Evaluating northern hardwood management using retrospective analysis and diameter distributions

Northern hardwood management was assessed throughout the state of Michigan using data collected on recently harvested stands in 2010 and 2011. Methods of forensic estimation of diameter at breast height were compared and an ideal, localized equation form was selected for use in reconstructing pre-harvest stand structures. Comparisons showed differences in predictive ability among available equation forms which led to substantial financial differences when used to estimate the value of removed timber. Management on all stands was then compared among state, private, and corporate landowners. Comparisons of harvest intensities against a liberal interpretation of a well-established management guideline showed that approximately one third of harvests were conducted in a manner which may imply that the guideline was followed. One third showed higher levels of removals than recommended, and one third of harvests were less intensive than recommended. Multiple management guidelines and postulated objectives were then synthesized into a novel system of harvest taxonomy, against which all harvests were compared. This further comparison showed approximately the same proportions of harvests, while distinguishing sanitation cuts and the future productive potential of harvests cut more intensely than suggested by guidelines. Stand structures are commonly represented using diameter distributions. Parametric and nonparametric techniques for describing diameter distributions were employed on pre-harvest and post-harvest data. A common polynomial regression procedure was found to be highly sensitive to the method of histogram construction which provides the data points for the regression. The discriminative ability of kernel density estimation was substantially different from that of the polynomial regression technique.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.