Statistical Analyses of Lumber Strength Properties and a Likelihood-Free Method using Empirical Likelihood

Abstract

Wood materials should meet expected strength and reliability standards for safe and stable construction. The strength of lumber and wood products may degrade over time due to sustained applied stresses, a phenomenon known as the duration-of-load (DOL) effect. The inherent variability of lumber, combined with DOL, makes structural reliability analyses particularly challenging. This thesis develops statistical methodologies to address these challenges, focusing on reliability analysis, wood strength modeling, and likelihood-free inference.

Chapter 2 evaluates the reliability of lumber, accounting for the DOL effect under different load profiles based on a multimodel Bayesian framework. Three individual DOL models previously used for reliability assessment are considered: the US model, the Canadian model, and the Gamma process model. Procedures for stochastic generation of residential, snow, and wind loads are also described. We propose Bayesian model-averaging (BMA) as a method for combining the reliability estimates of individual models under a given load profile that coherently accounts for statistical uncertainty in the choice of model and parameter values. The method is applied to the analysis of a Hemlock experimental dataset, where the BMA results are illustrated via estimated reliability indices together with 95% interval bands.

Chapter 3 explores proof-loading experiments, another industrial procedure for ensuring lumber reliability and quality, besides the DOL experiment from Chapter 2. In proof-loading, a pre-determined load is applied to remove weak specimens, but this may also weaken the surviving specimens (survivors) — a phenomenon we term the damage effect. To capture and assess this effect, we propose a statistical framework that includes a damage model and a likelihood ratio test, offering advantages over existing methods by directly quantifying the damage effect. When applied to experimental data, the proposed framework successfully detects and measures the damage effect while showing good model fit. The framework also provides correlation estimates between strength properties, potentially reducing monitoring costs in industry.

Chapter 4 investigates statistical models with intractable likelihoods, such as the Canadian model discussed in Chapter 2. To address the challenge they pose to parameter inference, various likelihood-free methods have been developed, including a recently proposed synthetic empirical likelihood (SEL) approach. We introduce a new SEL estimator based on the reparametrization trick, which greatly reduces the computational burden. The asymptotic property of our SEL estimator is derived for the situation where the number of parameters equals the number of summary statistics, leading to a method that is not only faster, but also yields more accurate uncertainty quantification than conventional MCMC. The SEL approach is further extended by incorporating exponential tilting, which empirically improves performance when summary statistics outnumber parameters. Simulation studies validate the robustness and efficiency of our approach across various scenarios.