scholarly journals Models for Tree Taper Form: The Gompertz and Vasicek Diffusion Processes Framework

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 80 ◽  
Author(s):  
Martynas Narmontas ◽  
Petras Rupšys ◽  
Edmundas Petrauskas
Keyword(s):  
Goodness Of Fit ◽  
Diffusion Processes ◽  
Parameters Estimation ◽  
Data Set ◽  
Mixed Effect ◽  
Fit Statistics ◽  
Stem Taper ◽  
Longitudinal Measurements ◽  
High Level ◽  
Taper Models

In this work, we employ stochastic differential equations (SDEs) to model tree stem taper. SDE stem taper models have some theoretical advantages over the commonly employed regression-based stem taper modeling techniques, as SDE models have both simple analytic forms and a high level of accuracy. We perform fixed- and mixed-effect parameters estimation for the stem taper models by developing an approximated maximum likelihood procedure and using a data set of longitudinal measurements from 319 mountain pine trees. The symmetric Vasicek- and asymmetric Gompertz-type diffusion processes used adequately describe stem taper evolution. The proposed SDE stem taper models are compared to four regression stem taper equations and four volume equations. Overall, the best goodness-of-fit statistics are produced by the mixed-effect parameters SDEs stem taper models. All results are obtained in the Maple computer algebra system.

scholarly journals Stochastic Models to Qualify Stem Tapers

Algorithms ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 94
Author(s):  
Edmundas Petrauskas ◽  
Petras Rupšys ◽  
Martynas Narmontas ◽  
Marius Aleinikovas ◽  
Lina Beniušienė ◽  
...  
Keyword(s):  
Tree Species ◽  
Boreal Forests ◽  
Goodness Of Fit ◽  
Diffusion Processes ◽  
Gompertz Model ◽  
Stem Volume ◽  
Black Alder ◽  
Longitudinal Measurements ◽  
Performance Statistics ◽  
Taper Models

This study examines the performance of 11 tree taper models to predict the diameter of bark at any given height and the total stem volume of eight dominant tree species in the boreal forests of Lithuania. Here, we develop eight new models using stochastic differential equations (SDEs). The symmetrical Vasicek model and asymmetrical Gompertz model are used to describe tree taper evolution, as well as geometric-type diffusion processes. These models are compared with those traditionally used for four tree taper models by using performance statistics and residual analysis. The observed dataset consists of longitudinal measurements of 3703 trees, representing the eight dominant tree species in Lithuania (pine, spruce, oak, ash, birch, black alder, white alder, and aspen). Overall, the best goodness of fit statistics of diameter predictions produced the SDE taper models. All results have been implemented in the Maple computer algebra system using the “Statistics” and “VectorCalculus” packages.

QUANTIFYING TREE DIAMETER DISTRIBUTIONS WITH ONE-DIMENSIONAL DIFFUSION PROCESSES

2010 ◽  
Vol 18 (01) ◽  
pp. 205-221 ◽  
Author(s):  
PETRAS RUPŠYS ◽  
EDMUNDAS PETRAUSKAS
Keyword(s):  
Probability Density ◽  
Goodness Of Fit ◽  
Diffusion Processes ◽  
Growth Models ◽  
Transition Probability ◽  
Diameter Distribution ◽  
Discrete Observations ◽  
Data Set ◽  
Tree Diameter ◽  
Tree Diameter Distribution

This study presents diffusion processes methodology on tree diameter distribution problem. We use stochastic differential equation methodology to derive a univariate age-dependent probability density function of a tree diameter distribution. The purpose of this paper is to investigate the relationship between the stochastic linear and logistic shape diameter growth models and diameter distribution laws. We establish the probabilistic characteristics of stochastic growth models, such as the univariate transition probability density of tree diameter, the mean and variance of tree diameter. We carry out comparison of proposed continuous time stochastic models on the basis of Hong-Li, Gini, Shapiro-Wilk goodness-of-fit statistics and normal probability plot. Parameter estimations are based on discrete observations over age of trees. To model the tree diameter distribution, as an illustrative experience, a real data set from repeated measurements on a permanent sample plot of pine (Pinus sylvestris) stand in the Kazlu Ruda district at Lithuania is used. The results are implemented in the symbolic computational language MAPLE.

