Edwin J. Green

Redefine Statistical Significance

We propose to change the default P-value threshold for statistical significance from 0.05 to 0.005 for claims of new discoveries.

A Bayesian growth and yield model for slash pine plantations

We formulate a traditional growth and yield model as a Bayes model. We attempt to introduce as few new assumptions as possible. Zellners Bayesian method of moments procedure is used, because the published model did not include any distributional assumptions. We generate predictive posterior samples for a number of stand variables using the Gibbs sampler. The means of the samples compare favorably with the predictions from the published model. In addition, our model delivers distributions of outcomes, from which it is easy to establish measures of uncertainty, such as highest posterior density regions.

A James-Stein Type Estimator for Combining Unbiased and Possibly Biased Estimators

Abstract We present a method for combining unbiased sample data with possibly biased auxiliary information. The estimator we derive is similar in spirit to the James–Stein estimator. We prove that the estimator dominates the sample mean under quadratic loss. When the auxiliary information is unbiased, our estimator has risk slightly greater than the usual combined estimator. As the bias increases, however, the risk of the usual estimator is unbounded, while the risk of our estimator is bounded by the risk of the sample mean. We show how our estimator can be considered an approximation to the best linear combination of the sample data and the auxiliary information, allude to how it can be derived as an empirical Bayes estimator, and suggest a method for constructing confidence sets. Finally, the performance of our estimator is compared to that of the sample mean and the usual combined estimator using real forestry data.

Landscape factors facilitating the invasive dynamics and distribution of the brown marmorated stink bug, Halyomorpha halys (Hemiptera: Pentatomidae), after arrival in the United States.

The brown marmorated stink bug, Halyomorpha halys, a native of Asia, has become a serious invasive pest in the USA. H. halys was first detected in the USA in the mid 1990s, dispersing to over 41 other states. Since 1998, H. halys has spread throughout New Jersey, becoming an important pest of agriculture, and a major nuisance in urban developments. In this study, we used spatial analysis, geostatistics, and Bayesian linear regression to investigate the invasion dynamics and colonization processes of this pest in New Jersey. We present the results of monitoring H. halys from 51 to 71 black light traps that were placed on farms throughout New Jersey from 2004 to 2011 and examined relationships between total yearly densities of H. halys and square hectares of 48 landscape/land use variables derived from urban, wetland, forest, and agriculture metadata, as well as distances to nearest highways. From these analyses we propose the following hypotheses: (1) H. halys density is strongly associated with urban developments and railroads during its initial establishment and dispersal from 2004 to 2006; (2) H. halys overwintering in multiple habitats and feeding on a variety of plants may have reduced the Allee effect, thus facilitating movement into the southernmost regions of the state by railroads from 2005 to 2008; (3) density of H. halys contracted in 2009 possibly from invading wetlands or sampling artifact; (4) subsequent invasion of H. halys from the northwest to the south in 2010 may conform to a stratified-dispersal model marked by rapid long-distance movement, from railroads and wetland rights-of-way; and (5) high densities of H. halys may be associated with agriculture in southern New Jersey in 2011. These landscape features associated with the invasion of H. halys in New Jersey may predict its potential rate of invasion across the USA and worldwide.

Incorporating uncertainty into the parameters of a forest process model

Abstract ‘Process-based’ models have been advanced to incorporate current knowledge regarding forest processes explicitly into model structure, yet uncertainty regarding these processes is often omitted from parameter estimation. This problem reflects the fact that parameters have been traditionally viewed as constants. In process models this is often unrealistic, since physiological rates and morphological characteristics, which have known variation, are often parametrized. Reasonable estimates for parameters can, and should be, abstracted from the vast body of forestry literature, and formulated into probability distributions which reflect uncertainty in their potential value. Here probability distributions are estimated for 14 physiological or morphological parameters of Pipestem , a stand-level model of carbon allocation and growth for loblolly pine ( Pinus taeda ), based on an extensive review of published information. Investigation of parameters revealed a wide range of variation in accumulated knowledge regarding their value, and led to the development of generic parameters which may be transferrable to other similar models. Parameter uncertainty also appeared tractable in some cases and might be reduced through reformulation of the model. Some parameters investigated had known co-dependency on model variables or other parameters, and may be better expressed as dependent variables. This study was part of a larger study in which a Bayesian analysis was used to assess the uncertainty in the predictions of a forest growth model.

