Estimation of the diameter distribution of a stand marked for cutting using finite mixtures

2007 ◽  
Vol 37 (4) ◽  
pp. 817-824 ◽  
Author(s):  
Klaus Nordhausen ◽  
Tapio Nummi
Keyword(s):  
Sample Size ◽  
Finite Mixture Models ◽  
Mixture Distribution ◽  
Parametric Model ◽  
Finite Mixture ◽  
Diameter Distribution ◽  
Practical Implementation ◽  
Production Potential ◽  
Component Mixture ◽  
Reasonable Choice

The aim of this paper is to find a parametric model for the diameter distribution when a sample of trees in a stand is measured by a harvester. It has important applications prior to and during harvesting for the assessment of the production potential of the stand marked for cutting. We apply the finite mixture models for tree species separately. Our data consist of six real forest stands measured in Finland. Our results showed that, for practical implementation, a three-component Lognormal mixture distribution seemed to be a reasonable choice. The subsample analysis indicated that, for certain stands, a sample size as low as 100 provides a quite good average fit for the chosen three-component mixture distribution, but for other stands, the sample size should be much larger.

Finite Mixture Examples; MAPIS Details

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Sample Size ◽  
Importance Sampling ◽  
Mixture Distribution ◽  
Finite Mixture ◽  
Practical Implementation ◽  
Posterior Distributions ◽  
Normal Mixture ◽  
Data Set ◽  
Numerical Examples ◽  
Normal Mixture Models

Two detailed numerical examples are given in this chapter illustrating and comparing mainly the reversible jump Markov chain Monte Carlo (RJMCMC) and the maximum a posteriori/importance sampling (MAPIS) methods. The numerical examples are the well-known galaxy data set with sample size 82, and the Hidalgo stamp issues thickness data with sample size 485. A comparison is made of the estimates obtained by the RJMCMC and MAPIS methods for (i) the posterior k-distribution of the number of components, k, (ii) the predictive finite mixture distribution itself, and (iii) the posterior distributions of the component parameters and weights. The estimates obtained by MAPIS are shown to be more satisfactory and meaningful. Details are given of the practical implementation of MAPIS for five non-normal mixture models, namely: the extreme value, gamma, inverse Gaussian, lognormal, and Weibull. Mathematical details are also given of the acceptance-rejection importance sampling used in MAPIS.

An application niche for finite mixture models in forest resource surveys

2019 ◽  
Vol 49 (11) ◽  
pp. 1453-1462 ◽  
Author(s):  
Steen Magnussen ◽  
Erik Næsset ◽  
Terje Gobakken
Keyword(s):  
Mixture Models ◽  
Finite Mixture Models ◽  
Finite Mixture ◽  
Reliable Estimate ◽  
Practical Implementation ◽  
Large Sample Size ◽  
Forest Resource ◽  
Estimation Model ◽  
Southern Norway

We propose design-based inference with finite mixture models (FMM) in settings where heterogeneity cannot be addressed by more conventional modelling. In FMM, a model is estimated for each of K latent model subgroups in a population under study. We evaluated the FMM approach with a difference estimator with K = 2 in 600 replications of simulated equal probability sampling from 12 artificial populations. An example with a forest population in southern Norway demonstrated a practical implementation. The artificial populations were composed of one, two, three, or four actual model subgroups generated from models that were either of the same form as the estimation model or different. We compare bias and variance in estimates of a population mean with standard results for K = 1. All estimates with K = 2 were nearly unbiased. Bias was largest when actual subgroups were clustered on y. Variances in sample means with K = 1 were 60% larger than with K = 2. An important reduction in variance with K = 2 was confirmed in the case study. A reliable estimate of variance requires a medium to large sample size.

A finite mixture of two Weibull distributions for modeling the diameter distributions of rotated-sigmoid, uneven-aged stands

2001 ◽  
Vol 31 (9) ◽  
pp. 1654-1659 ◽  
Author(s):  
Lianjun Zhang ◽  
Jeffrey H Gove ◽  
Chuangmin Liu ◽  
William B Leak
Keyword(s):  
Model Fitting ◽  
Mixture Distribution ◽  
Finite Mixture ◽  
Diameter Distribution ◽  
Weibull Distributions ◽  
Forest Stands ◽  
Negative Exponential Function ◽  
Diameter Frequency Distribution ◽  
Negative Exponential ◽  
Diameter Distributions

The rotated-sigmoid form is a characteristic of old-growth, uneven-aged forest stands caused by past disturbances such as cutting, fire, disease, and insect attacks. The diameter frequency distribution of the rotated-sigmoid form is bimodal with the second rounded peak in the midsized classes, rather than a smooth, steeply descending, monotonic curve. In this study a finite mixture of two Weibull distributions is used to describe the diameter distributions of the rotated-sigmoid, uneven-aged forest stands. Four example stands are selected to demonstrate model fitting and comparison. Compared with a single Weibull or negative exponential function, the finite finite mixture model is the only one that fits the diameter distributions well and produces root mean square error at least four times smaller than the other two. The results show that the finite mixture distribution is a better alternative method for modeling the diameter distribution of the rotated-sigmoid, uneven-aged forest stands.