Territorial Distribution of Alcohol and Drug Addictions Mortality Concerning Regional Disparities in the Slovak Republic from Year 1996 to Year 2015

2020 ◽  
Keyword(s):  
Mortality Rate ◽  
Slovak Republic ◽  
Regional Disparities ◽  
Point Of View ◽  
Extreme Position ◽  
Data Set ◽  
Female Sex ◽  
Male Sex ◽  
The Individual ◽  
High Level

BACKGROUND: This paper deals with territorial distribution of the alcohol and drug addictions mortality at a level of the districts of the Slovak Republic. AIM: The aim of the paper is to explore the relations within the administrative territorial division of the Slovak Republic, that is, between the individual districts and hence, to reveal possibly hidden relation in alcohol and drug mortality. METHODS: The analysis is divided and executed into the two fragments – one belongs to the female sex, the other one belongs to the male sex. The standardised mortality rate is computed according to a sequence of the mathematical relations. The Euclidean distance is employed to compute the similarity within each pair of a whole data set. The cluster analysis examines is performed. The clusters are created by means of the mutual distances of the districts. The data is collected from the database of the Statistical Office of the Slovak Republic for all the districts of the Slovak Republic. The covered time span begins in the year 1996 and ends in the year 2015. RESULTS: The most substantial point is that the Slovak Republic possesses the regional disparities in a field of mortality expressed by the standardised mortality rate computed particularly for the diagnoses assigned to the alcohol and drug addictions at a considerably high level. However, the female sex and the male sex have the different outcome. The Bratislava III District keeps absolutely the most extreme position. It forms an own cluster for the both sexes too. The Topoľčany District bears a similar extreme position from a point of view of the male sex. All the Bratislava districts keep their mutual notable dissimilarity. Contrariwise, evaluation of a development of the regional disparities among the districts looks like notably heterogeneously. CONCLUSIONS: There are considerable regional discrepancies throughout the districts of the Slovak Republic. Hence, it is necessary to create a common platform how to proceed with the solution of this issue.

Simple Index to Assess the Calibration Quality of Safety Performance Functions Based on Multiple Goodness-of-Fit Metrics

2021 ◽  
pp. 036119812110088
Author(s):  
Raul E. Avelar ◽  
Karen Dixon ◽  
Boniphace Kutela ◽  
Sam Klump ◽  
Beth Wemple ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Synthetic Data ◽  
Calibration Procedure ◽  
Safety Performance ◽  
Absolute Deviation ◽  
Data Set ◽  
Safety Database ◽  
Simple Index ◽  
Safety Performance Functions

The calibration of safety performance functions (SPFs) is a mechanism included in the Highway Safety Manual (HSM) to adjust SPFs in the HSM for use in intended jurisdictions. Critically, the quality of the calibration procedure must be assessed before using the calibrated SPFs. Multiple resources to aid practitioners in calibrating SPFs have been developed in the years following the publication of the HSM 1st edition. Similarly, the literature suggests multiple ways to assess the goodness-of-fit (GOF) of a calibrated SPF to a data set from a given jurisdiction. This paper uses the calibration results of multiple intersection SPFs to a large Mississippi safety database to examine the relations between multiple GOF metrics. The goal is to develop a sensible single index that leverages the joint information from multiple GOF metrics to assess overall quality of calibration. A factor analysis applied to the calibration results revealed three underlying factors explaining 76% of the variability in the data. From these results, the authors developed an index and performed a sensitivity analysis. The key metrics were found to be, in descending order: the deviation of the cumulative residual (CURE) plot from the 95% confidence area, the mean absolute deviation, the modified R-squared, and the value of the calibration factor. This paper also presents comparisons between the index and alternative scoring strategies, as well as an effort to verify the results using synthetic data. The developed index is recommended to comprehensively assess the quality of the calibrated intersection SPFs.

