scholarly journals Analysis of Error Structure for Additive Biomass Equations on the Use of Multivariate Likelihood Function

Forests ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 298 ◽  
Author(s):  
Lei Cao ◽  
Haikui Li
Keyword(s):  
Correction Factor ◽  
Tree Species ◽  
Likelihood Function ◽  
Weighted Average ◽  
Correction Factors ◽  
Additive Property ◽  
Error Structure ◽  
Joint Likelihood ◽  
Biomass Equations ◽  
Multivariate Likelihood

Research Highlights: this study developed additive biomass equations respectively from nonlinear regression (NLR) on original data and linear regression (LR) on a log-transformed scale by nonlinear seemingly unrelated regression (NSUR). To choose appropriate regression form, the error structures (additive vs. multiplicative) of compatible biomass equations were determined on the use of the multivariate likelihood function which extended the method of likelihood analysis to the general occasion of a contemporaneously correlated set of equations. Background and Objectives: both NLR and LR could yield the expected predictions for allometric scaling relationship. In recent studies, there are vigorous debates on which regression (NLR or LR) should apply. The main aim of this paper is to analyze the error structure of a compatible system of biomass equations to choose more appropriate regression. Materials and Methods: based on biomass data of 270 trees for three tree species, additive biomass equations were developed respectively for NLR and LR by NSUR. Multivariate likelihood functions were computed to determine the error structure based on the multivariate probability density function. The anti-log correction factor which kept the additive property was obtained separately using the arithmetic and weighted average of basic correction factors from each equation to assess two model specifications on the comparably original scale. Results: the assumption of additive error structure was well favored for an additive system of three species based on the joint likelihood function. However, the error structure of each component equation calculated from the conditional likelihood function for compatible equations might be different. The performance of additive equations corrected by a weighted average of basic correction factor from each component equation performed better than that of the arithmetic average and held good property of compatibility after corrected. Conclusions: NLR provided a better fit for additive biomass equations of three tree species. Additive equations which confirmed the responding assumption of error structure performed better. The joint likelihood function on the use of the multivariate likelihood function could be used to analyze the error structure of the additive system which was a result of a tradeoff for each component equation. Based on the average of correction factors from each component equation to correct the bias of additive equations was feasible for the hold of additive property, which might lead to a poor correction effect for some component equation.

scholarly journals Effect of aerosol composition on the performance of low-cost optical particle counter correction factors

2019 ◽  
Author(s):  
Leigh R. Crilley ◽  
Ajit Singh ◽  
Louisa J. Kramer ◽  
Marvin D. Shaw ◽  
Mohammed S. Alam ◽  
...  
Keyword(s):  
Correction Factor ◽  
Low Cost ◽  
Particle Mass ◽  
Ambient Atmosphere ◽  
Correction Factors ◽  
Aerosol Composition ◽  
Kohler Theory ◽  
Suitable Reference ◽  
Aerosol Hygroscopicity ◽  
Mass Concentrations

Abstract. There is considerable interest in using low-cost optical particle counters (OPC) to supplement existing routine air quality networks that monitor particle mass concentrations. In order to do this, low-cost OPC data needs to be cross-comparable with particle mass reference instrumentation, and as yet, there is no widely agreed methodology. Aerosol hygroscopicity is known to be a key parameter to consider when correcting particle mass concentrations derived from a low-cost OPC, particularly at high ambient Relative Humidity (RH). Correction factors have been developed that apply κ-Köhler theory to correct for the influence of water uptake by hygroscopic aerosols. We have used datasets of co-located reference particle measurements and a low-cost OPC (OPC-N2, Alphasense), collected in four cities in three continents, to explore the performance of this correction factor. We report evidence that the elevated particle mass concentrations, reported by the low-cost OPC relative to reference instrumentation, is due to bulk aerosol hygroscopicity under different RH conditions, which is determined by aerosol composition and in particular the levels of hygroscopic aerosols (sulphate and nitrate). We exploit measurements made in volcanic plumes in Nicaragua, that are predominantly composed of sulphate aerosol, as a natural experiment to demonstrate this behaviour in the ambient atmosphere, with the observed humidogram closely resembling the calculated pure sulphuric acid humidogram. The results indicate that the particle mass concentrations derived from low-cost OPCs during periods of high RH (> 60 %) need to be corrected for aerosol hygroscopic growth. We employed a correction factor based on κ-Köhler theory and observed corrected OPC-N2 PM2.5 mass concentrations to be within 33 % of reference measurements at all sites. The results indicated that an in situ derived κ (using suitable reference instrumentation) would lead to the most accurate correction relative to co-located reference instruments. Applying literature κ in the correction factor also resulted in improved performance of OPC-N2, to be within 50 % of reference. Therefore, for areas where suitable reference instrumentation for developing a local correction factor is lacking, using a literature κ value can result in a reasonable correction. For locations with low levels of hygroscopic aerosols and RH, a simple calibration against gravimetric measurements (using suitable reference instrumentation) would likely be sufficient. Whilst this study generated correction factors specific for the Alphasense OPC-N2 sensor, the calibration methodology developed is likely amenable to other low cost PM sensors.

