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Christopher P Favazza - One of the best experts on this subject based on the ideXlab platform.
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direct estimation and correction of bias from temporally variable non stationary noise in a channelized Hotelling Model observer
Physics in Medicine and Biology, 2016Co-Authors: Kenneth A Fetterly, Christopher P FavazzaAbstract:Channelized Hotelling Model observer (CHO) methods were developed to assess performance of an x-ray angiography system. The analytical methods included correction for known bias error due to finite sampling. Detectability indices ([Formula: see text]) corresponding to disk-shaped objects with diameters in the range 0.5-4 mm were calculated. Application of the CHO for variable detector target dose (DTD) in the range 6-240 nGy frame(-1) resulted in [Formula: see text] estimates which were as much as 2.9× greater than expected of a quantum limited system. Over-estimation of [Formula: see text] was presumed to be a result of bias error due to temporally variable non-stationary noise. Statistical theory which allows for independent contributions of 'signal' from a test object (o) and temporally variable non-stationary noise (ns) was developed. The theory demonstrates that the biased [Formula: see text] is the sum of the detectability indices associated with the test object [Formula: see text] and non-stationary noise ([Formula: see text]). Given the nature of the imaging system and the experimental methods, [Formula: see text] cannot be directly determined independent of [Formula: see text]. However, methods to estimate [Formula: see text] independent of [Formula: see text] were developed. In accordance with the theory, [Formula: see text] was subtracted from experimental estimates of [Formula: see text], providing an unbiased estimate of [Formula: see text]. Estimates of [Formula: see text] exhibited trends consistent with expectations of an angiography system that is quantum limited for high DTD and compromised by detector electronic readout noise for low DTD conditions. Results suggest that these methods provide [Formula: see text] estimates which are accurate and precise for [Formula: see text]. Further, results demonstrated that the source of bias was detector electronic readout noise. In summary, this work presents theory and methods to test for the presence of bias in Hotelling Model observers due to temporally variable non-stationary noise and correct this bias when the temporally variable non-stationary noise is independent and additive with respect to the test object signal.
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su f i 80 correction for bias in a channelized Hotelling Model observer caused by temporally variable non stationary noise
Medical Physics, 2016Co-Authors: Christopher P Favazza, Kenneth A FetterlyAbstract:Purpose: Application of a channelized Hotelling Model observer (CHO) over a wide range of x-ray angiography detector target dose (DTD) levels demonstrated substantial bias for conditions yielding low detectability indices (d’), including low DTD and small test objects. The purpose of this work was to develop theory and methods to correct this bias. Methods: A hypothesis was developed wherein the measured detectability index (d'b) for a known test object is positively biased by temporally variable non-stationary noise in the images. Hotelling's T2 test statistic provided the foundation for a mathematical theory which accounts for independent contributions to the measured d'b value from both the test object (d'o) and non-stationary noise (d'ns). Experimental methods were developed to directly estimate d'o by determining d'ns and subtracting it from d'b, in accordance with the theory. Specifically, d'ns was determined from two sets of images from which the traditional test object was withheld. This method was applied to angiography images with DTD levels in the range 0 to 240 nGy and for disk-shaped iodine-based contrast targets with diameters 0.5 to 4.0 mm. Results: Bias in d’ was evidenced by d'b values which exceeded values expected from a quantum limited imaging system and decreasing object size and DTD. d'ns increased with decreasing DTD, reaching a maximum of 2.6 for DTD = 0. Bias-corrected d'o estimates demonstrated sub-quantum limited performance of the x-ray angiography for low DTD. Findings demonstrated that the source of non-stationary noise was detector electronic readout noise. Conclusion: Theory and methods to estimate and correct bias in CHO measurements from temporally variable non-stationary noise were presented. The temporal non-stationary noise was shown to be due to electronic readout noise. This method facilitates accurate estimates of d’ values over a large range of object size and detector target dose.
