Comparing local calibration using random effects estimation and Bayesian calibrations: a case study with a mixed effect stem profile model

Abstract

& Key message Local site-level calibration of allometric models was scrutinized. Two Bayesian calibration methods were compared to local random effects estimations. The Bayesian calibration methods proved more effective than local estimation of random effects in reducing prediction bias. The simplest literature-based calibration can be recommended. The local calibration had minor effects on stem volume estimations. & Context The spatial variability of trees allometry has long prompted the necessity for local, site-or stand-level calibrations. Mixed-effect models have enabled a quantitative progress through a local calibration where data are available. More recently, Bayesian statistics brought new alternatives owing to their formal definition of the random effects from prior information. & Aims To compare three local calibration methods: (i) a calibration based on the estimation of the local random effects, (ii) a Bayesian calibration where prevailing measurements are used to produce prior estimations, and (iii) a Bayesian calibration reproducing a calibration based on literature data only. & Methods The three calibrations were compared using a stem taper model developed for Norway spruce in Romania. The taper model was fitted to a large dataset, then applied locally to two high-elevation sites with contrasting growing conditions. & Results The local calibration of mixed-effect models resulted in small gains and high biases. The Bayesian calibrations yielded better results, mostly because the Monte Carlo Markov Chain implementation permitted to tune of all the model's parameters simultaneously. The differences in stem volume estimations were however always very small ranging from − 5.2 to 3.3% of the non-calibrated volume. & Conclusion The Bayesian literature-like calibration performed as well as the calibration using the large dataset (4-97% bias reduction according to the tree) and can be preferred for its ease of use.

Biomass allometric models for Larix rupprechtii based on Kosak’s taper curve equations and nonlinear seemingly unrelated regression

“…In addition to the regression technique, the sample size of individual tree biomass has a substantial influence on the allometric exponent (Bouriaud et al, 2019). The allometric Linear relationship between observed and simulated data for foliage biomass.…”

Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data

“…Calibration. One feature of our model is that learned distribution of mixed effects w can be used for personalized prediction during extrapolation [Wang et al, 2014, Ditlevsen and De Gaetano, 2005, Bouriaud et al, 2019. First, we train our model to learn the parameters of distribution of z 0 , fixed effects β, and variance of random effect Σ b .…”

Calibração De Equações De Volume Em Nível De Povoamento E Parcela Para Acácia Negra

“…Este fato acontece porque as parcelas do presente estudo estão em condições de plantios e tratos silviculturais semelhantes (de SOUZA VISMARA et al, 2016). Resultados contrários foram encontrados por Bouriaud et al (2019), em que o ganho no uso de efeitos aleatórios foi maximizado, pois os talhões usados para calibração foram amostrados em locais com condições de cultivo muito diferentes. Os coeficientes 𝑏 ̂1, 𝑏 ̂2, 𝑏 ̂12 e 𝑏 ̂22 não apresentaram uma variação sistemática entre os povoamentos, ressaltando a necessidade de adicionar os povoamentos como um efeito aleatório.…”