Finite Mixture Models for Nonidentical Multiple Tooled Manufacturing

2006 ◽  
Vol 128 (4) ◽  
pp. 996-1005
Author(s):  
Allen T. Bracken
Keyword(s):  
Injection Molding ◽  
Mixture Models ◽  
Finite Mixture Models ◽  
Mixture Distribution ◽  
Tail Probability ◽  
Finite Mixture ◽  
Manufacturing Processes ◽  
Tail Probabilities ◽  
Comparison Methods ◽  
Novel Method

This paper presents a novel method to assess nonidentical multiple tooled (NIMT) manufacturing processes (like multiple cavity injection molding) using finite mixture distribution (FMD) models. A stepwise methodology is presented, including supporting mathematics and statistics. The methodology is illustrated and supported by its application to two sets of real multicavity injection molding data. The method is commercially relevant and is significant in that it allows enhanced examination of the fraction of the parts nonconforming or better setting of the specification level. Included are discussions of FMD models versus normal models and novel tail probability comparison methods (ratio of tail probabilities and log PDF comparisons). The methodology is recommended for NIMT processes, and is thought to better address the adequacy evaluation of processes where there are multiple nonidentical distributions mixing in production.

Characterizing Stand and Biomass Tables from Diameter Distribution Models: A Case Study for Mixed-Hardwood Forests in Eastern Tennessee, USA

2021 ◽  
Author(s):  
Sheng-I Yang ◽  
Quang V Cao ◽  
David T Shoch ◽  
Trisha Johnson
Keyword(s):  
Mixture Model ◽  
Forest Structure ◽  
Prediction Accuracy ◽  
Hardwood Forests ◽  
Finite Mixture ◽  
Diameter Distribution ◽  
Weibull Function ◽  
Distribution Models ◽  
Component Mixture ◽  
Two Component

Abstract Accurately assessing forest structure and productivity is critical to making timely management decisions and monitoring plant communities. This study aims to evaluate the prediction accuracy of site-level stand and biomass tables from the diameter distribution models. The efficacy of the single Weibull function and two finite mixture models was compared for six species groups on three mixed-hardwood sites in eastern Tennessee, USA. To evaluate model performance, two types of stand/biomass tables were generated. The first type was constructed from all species on a given site (site-specific), whereas the second type was built for a single species from all sites (species-specific). Results indicate that both types of stand and biomass tables were consistently well quantified by the two-component mixture model in terms of goodness of fit, parsimony and robustness. The two-component mixture model better characterized the complex, multimodal diameter distributions than the single Weibull model, which underpredicted the upper portion of the distributions. The three-component model tends to overfit the data, which results in lower prediction accuracy. Among the three models examined, the two-Weibull mixture model is suggested to construct site-level stand/biomass tables, which provides more reliable and accurate predictions to assess forest structure and product class. Study Implications Compared to pine monocultures, diameter distribution models for upland mixed-hardwood forests in the Southeastern United States have not been widely explored. Mixed-hardwood forests not only supply high-quality timber for domestic and international uses, but also provide various ecosystem services and essential habitats for wildlife. The finite mixture model has been proposed for characterizing the irregular forms of diameter distribution curves, but the reliability of this method has not been explicitly examined for a wide variety of species. This study provided insights for natural resources managers to select appropriate models when modeling stand and biomass tables for mixed-hardwood forests.

scholarly journals A Finite Mixture Modelling Perspective for Combining Experts’ Opinions with an Application to Quantile-Based Risk Measures

Risks ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 115
Author(s):  
Despoina Makariou ◽  
Pauline Barrieu ◽  
George Tzougas
Keyword(s):  
Decision Making ◽  
Mixture Models ◽  
Finite Mixture Models ◽  
Risk Measures ◽  
Finite Mixture ◽  
Parametric Family ◽  
Collective Decision Making ◽  
Multiple Sources ◽  
Mixture Modelling ◽  
Expert Opinions

The key purpose of this paper is to present an alternative viewpoint for combining expert opinions based on finite mixture models. Moreover, we consider that the components of the mixture are not necessarily assumed to be from the same parametric family. This approach can enable the agent to make informed decisions about the uncertain quantity of interest in a flexible manner that accounts for multiple sources of heterogeneity involved in the opinions expressed by the experts in terms of the parametric family, the parameters of each component density, and also the mixing weights. Finally, the proposed models are employed for numerically computing quantile-based risk measures in a collective decision-making context.

scholarly journals Non-local spatially varying finite mixture models for image segmentation

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Javier Juan-Albarracín ◽  
Elies Fuster-Garcia ◽  
Alfons Juan ◽  
Juan M. García-Gómez
Keyword(s):  
Image Segmentation ◽  
Mixture Models ◽  
Finite Mixture Models ◽  
Finite Mixture ◽  
Non Local ◽  
Spatially Varying

Numerical Assessment on Edgewise Compressive Strength of Heavy Sandwich Fiberboard

2015 ◽  
Vol 724 ◽  
pp. 74-78
Author(s):  
Guang Jun Hua ◽  
Wei Min Fei ◽  
Ze Shun Liao ◽  
Yong Xie
Keyword(s):  
Compressive Strength ◽  
Sample Size ◽  
Simulation Method ◽  
Large Sample Size ◽  
Heavy Duty ◽  
Material Consumption ◽  
Shape Processing ◽  
Reasonable Choice ◽  
Correct Understanding ◽  
Corrugated Fiberboard

The application status of heavy duty corrugated paperboard and honeycomb fiberboard were reviewed. In order to contrast the edgewise compressive strength of the two typical sandwich fiberboards, the finite element models of honeycomb fiberboard and AAB flute corrugated fiberboard with large sample size were established. By numerical simulation method, the effect of structure on the edgewise compressive strength were decoupled from the factor such as the materials, material consumption, sample size and shape, processing technology and environmental conditions etc. Under the same material, material consumption and sample size, bulking analysis based on numerical method was carried out. The results show that the edgewise compressive strength of both sides of the honeycomb fiberboard is about 50% higher than that of AAB flute corrugated fiberboard, and honeycomb fiberboard is similar to bi-isotropic material. The conclusions obtained are valuable to reasonable choice of the honeycomb fiberboard and heavy duty corrugated fiberboard and correct understanding the mechanical properties of the two sandwich fiberboard.

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