scholarly journals SURG-29. A SINGLE CENTRE EXPERIENCE OF USING INTRA-OPERATIVE MRI IN MANAGING PEDIATRIC CRANIAL NEURO-ONCOLOGY CASES

2020 ◽  
Vol 22 (Supplement_3) ◽  
pp. iii464-iii464
Author(s):  
Dharmendra Ganesan ◽  
Nor Faizal Ahmad Bahuri ◽  
Revathi Rajagopal ◽  
Jasmine Loh PY ◽  
Kein Seong Mun ◽  
...  
Keyword(s):  
Standard Operating Procedure ◽  
Ferromagnetic Material ◽  
Extent Of Resection ◽  
Kuala Lumpur ◽  
Data Set ◽  
Single Centre Experience ◽  
Physical Setting ◽  
Paediatric Case ◽  
High Level ◽  
The University

Abstract The University of Malaya Medical Centre, Kuala Lumpur had acquired a intraoperative MRI (iMRI) brain suite via a public private initiative in September 2015. The MRI brain suite has a SIEMENS 1.5T system with NORAS coil system and NORAS head clamps in a two room solution. We would like to retrospectively review the cranial paediatric neuro-oncology cases that had surgery in this facility from September 2015 till December 2019. We would like to discuss our experience with regard to the clear benefits and the challenges in using such technology to aid in the surgery. The challenges include the physical setting up the paediatric case preoperatively, the preparation and performing the intraoperative scan, the interpretation of intraoperative images and making a decision and the utilisation of the new MRI data set to assist in the navigation to locate the residue safely. Also discuss the utility of the intraoperative images in the decision of subsequent adjuvant management. The use of iMRI also has other technical challenges such as ensuring the perimeter around the patient is free of ferromagnetic material, the process of transfer of the patient to the scanner and as a consequence increased duration of the surgery. CONCLUSION: Many elements in the use of iMRI has a learning curve and it improves with exposure and experience. In some areas only a high level of vigilance and SOP (Standard operating procedure) is required to minimize mishaps. Currently, the iMRI gives the best means of determining extent of resection before concluding the surgery.

scholarly journals Using Ultrasound and Inflammation to Improve Prediction of Ischemic Stroke: A Secondary Analysis of the Multi-Ethnic Study of Atherosclerosis

2021 ◽  
pp. 37-43
Author(s):  
Hediyeh Baradaran ◽  
Alen Delic ◽  
Ka-Ho Wong ◽  
Nazanin Sheibani ◽  
Matthew Alexander ◽  
...  
Keyword(s):  
Ischemic Stroke ◽  
Goodness Of Fit ◽  
Primary Outcome ◽  
Stroke Risk ◽  
Secondary Analysis ◽  
Predictor Variables ◽  
Baseline Model ◽  
Fit Statistics ◽  
Ischemic Stroke Risk

Introduction: Current ischemic stroke risk prediction is primarily based on clinical factors, rather than imaging or laboratory markers. We examined the relationship between baseline ultrasound and inflammation measurements and subsequent primary ischemic stroke risk. Methods: In this secondary analysis of the Multi-Ethnic Study of Atherosclerosis (MESA), the primary outcome is the incident ischemic stroke during follow-up. The predictor variables are 9 carotid ultrasound-derived measurements and 6 serum inflammation measurements from the baseline study visit. We fit Cox regression models to the outcome of ischemic stroke. The baseline model included patient age, hypertension, diabetes, total cholesterol, smoking, and systolic blood pressure. Goodness-of-fit statistics were assessed to compare the baseline model to a model with ultrasound and inflammation predictor variables that remained significant when added to the baseline model. Results: We included 5,918 participants. The primary outcome of ischemic stroke was seen in 105 patients with a mean follow-up time of 7.7 years. In the Cox models, we found that carotid distensibility (CD), carotid stenosis (CS), and serum interleukin-6 (IL-6) were associated with incident stroke. Adding tertiles of CD, IL-6, and categories of CS to a baseline model that included traditional clinical vascular risk factors resulted in a better model fit than traditional risk factors alone as indicated by goodness-of-fit statistics. Conclusions: In a multiethnic cohort of patients without cerebrovascular disease at baseline, we found that CD, CS, and IL-6 helped predict the occurrence of primary ischemic stroke. Future research could evaluate if these basic ultrasound and serum measurements have implications for primary prevention efforts or clinical trial inclusion criteria.

