whereas, 
in the frequentist approach used by Contreras-Reyes 
and Arellano-Valle (2013) and Contreras-Reyes et al. 
(2014), they are obtained manually by using profiles 
of the log-likelihood function. Thirdly, an additional 
parameter A is also considered by the log-skew-^ ap- 
proach, allowing us to model different degrees of skew- 
ness in data — something that the traditional log-nor- 
mal model does not make possible. Finally, boundary 
restrictions on each prior density can be incorporated 
in Bayesian analysis, and avoids deriving nonsensical 
parameters of the VBGF (Gasbarra et al., 2007). 
Contreras-Reyes et al. (2014) computed the VBGF 
for both sexes in southern blue whiting using the 
maximum-likelihood method and a heteroscedastic log- 
skew-^ model. Estimates reported in Contreras-Reyes 
et al. (2014) are similar to those reported here for 
southern blue whiting, except for the heteroscedastic 
parameter p. In this study, p was significantly higher 
than the one reported in Contreras-Reyes et al. (2014) 
because a prior distribution was specified for the het- 
eroscedastic parameter. This specification allows us to 
model the decreasing variance of lengths better across 
ages, given the paucity of observations in young (1-5 
years) and older (16-24 years) fish (Fig. 1C). An ad- 
equate modeling of variance, especially in young ages, 