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WE-G-204-02: Utility of a Channelized Hotelling Model Observer Over a Large Range of Angiographic Exposure Levels
Medical Physics, 2015Co-Authors: Kenneth A Fetterly, Christopher P FavazzaAbstract:Purpose: Mathematical Model observers provide a figure of merit that simultaneously considers a test object and the contrast, noise, and spatial resolution properties of an imaging system. The purpose of this work was to investigate the utility of a channelized Hotelling Model observer (CHO) to assess system performance over a large range of angiographic exposure conditions. Methods: A 4 mm diameter disk shaped, iodine contrast test object was placed on a 20 cm thick Lucite phantom and 1204 image frames were acquired using fixed x-ray beam quality and for several detector target dose (DTD) values in the range 6 to 240 nGy. The CHO was implemented in the spatial domain utilizing 96 Gabor functions as channels. Detectability index (DI) estimates were calculated using the “resubstitution” and “holdout” methods to train the CHO. Also, DI values calculated using discrete subsets of the data were used to estimate a minimally biased DI as might be expected from an infinitely large dataset. The relationship between DI, independently measured CNR, and changes in results expected assuming a quantum limited detector were assessed over the DTD range. Results: CNR measurements demonstrated that the angiography system is not quantum limited due to relatively increasing contamination from electronic noise that reduces CNR for low DTD. Direct comparison of DI versus CNR indicates that the CHO relatively overestimates DI for low DTD and/or underestimates DI values for high DTD. The relative magnitude of the apparent bias error in the DI values was ∼20% over the 40x DTD range investigated. Conclusion: For the angiography system investigated, the CHO can provide a minimally biased figure of merit if implemented over a restricted exposure range. However, bias leads to overestimates of DI for low exposures. This work emphasizes the need to verify CHO Model performance during real-world application.
Kenneth A Fetterly - One of the best experts on this subject based on the ideXlab platform.
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direct estimation and correction of bias from temporally variable non stationary noise in a channelized Hotelling Model observer
Physics in Medicine and Biology, 2016Co-Authors: Kenneth A Fetterly, Christopher P FavazzaAbstract:Channelized Hotelling Model observer (CHO) methods were developed to assess performance of an x-ray angiography system. The analytical methods included correction for known bias error due to finite sampling. Detectability indices ([Formula: see text]) corresponding to disk-shaped objects with diameters in the range 0.5-4 mm were calculated. Application of the CHO for variable detector target dose (DTD) in the range 6-240 nGy frame(-1) resulted in [Formula: see text] estimates which were as much as 2.9× greater than expected of a quantum limited system. Over-estimation of [Formula: see text] was presumed to be a result of bias error due to temporally variable non-stationary noise. Statistical theory which allows for independent contributions of 'signal' from a test object (o) and temporally variable non-stationary noise (ns) was developed. The theory demonstrates that the biased [Formula: see text] is the sum of the detectability indices associated with the test object [Formula: see text] and non-stationary noise ([Formula: see text]). Given the nature of the imaging system and the experimental methods, [Formula: see text] cannot be directly determined independent of [Formula: see text]. However, methods to estimate [Formula: see text] independent of [Formula: see text] were developed. In accordance with the theory, [Formula: see text] was subtracted from experimental estimates of [Formula: see text], providing an unbiased estimate of [Formula: see text]. Estimates of [Formula: see text] exhibited trends consistent with expectations of an angiography system that is quantum limited for high DTD and compromised by detector electronic readout noise for low DTD conditions. Results suggest that these methods provide [Formula: see text] estimates which are accurate and precise for [Formula: see text]. Further, results demonstrated that the source of bias was detector electronic readout noise. In summary, this work presents theory and methods to test for the presence of bias in Hotelling Model observers due to temporally variable non-stationary noise and correct this bias when the temporally variable non-stationary noise is independent and additive with respect to the test object signal.
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su f i 80 correction for bias in a channelized Hotelling Model observer caused by temporally variable non stationary noise
Medical Physics, 2016Co-Authors: Christopher P Favazza, Kenneth A FetterlyAbstract:Purpose: Application of a channelized Hotelling Model observer (CHO) over a wide range of x-ray angiography detector target dose (DTD) levels demonstrated substantial bias for conditions yielding low detectability indices (d’), including low DTD and small test objects. The purpose of this work was to develop theory and methods to correct this bias. Methods: A hypothesis was developed wherein the measured detectability index (d'b) for a known test object is positively biased by temporally variable non-stationary noise in the images. Hotelling's T2 test statistic provided the foundation for a mathematical theory which accounts for independent contributions to the measured d'b value from both the test object (d'o) and non-stationary noise (d'ns). Experimental methods were developed to directly estimate d'o by determining d'ns and subtracting it from d'b, in accordance with the theory. Specifically, d'ns was determined from two sets of images from which the traditional test object was withheld. This method was applied to angiography images with DTD levels in the range 0 to 240 nGy and for disk-shaped iodine-based contrast targets with diameters 0.5 to 4.0 mm. Results: Bias in d’ was evidenced by d'b values which exceeded values expected from a quantum limited imaging system and decreasing object size and DTD. d'ns increased with decreasing DTD, reaching a maximum of 2.6 for DTD = 0. Bias-corrected d'o estimates demonstrated sub-quantum limited performance of the x-ray angiography for low DTD. Findings demonstrated that the source of non-stationary noise was detector electronic readout noise. Conclusion: Theory and methods to estimate and correct bias in CHO measurements from temporally variable non-stationary noise were presented. The temporal non-stationary noise was shown to be due to electronic readout noise. This method facilitates accurate estimates of d’ values over a large range of object size and detector target dose.
