constrained model
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2022 ◽  
pp. 096228022110651
Mohammed Baragilly ◽  
Brian Harvey Willis

Tailored meta-analysis uses setting-specific knowledge for the test positive rate and disease prevalence to constrain the possible values for a test's sensitivity and specificity. The constrained region is used to select those studies relevant to the setting for meta-analysis using an unconstrained bivariate random effects model (BRM). However, sometimes there may be no studies to aggregate, or the summary estimate may lie outside the plausible or “applicable” region. Potentially these shortcomings may be overcome by incorporating the constraints in the BRM to produce a constrained model. Using a penalised likelihood approach we developed an optimisation algorithm based on co-ordinate ascent and Newton-Raphson iteration to fit a constrained bivariate random effects model (CBRM) for meta-analysis. Using numerical examples based on simulation studies and real datasets we compared its performance with the BRM in terms of bias, mean squared error and coverage probability. We also determined the ‘closeness’ of the estimates to their true values using the Euclidian and Mahalanobis distances. The CBRM produced estimates which in the majority of cases had lower absolute mean bias and greater coverage probability than the BRM. The estimated sensitivities and specificity for the CBRM were, in general, closer to the true values than the BRM. For the two real datasets, the CBRM produced estimates which were in the applicable region in contrast to the BRM. When combining setting-specific data with test accuracy meta-analysis, a constrained model is more likely to yield a plausible estimate for the sensitivity and specificity in the practice setting than an unconstrained model.

2021 ◽  
Vol 21 (24) ◽  
pp. 18227-18245
Amir H. Souri ◽  
Kelly Chance ◽  
Juseon Bak ◽  
Caroline R. Nowlan ◽  
Gonzalo González Abad ◽  

Abstract. Questions about how emissions are changing during the COVID-19 lockdown periods cannot be answered by observations of atmospheric trace gas concentrations alone, in part due to simultaneous changes in atmospheric transport, emissions, dynamics, photochemistry, and chemical feedback. A chemical transport model simulation benefiting from a multi-species inversion framework using well-characterized observations should differentiate those influences enabling to closely examine changes in emissions. Accordingly, we jointly constrain NOx and VOC emissions using well-characterized TROPOspheric Monitoring Instrument (TROPOMI) HCHO and NO2 columns during the months of March, April, and May 2020 (lockdown) and 2019 (baseline). We observe a noticeable decline in the magnitude of NOx emissions in March 2020 (14 %–31 %) in several major cities including Paris, London, Madrid, and Milan, expanding further to Rome, Brussels, Frankfurt, Warsaw, Belgrade, Kyiv, and Moscow (34 %–51 %) in April. However, NOx emissions remain at somewhat similar values or even higher in some portions of the UK, Poland, and Moscow in March 2020 compared to the baseline, possibly due to the timeline of restrictions. Comparisons against surface monitoring stations indicate that the constrained model underrepresents the reduction in surface NO2. This underrepresentation correlates with the TROPOMI frequency impacted by cloudiness. During the month of April, when ample TROPOMI samples are present, the surface NO2 reductions occurring in polluted areas are described fairly well by the model (model: −21 ± 17 %, observation: −29 ± 21 %). The observational constraint on VOC emissions is found to be generally weak except for lower latitudes. Results support an increase in surface ozone during the lockdown. In April, the constrained model features a reasonable agreement with maximum daily 8 h average (MDA8) ozone changes observed at the surface (r=0.43), specifically over central Europe where ozone enhancements prevail (model: +3.73 ± 3.94 %, +1.79 ppbv, observation: +7.35 ± 11.27 %, +3.76 ppbv). The model suggests that physical processes (dry deposition, advection, and diffusion) decrease MDA8 surface ozone in the same month on average by −4.83 ppbv, while ozone production rates dampened by largely negative JNO2[NO2]-kNO+O3[NO][O3] become less negative, leading ozone to increase by +5.89 ppbv. Experiments involving fixed anthropogenic emissions suggest that meteorology contributes to 42 % enhancement in MDA8 surface ozone over the same region with the remaining part (58 %) coming from changes in anthropogenic emissions. Results illustrate the capability of satellite data of major ozone precursors to help atmospheric models capture ozone changes induced by abrupt emission anomalies.

2021 ◽  
Vol 154 (A2) ◽  
G J Macfarlane ◽  
M R Renilson ◽  
T Turner

In order to provide data to assist in developing and validating a numerical code to simulate the flooding immediately following damage scale model experiments were conducted on a fully constrained model to investigate the progressive flooding through a complex series of internal compartments within a generic destroyer type hull form. A 3.268 metre long model of a generic destroyer hull form with a simplified, typical internal arrangement was constructed to cover the configuration of greatest interest. A very rapid damage opening scenario was simulated by rupturing a taut membrane covering an opening. The model was instrumented to measure the levels of water and the air pressures in various compartments. In addition, video footage was obtained of the flooding process from both internally and externally of the model. Previous work presented by Macfarlane et al. (2010) showed the results for the unconstrained model. This paper reports on the outcomes from the experimental program where the model was fully constrained in all six degrees of freedom. Firstly, tests were conducted in calm water with damage opening extents ranging from 50% to 100%. When the damage opening was only 50% the rate of rise of water in each of the compartments was only marginally slower than for the 100% damage extent case. Secondly, the test results in calm water were compared against results from tests in regular beam seas. A ‘set-up’ of water inside each of the compartments on the 2nd Deck was found during the wave tests. The result of this is that the mean equilibrium water level in each compartment in the regular beam sea cases is noticeably higher than the equivalent calm water case, particularly for the two compartments on the port side, away from the damage. Finally, analysis of the data from further calm water and beam sea tests suggests that a similar result also occurs when the model is fixed at various non-zero heel angles.

2021 ◽  
Arne Monsees ◽  
Kay-Michael Voit ◽  
Damian J Wallace ◽  
Juergen Sawinski ◽  
Edyta Leks ◽  

Forming a complete picture of the relationship between neural activity and body kinetics requires quantification of skeletal joint biomechanics during behavior. However, without detailed knowledge of the underlying skeletal motion, inferring joint kinetics from surface tracking approaches is difficult, especially for animals where the relationship between surface anatomy and skeleton changes during motion. Here we developed a videography-based method enabling detailed three-dimensional kinetic quantification of an anatomically defined skeleton in untethered freely-behaving animals. This skeleton-based model has been constrained by anatomical principles and joint motion limits and provided skeletal pose estimates for a range of rodent sizes, even when limbs were occluded. Model-inferred joint kinetics for both gait and gap-crossing behaviors were verified by direct measurement of limb placement, showing that complex decision making behaviors can be accurately reconstructed at the level of skeletal kinetics using our anatomically constrained model.

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