scholarly journals The Relative Pollen Productivity and Pollen Representation of North European Trees, and Correction Factors for Tree Pollen Spectra. Determined by Surface Pollen Analyses from Forests

1970 ◽  
Vol 96 ◽  
pp. 1-99
Author(s):  
Svend Th. Andersen
Keyword(s):  
Tree Species ◽  
Small Sample ◽  
Forest Composition ◽  
Pollen Deposition ◽  
Correction Factors ◽  
Tree Crown ◽  
Tree Pollen ◽  
Surface Samples ◽  
Pollen Productivity ◽  
Pollen Analyses

The present work deals primarily with a determination of the relative pollen productivity of various trees from North Europe by means of their representation in pollen analyses of surface samples from forests, with the aim to calculate correction factors for pollen diagrams.Surface samples from 2 forests in Denmark were examined. The forest composition was determined by tree crown areas and tree basal areas in small sample plots. The relation of the tree crown areas to the tree basal areas was determined for the various tree species, and the data for crown area composition, basal area composition and tree frequency were compared.The pollen preservation in the various surface samples was examined.Data on wind conditions are mentioned in the chapter about pollen dispersal in the forest, and the various modes of pollen transfer are discussed. The amount of exotic pollen in the samples is used as a calculation basis for the tree pollen frequencies, and the occurrence and composition of the exotic pollen is discussed.The relationship of the forest composition to the tree pollen deposition is discussed. Pollen deposition and pollen productivity is expressed by a regression equation. The relative pollen productivity of the tree species is expressed in relation to a reference species, in the present case Fagus silvatica. Pollen representation and relative pollen representation are determined by a comparison of pollen percentages with percentages for areal frequency.Pollen productivity factors, pollen representation and correction factors were determined for Danish species of Quercus, Betula, Alnus, Carpinus, Ulmus, Fagus, Tilia and Fraxinus by means of the pollen frequencies in the surface samples. Corrected pollen percentages were compared with the tree areal percentages in the sample plots. Data for the pollen frequencies of forest plants other than the trees are presented. The data on trees from Denmark are compared with other data from Northern Europe, and correction factors were calculated for species of Pinus, Picea and Abies.Tree pollen spectra from outside the forest are discussed and the relative pollen representation is calculated. The present calculations of the relative pollen productivity of the trees are compared with previous estimates, and the application of the correction factors to pollen diagrams is discussed.

Strain Control Correction for Fatigue Testing in LWR Environments

2020 ◽  
Author(s):  
Marc Vankeerberghen ◽  
Alec Mclennan ◽  
Igor Simonovski ◽  
German Barrera ◽  
Sergio Arrieta Gomez ◽  
...  
Keyword(s):  
Correction Factor ◽  
Fatigue Testing ◽  
Crack Nucleation ◽  
Gauge Length ◽  
Correction Factors ◽  
Element Analysis ◽  
Cross Sectional ◽  
Strain Control ◽  
Specimen Diameter ◽  
Contact Points

Abstract During strain-controlled fatigue testing of solid bar specimens in a LWR environment within an autoclave, it is common practice to avoid the use of a gauge length extensometer to remove the risk of preferential corrosion and early crack nucleation from the extensometer contact points. Instead, displacement- or strain-control is applied at the specimen shoulders, where the cross-sectional area of the specimen is higher and so surface stress levels are lower. A correction factor is applied to the control waveform at the shoulder in order to achieve approximately the target waveform within the specimen gauge length. The correction factor is generally derived from trials conducted in air by cycling samples with extensometers attached to both the shoulders and the gauge length; typically, the average ratio between the strains or the ratio at half-life in these locations is taken to be the correction factor used in testing. These calibration trials may be supplemented by Finite Element Analysis modelling of the specimens, or by other analysis of results from the calibration trials. Within the INCEFA+ collaborative fatigue research project, a total of six organizations are performing fatigue testing in LWR environments within an autoclave. Of these, one organization is performing tests in an autoclave using extensometers attached to both the specimen shoulders and the specimen gauge length. Therefore the INCEFA+ project provides a unique opportunity to compile and compare methods of shoulder control correction used by different organizations when fatigue testing in LWR environments. This paper presents the different methods of correcting shoulder control waveforms used by partners within the INCEFA+ project, compares the correction factors used, and assesses sensitivities of the correction factor to parameters such as specimen diameter. In addition, correction factors for air and PWR environments are compared. Conclusions are drawn and recommendations made for future fatigue testing in LWR environments within autoclaves.