scholarly journals Dark energy survey internal consistency tests of the joint cosmological probes analysis with posterior predictive distributions

2021 ◽  
Vol 503 (2) ◽  
pp. 2688-2705
Author(s):  
C Doux ◽  
E Baxter ◽  
P Lemos ◽  
C Chang ◽  
A Alarcon ◽  
...  
Keyword(s):  
Dark Energy ◽  
Internal Consistency ◽  
Goodness Of Fit ◽  
Small Scale ◽  
P Value ◽  
Posterior Predictive Distribution ◽  
Data Set ◽  
Dark Energy Survey ◽  
Data Vector ◽  
Energy Survey

ABSTRACT Beyond ΛCDM, physics or systematic errors may cause subsets of a cosmological data set to appear inconsistent when analysed assuming ΛCDM. We present an application of internal consistency tests to measurements from the Dark Energy Survey Year 1 (DES Y1) joint probes analysis. Our analysis relies on computing the posterior predictive distribution (PPD) for these data under the assumption of ΛCDM. We find that the DES Y1 data have an acceptable goodness of fit to ΛCDM, with a probability of finding a worse fit by random chance of p = 0.046. Using numerical PPD tests, supplemented by graphical checks, we show that most of the data vector appears completely consistent with expectations, although we observe a small tension between large- and small-scale measurements. A small part (roughly 1.5 per cent) of the data vector shows an unusually large departure from expectations; excluding this part of the data has negligible impact on cosmological constraints, but does significantly improve the p-value to 0.10. The methodology developed here will be applied to test the consistency of DES Year 3 joint probes data sets.

A comparison of methodological approaches to the subfamilial classification of the Naididae (Oligochaeta)

1987 ◽  
Vol 65 (3) ◽  
pp. 691-707 ◽  
Author(s):  
A. F. L. Nemec ◽  
R. O. Brinkhurst
Keyword(s):  
Data Matrix ◽  
Jaccard Coefficient ◽  
Data Set ◽  
Parsimony Method ◽  
Fit Statistics ◽  
Reconstruction Methods ◽  
Linkage Methods ◽  
The Family ◽  
First Time

A data matrix of 23 generic or subgeneric taxa versus 24 characters and a shorter matrix of 15 characters were analyzed by means of ordination, cluster analyses, parsimony, and compatibility methods (the last two of which are phylogenetic tree reconstruction methods) and the results were compared inter alia and with traditional methods. Various measures of fit for evaluating the parsimony methods were employed. There were few compatible characters in the data set, and much homoplasy, but most analyses separated a group based on Stylaria from the rest of the family, which could then be separated into four groups, recognized here for the first time as tribes (Naidini, Derini, Pristinini, and Chaetogastrini). There was less consistency of results within these groups. Modern methods produced results that do not conflict with traditional groupings. The Jaccard coefficient minimizes the significance of symplesiomorphy and complete linkage avoids chaining effects and corresponds to actual similarities, unlike single or average linkage methods, respectively. Ordination complements cluster analysis. The Wagner parsimony method was superior to the less flexible Camin–Sokal approach and produced better measure of fit statistics. All of the aforementioned methods contain areas susceptible to subjective decisions but, nevertheless, they lead to a complete disclosure of both the methods used and the assumptions made, and facilitate objective hypothesis testing rather than the presentation of conflicting phylogenies based on the different, undisclosed premises of manual approaches.