Modeling loblolly pine canopy dynamics for a light capture model

Abstract Advances in forest modeling make it possible to estimate light capture for every tree in a stand, and may allow for improvements in modeling stand dynamics. A major difficulty in using such models is that they rely heavily on parameterization of crown characteristics, which presumably differ from stand to stand. We reformulated crown parameters of the tRAYci light capture model for describing crown shape, relative foliar shell thickness and leaf area density (LAD) into generalized equations, which can be used to describe canopy dynamics in even-aged loblolly pine ( P. taeda L . ) stands. We used parameter equations to model 8 years of change in the canopy of 36, 17-year-old experimental loblolly pine stands, planted under a variety conditions, and estimated annual light capture for every tree over the study period. The results of our analysis suggest that differences in LAD between stands were effectively captured by our parameter estimation methods, but model predictions remained sensitive to parameters describing crown shape and foliar shell thickness. Our results suggest that estimated light capture from tRAYci is somewhat robust to different parameter settings because light capture estimation is strongly influenced by individual tree dimensions, and our methods enhanced this quality. General regression equations were developed for predicting crown characterization parameters from site index, stand age and stand density, but these equations did not fully capture differences in parameter values predicted from stand measurement data. Regression analysis and C p analysis suggest that planting density was a superior predictor variable for characterizing canopy dynamics when compared to current density. Also discussed in this manuscript are general patterns in canopy dynamics with special references to tRAYci model structure and behavior.

Empirische Bayes-Schätzer zur Datenanalyse in Forstinventuren

ZusammenfassungWerden Spezialauswertungen von Forstinventuren für kleinere als die ursprünglich geplanten Aussageeinheiten verlangt, sind Ergebnisse häufig nur mit einem hohen Schätzfehler herzuleiten. Die Eignung von empirischen Bayes-Schätzern zur Verbesserung von Schätzungen für kleine Aussageeinheiten wird am Beispiel des ersten Schweizer Landesforstinventars untersucht. Eine Einführung in die Theorie empirischer Bayes-Schätzer wird gegeben, wobei einer Prozedur gefolgt wird, die auf dem James-Stein-Schätzer aufbaut und von Morris vorgestellt wurde.Der Standardfehler konnte bei der Herleitung von Volumen und Stammzahlwerten für die einzelnen Schweizer Kantone in jedem Fall verringert werden. Die einzelnen Mittelwerte wurden bei der Stammzahlschätzung durchschnittlich um etwas weniger als 25% ihres Abstandes vom Gesamtmittelwert “geschrumpft”, bei der Vorratsschätzung um 7%.Die Anwendungsmöglichkeiten von Bayes-Schätzern werden vor dem Hintergrund des gezeigten Beispiels diskutiert.SummarySpecial evaluations of forest inventories for units that are smaller than the originally planned ones can in many cases only be derived with a large error of the estimate. The feasibility of using empirical Bayes estimators for the improvement of estimates for such smaller units is investigated with the first Swiss country-wide forest survey serving as an example. An introduction into the theory of empirical Bayes estimators is given following a procedure that is based on the James-Stein estimators and has been presented by Morris.It has been possible in every instance to reduce the standard error of volume and tree number estimates for the individual Swiss cantons. Deviations of individual means from the overall mean could be “shrunk” by somewhat less than 25 percent for tree number estimates and by 7 percent for such of the standing volume.Possibilities for the application of Bayes estimators are discussed using the example presented in the paper.

Estimating tree diameter class frequencies

The problem of estimating stand tables in stands with few sample points is considered. The usual point sampling estimate of trees per hectare by diameter class is examined, along with two alternative estimators: a precision-weighted composite estimator and a pseudo-Bayes estimator. Stand tables are estimated for a subject stand with each of the three estimators in a simulation experiment. Both the composite and pseudo-Bayes estimator appear superior (in terms of average absolute error and mean squared error) to the usual estimator, although they do introduce a slight bias. The pseudo-Bayes estimator appears to perform the best. This estimator is also easier to use than the composite estimator because it does not require variance estimates.