Field Comparison of TSI DustTrak versus TEOM in Two Poultry Houses

2018 ◽  
Vol 61 (2) ◽  
pp. 653-660
Author(s):  
Xufei Yang ◽  
Chen Zhang ◽  
Hong Li
Keyword(s):  
Light Scattering ◽  
Correction Factor ◽  
Mass Concentration ◽  
Field Performance ◽  
Mie Scattering ◽  
Correction Factors ◽  
Poultry Houses ◽  
Equivalent Method ◽  
Tapered Element Oscillating Microbalance ◽  
Broiler House

Abstract. The TSI DustTrak monitor has been used for particulate matter (PM) monitoring at various animal facilities. The instrument determines PM concentrations based on the principle of light scattering. Several assumptions (e.g., particle size, refractive index, and density) are imposed during the calibration process; however, they may not apply to PM emanating from agricultural settings. In this study, PM10 monitoring was conducted at a broiler house and a layer breeding house with four collocated instruments: three DustTrak monitors and one tapered element oscillating microbalance (TEOM). Being a federal equivalent method (FEM) for PM10 monitoring, TEOM was selected here as a transfer standard for assessing the field performance of DustTrak. Results revealed a good linearity between DustTrak and TEOM PM10 readings (R2 =0.92 and 0.85 in the broiler and layer breeding houses, respectively). However, DustTrak significantly underestimated PM10 concentrations in both houses. To correct for the monitoring bias by DustTrak, an average correction factor was derived from correlation analysis that characterized the ratio of DustTrak’s PM10 response to TEOM’s. The factor was calculated as 0.267 for the broiler house and 0.244 for the layer breeding house. Mie scattering simulation was performed to further verify the derived correction factors. A factor of 0.204 was estimated from the simulation, and it accorded well with experimental results. A dependence of the correction factor on PM10 concentration was noted in both poultry houses, indicating the feasibility of developing a concentration-dependent correction factor for future monitoring efforts. Such a relationship could also be explained by Mie scattering. This study is expected to facilitate a better understanding of the limitations and perspectives of the TSI DustTrak and other light scattering PM monitors for agricultural air quality research. Keywords: DustTrak, Mass concentration, Mie scattering, PM10, Poultry, TEOM.

A theory of palaeoclimate reconstruction

2020 ◽  
Author(s):  
Mengmeng Liu ◽  
Iain Colin Prentice ◽  
Cajo ter Braak ◽  
Sandy Harrison
Keyword(s):  
Climate Models ◽  
Compositional Data ◽  
Likelihood Function ◽  
Multinomial Distribution ◽  
Weighted Average ◽  
Weighted Averaging ◽  
Northern Eurasia ◽  
Data Set ◽  
Best Estimate ◽  
Special Case

<p>Past climate states can be used to test climate models for present-day changes and future responses. Past states can be reconstructed from fossil assemblages, and WA-PLS (weighted averaging–partial least squares) is one of the most widely used statistical methods to do this. However, WA-PLS has a marked bias. Whatever biotic indicator is being used, reconstructed climate values are artificially compressed and biased towards the centre of the range used for calibration.</p><p>Here we developed an improvement of the method, derived rigorously from theory. It makes three assumptions:</p><p>a) the theoretical abundance of each taxon follows a Gaussian (unimodal) curve with respect to each climate variable considered;</p><p>b) the abundances of taxa are compositional data, so they sum to unity and follow a multinomial distribution;</p><p>c) the best estimate of the climate value at the site to be reconstructed maximizes the log-likelihood function – in other words, it minimizes the difference between theoretical and actual abundances as assessed by the likelihood criterion.</p><p>The best estimate of the climate value is approximated by a tolerance-weighted version of the weighted average in which the abundances of taxa are weighted by the inverse square of their tolerances (a measure of the range of environments in which a taxon is found). WA-PLS thus corresponds to the special case when all taxon tolerances are equal. The fact that this special case is far from reality generally is part of the the cause of the “compression and bias”. The new method can be applied using the existing functions for WA-PLS in the R package rioja. We show that it greatly reduces the compression bias in reconstructions based on a large modern pollen data set from Europe, northern Eurasia and the Middle East.</p>

Markov Breaks in Regression Models

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Aaron Smith
Keyword(s):  
Regression Models ◽  
Yield Curve ◽  
Likelihood Function ◽  
Weighted Average ◽  
Predictive Ability ◽  
Error Variance ◽  
Monte Carlo Integration ◽  
Linear Regression Models ◽  
Out Of Sample ◽  
Low Dimensional

This article develops a new Markov breaks (MB) model for forecasting and making inference in linear regression models with breaks that are stochastic in both timing and magnitude. The MB model permits an arbitrarily large number of abrupt breaks in the regression coefficients and error variance, but it maintains a low-dimensional state space, and therefore it is computationally straightforward. In particular, the likelihood function can be computed analytically using a single iterative pass through the data and thereby avoids Monte Carlo integration. The model generates forecasts and conditional coefficient predictions using a probability weighted average over regressions that include progressively more historical data. I employ the MB model to study the predictive ability of the yield curve for quarterly GDP growth. I show evidence of breaks in the predictive relationship, and the MB model outperforms competing breaks models in an out-of-sample forecasting experiment.

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