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WE-G-204-02: Utility of a Channelized Hotelling Model Observer Over a Large Range of Angiographic Exposure Levels
Medical Physics, 2015Co-Authors: Kenneth A Fetterly, Christopher P FavazzaAbstract:Purpose: Mathematical Model observers provide a figure of merit that simultaneously considers a test object and the contrast, noise, and spatial resolution properties of an imaging system. The purpose of this work was to investigate the utility of a channelized Hotelling Model observer (CHO) to assess system performance over a large range of angiographic exposure conditions. Methods: A 4 mm diameter disk shaped, iodine contrast test object was placed on a 20 cm thick Lucite phantom and 1204 image frames were acquired using fixed x-ray beam quality and for several detector target dose (DTD) values in the range 6 to 240 nGy. The CHO was implemented in the spatial domain utilizing 96 Gabor functions as channels. Detectability index (DI) estimates were calculated using the “resubstitution” and “holdout” methods to train the CHO. Also, DI values calculated using discrete subsets of the data were used to estimate a minimally biased DI as might be expected from an infinitely large dataset. The relationship between DI, independently measured CNR, and changes in results expected assuming a quantum limited detector were assessed over the DTD range. Results: CNR measurements demonstrated that the angiography system is not quantum limited due to relatively increasing contamination from electronic noise that reduces CNR for low DTD. Direct comparison of DI versus CNR indicates that the CHO relatively overestimates DI for low DTD and/or underestimates DI values for high DTD. The relative magnitude of the apparent bias error in the DI values was ∼20% over the 40x DTD range investigated. Conclusion: For the angiography system investigated, the CHO can provide a minimally biased figure of merit if implemented over a restricted exposure range. However, bias leads to overestimates of DI for low exposures. This work emphasizes the need to verify CHO Model performance during real-world application.
Stefano Colombo - One of the best experts on this subject based on the ideXlab platform.
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Cartels in the unidirectional Hotelling Model
Economic Modelling, 2013Co-Authors: Stefano ColomboAbstract:We study the impact of space on perfect collusion sustainability within the unidirectional Hotelling Model where the firms are constrained to move to the left. We obtain that when the firm that located to the left of the Hotelling segment has the greater incentive to deviate, the distance between the firms has a negative impact on the capability of the firms to sustain the collusion in equilibrium. On the other hand, when the firm that located to the right has the greater incentive to deviate, greater spatial distance makes the collusion easier to sustain in equilibrium. These results substantially differ from the bidirectional Hotelling Model.
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Direct price discrimination in the Hotelling Model: competition and collusion
2011Co-Authors: Stefano ColomboAbstract:This paper reviews the main contributions of the literature regarding the effects of direct price discrimination within the Hotelling Model. Moreover, we introduce an asymmetric Hotelling Model and we show that the assumption of spatial asymmetry between firms is likely to alter the implications of price discrimination.
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Spatial price discrimination in the unidirectional Hotelling Model with elastic demand
Journal of Economics, 2010Co-Authors: Stefano ColomboAbstract:The unidirectional Hotelling Model is extended to allow for elastic demand functions. A two-stage Bertrand-type Model and a two-stage Cournot-type Model are considered. If firms choose location and then set prices, agglomeration never arises; instead, if firms choose location and then set quantities, agglomeration arises at one endpoint of the segment when the transportation costs are low enough. Instead, when the transportation costs are high enough, a dispersed equilibrium arises in Cournot. The equilibrium distance between the firms is lower in Cournot than in Bertrand. When the transportation costs are high (low) the Bertrand equilibrium is welfare superior (inferior) to the Cournot equilibrium.
