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\section{Introduction}  The main use of plantation \textit{Eucalyptus} species is the production of biomass for pulp and paper, and bioenergy. These trees are fast growing fast-growing  and can potentially produce high-quality timber for appearance, structural and engineered wood products. Unfortunately, this potential is hindered by the frequent presence of large growth-strains, which are associated with log splitting, warp, collapse and brittleheart, imposing substantial costs on processing \cite{yamamoto2007slides}. A few technological mitigation strategies have been developed to reduce the incidence of wood defects caused by growth-strain, but they are costly and only partially effective \cite{yamamoto2007slides}. An alternative approach to the problem is to rely on the genetic control of growth-strain---shown in this article to be highly heritable---to select and grow individuals with low growth-strain. However, measuring growth strains in large numbers of trees (as needed for a successful breeding programme) has been difficult, time consuming and expensive until now. As an example, the largest reported studies to date assessed only 164 \cite{Murphy_2005} and 216 \cite{naranjo2012early} trees respectively.  Utilising the developments made by \cite{Chauhan_2010} \cite{Entwistle_2014}, The University of Canterbury has developed and implemented  a rapid growth strain growth-strain  testing procedure has been developed. procedure, based on the work by \citet{Chauhan_2010} and \citet{Entwistle_2014}.  In order to minimise the time taken to conduct the growth strain testing on each individual the rapid testing procedure can not account for negative values, where the wood in the centre of the stem is under tension rather than compression, resulting in a left censored dataset. Left censored data is common in research areas where detection limits are high compared to the measured values, such as testing for the presents of dugs within an animal. Bayesian statistics can be used to simulate the missing data from known data, reducing the error induced by zero inflated data sets.