Ba-, Si- and vacancy-rich phlogopites from the talc-bearing sulfide ore deposit of La Creuse, Beaujolais, France

2018 ◽  
Vol 82 (5) ◽  
pp. 1187-1210
Author(s):  
Marie-Lola Pascal ◽  
Michel Fonteilles ◽  
Véronique Tournis ◽  
Benoît Baptiste ◽  
Jean-Louis Robert ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Monoclinic Space Group ◽  
Excess Charge ◽  
Formula Unit ◽  
X Ray Diffraction ◽  
Ore Deposit ◽  
Sulfide Ore ◽  
The Common ◽  
The Stability ◽  
High Level

ABSTRACTBa-rich and Si-rich phlogopites occur in the talc-bearing rocks of the La Creuse sulfide ore deposit in Beaujolais, France. They form a group of compositions completely separated from the common Al-rich phlogopites that occur in the surrounding talc-free metasiltites and metarhyolites, with higher Ba and Mg and lower Al contents. The Ba-rich phlogopites have a relatively narrow compositional range (0.24 to 0.80 Ba per formula unit, for 44 valencies) with high and constant Si (5.8 atoms per formula unit, apfu) and Mg + Fe (5.6 apfu), probably buffered by the presence of talc. Compared to low-Al phlogopites from talc-free rocks, the excess charge introduced by the BaK–1 substitution is compensated by interlayer vacancies. Such a high level of interlayer vacancy (0.56 pfu), related to the talc-producing metasomatic conditions, is essential for the stability of this special group of Ba-rich and Si-rich phlogopites.Single crystal X-ray diffraction analyses were performed. Ba-rich and Si-rich phlogopite is monoclinic, space group C2/m, (R = 5.31%) with a = 5.3185(5), b = 9.2136(9), c = 10.1349(11) Å and β = 100.131(11)°. The occupancies of Mg/Fe and K/Ba were refined exploring different vacancies. The solutions giving the best R factor (4.77%) and goodness-of-fit (1.06) are obtained with 15% < vacancy < 40% at the interlayer site.

scholarly journals Estimation of baseflow parameters of variable infiltration capacity model with soil and topography properties for predictions in ungauged basins

2011 ◽  
Vol 8 (4) ◽  
pp. 7017-7053 ◽  
Author(s):  
Z. Bao ◽  
J. Liu ◽  
J. Zhang ◽  
G. Fu ◽  
G. Wang ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Model Simulation ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Ungauged Basins ◽  
Variable Infiltration Capacity ◽  
Infiltration Capacity ◽  
Ungauged Catchments ◽  
Vic Model ◽  
Predictions In Ungauged Basins

Abstract. Equifinality is unavoidable when transferring model parameters from gauged catchments to ungauged catchments for predictions in ungauged basins (PUB). A framework for estimating the three baseflow parameters of variable infiltration capacity (VIC) model, directly with soil and topography properties is presented. When the new parameters setting methodology is used, the number of parameters needing to be calibrated is reduced from six to three, that leads to a decrease of equifinality and uncertainty. This is validated by Monte Carlo simulations in 24 hydro-climatic catchments in China. Using the new parameters estimation approach, model parameters become more sensitive and the extent of parameters space will be smaller when a threshold of goodness-of-fit is given. That means the parameters uncertainty is reduced with the new parameters setting methodology. In addition, the uncertainty of model simulation is estimated by the generalised likelihood uncertainty estimation (GLUE) methodology. The results indicate that the uncertainty of streamflow simulations, i.e., confidence interval, is lower with the new parameters estimation methodology compared to that used by original calibration methodology. The new baseflow parameters estimation framework could be applied in VIC model and other appropriate models for PUB.

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