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Bertrand and Cournot in the unidirectional Hotelling Model
2010Co-Authors: Stefano ColomboAbstract:The unidirectional Hotelling Model where consumers can buy only from firms located on their right (left) is extended to allow for elastic demand functions. A Bertrand-type Model and a Cournot-type Model are considered. If firms choose location and then set prices, agglomeration never arises; instead, if firms choose location and then set quantities, agglomeration arises at one endpoint of the segment when transportation costs are low enough. Equilibrium distance between firms is lower in Cournot than Bertrand under the whole parameters’ set. We also study the impact of firms’ location on perfect collusion sustainability. We show that when consumers can buy only from firms located on their right (left), the incentive to deviate of each firm decreases the more the firm is located to the right (left) and the more the rival is located to the left (right).
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The unidirectional Hotelling Model with spatial price discrimination
Economics Bulletin, 2009Co-Authors: Stefano ColomboAbstract:The unidirectional Hotelling Model where consumers can buy only from firms located on their right (left) is extended to allow for price discriminating firms and a general class of transportation costs. In a two-stage location-price game one firm locates at 1/2 and the other locates at 1 (0). We also study collusion in an infinitely repeated game. The maximum collusive profits sustainable in equilibrium monotonically increase (decrease) with the location of the firm located at the right (left), while initially increase and then decrease with the location of the firm located at the left (right). A higher reservation price of consumers makes perfect collusion less sustainable in equilibrium, but allows firms to agree on higher (albeit imperfect) collusive profits.
C.-y. Cynthia Lin - One of the best experts on this subject based on the ideXlab platform.
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Insights from a Simple Hotelling Model of the World Oil Market
Natural Resources Research, 2009Co-Authors: C.-y. Cynthia LinAbstract:This paper uses annual data on world oil price and consumption from 1965 to 2006 to calibrate a Hotelling Model of optimal nonrenewable resource extraction. Numerical solutions are generated for various specifications of the elasticity of demand for both isoelastic demand and linear demand under each of two possible market structures: perfect competition and monopoly. Prior to the 1973 oil crisis, the Model that best fits actual data is one of perfect competition with linear demand and a demand elasticity of −0.4. For the periods 1973–1981 and 1981–1990, the Model that best fits actual data is one of monopoly with linear demand and demand elasticities of −0.8 and −0.7, respectively, suggesting that the market was strongly influenced by OPEC during this time. Under the Model that best fits the most recent period (perfect competition with linear demand and demand elasticity −0.5), the real oil price (in 1982–1984 U.S.$) should fall in the range $60.87–$66.31/barrel over the years 2010–2030.
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Steady-state growth in a Hotelling Model of resource extraction
Journal of Environmental Economics and Management, 2007Co-Authors: C.-y. Cynthia Lin, Gernot WagnerAbstract:This paper re-examines the Hotelling Model of optimal nonrenewable resource extraction in light of stock effects and technological progress. We assume functional forms for cost and demand so that the solution to the Hotelling problem is a steady-state consistent with the empirical observation that the growth rates of market prices have remained zero over a long period of time. We use data on 14 minerals from 1970 to 2004 to estimate the supply and demand functions using SUR and 3SLS and to test the Model. We validate the Model for 8 of 14 minerals. (c) 2007 Elsevier Inc. All rights reserved.
Xiangyu Wang - One of the best experts on this subject based on the ideXlab platform.
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Achieving Economically Sustainable Subcontracting through the Hotelling Model by Considering the Spillover Effect
Sustainability, 2018Co-Authors: Jianbo Zhu, Qianqian Shi, Zhaohan Sheng, Xiangyu WangAbstract:In the process of internationalization of construction contractors, international enterprises as main contractors (IMC) need to consider whether part of the contract should be subcontracted to local subcontractors (LSC) to gain a competitive advantage when competing with local main contractors (LMC). The involvement of local subcontractors can usually help reduce cost through the cost spillover effect. However, it should be noted that the share of local subcontractors with local main contractors with an inferior quality may lead to quality spillover. The Hotelling Model is therefore adopted to investigate the subcontracting decisions of main contractors considering both cost and quality spillover effects. Many scenarios are simulated and the results show that LMCs with inferior quality can always choose the subcontracting strategy to obtain increased profit regardless of the strategy that IMCs adopt. On the other hand, IMCs need to balance the cost spillover of subcontracting and the quality spillover for improving the quality level of LSCs. The results are useful for contractors to make decisions that are relevant to the adoption of subcontracting strategies to obtain competitive advantages.