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Uncertainty and Statistics
Published in Walter Fox Smith, Experimental Physics, 2020
To extend this idea to our least-squares function fitting, we need to weight deviations from the fit less for less-reliable data. In un-weighted least-squares, the metric for how discrepant any given point is from the fit is the squared difference between the observed value and the model value; to add inverse variance weighting, we will divide each difference by the squared error on the observation: χ2=∑i=1nxi−mi2σi2
Interval training versus moderate-intensity continuous training for cardiorespiratory fitness improvements in middle-aged and older adults: a systematic review and meta-analysis
Published in Journal of Sports Sciences, 2021
Eric Tsz-Chun Poon, Waris Wongpipit, Robin Sze-Tak Ho, Stephen Heung-Sang Wong
The meta-analysis was conducted using Review Manager software (RevMan 5.4; Cochrane Collaboration, Oxford, UK). The absolute change in mean difference and its respective 95% confidence interval (CI) of the VO2max value from pre- to post-intervention between groups (interval training vs. MICT) in each study was calculated and pooled using the random-effects model. Heterogeneity of included trials was assessed using the I2 statistic, in which values of <25%, 50%, and 75% were considered indicative of low, moderate, and high heterogeneity, respectively. Inverse variance weighting was used to compensate for the heterogeneity of sample sizes between studies. Publication bias was visually assessed using funnel plots. To improve the robustness of our findings, we conducted a series of sensitivity analyses to test the individual influence of each study on the overall results. In addition, we conducted subgroup analyses according to the type of comparison group (HIIT or SIT) and overall risk of bias level (“low, middle and high”).
Expert review with meta-analysis of randomized and nonrandomized controlled studies of Barricaid annular closure in patients at high risk for lumbar disc reherniation
Published in Expert Review of Medical Devices, 2020
Larry E. Miller, R. Todd Allen, Brad Duhon, Kris E. Radcliff
Random-effects meta-analysis models using inverse variance weighting were developed based on the a priori assumption that treatment effects may be heterogeneous among studies due to differences in patient characteristics and surgical techniques. The statistic of interest was the risk ratio and 95% confidence interval, where a risk ratio of less than 1 indicated lower risk with the Barricaid device and a risk ratio greater than 1 indicated higher risk with the Barricaid device. Forest plots were used to illustrate individual study findings and pooled meta-analysis results. We used the I2 statistic to estimate heterogeneity of effects across studies with values of ≤25%, 50%, and ≥75% representing low, moderate, and high inconsistency, respectively [21]. A subgroup analysis was performed to assess the main outcomes derived from randomized trials only. Statistical analyses were performed using RevMan version 5.3 (Cochrane Collaboration, Copenhagen, Denmark).
Improved prediction of oil drift pattern using ensemble of ocean currents
Published in Journal of Operational Oceanography, 2022
Prasad S.J, Balakrishnan Nair T.M, Balaji B
In the present study, the model-derived ocean currents were weighted using the inverse variance weighting technique while generating an ensemble of ocean currents. Inverse-variance weighting method is used in statistical meta-analysis. This technique was selected to obtain the weights directly after getting Root Mean Squared Deviation (RMSD). The obtained weights are assigned to models. This technique reduces the error variances, which is the error of model-derived estimates against the independent observations. The advantage of this method is it exploits the superiority of the numerical model which gives a better forecast of currents (zonal and meridional currents) and different sets of weights can be obtained for zonal and meridional currents (Lee et al. 2016; Shahar 2017). At INCOIS, the operational ROMS currents are generated and pushed to the oil spill server daily. Hence weighted ensemble ocean currents of ROMS, from pre-estimated weights can also be generated on daily basis. In this study, the weights are estimated based on the agreement between ocean currents of models and High Frequency (HF) Radar observations. The zonal and meridional components of HF Radar Ocean currents were obtained from their raw radial datasets, according to Gurgel (1994). National Institute of Ocean Technology (NIOT), Ministry of Earth Sciences (MoES), Government of India deployed a network of HF Radars called Indian coastal radar network (ICORN) comprising five pairs of radar along the coasts of Andhra Pradesh, Tamil Nadu, Odisha, Andaman and Gujarat of India in support to Tsunami Early Warning System at INCOIS (Jena et al. 2019). INCOIS located in Hyderabad stores and disseminates HF Radar data for scientific research and maritime operations. Surface current observations from HF Radar were used to evaluate and simulate the trajectory pattern (Abascal et al. 2009). HF Radar datasets are widely being used in various aspects of operational oceanography and applied research. Kolukula et al. (2020) explained a method to fill the gaps in HF Radar data using complex empirical orthogonal functions. In the present study, HF Radar currents of the Tamil Nadu region are used during the spill period. This paper elaborates on the method of hindcasting the oil drift pattern of the spilled HFO during January 2017 off Ennore using an ensemble of ocean currents. It involved the generation of weights for the respective ocean models by comparing the model currents with HF Radar currents. The derived weights obtained using the inverse variance weighting technique were assigned to the currents of ocean models and the new weighted ensemble of ocean currents was generated. The performance of the oil spill model is evaluated using individual and ensemble of ocean currents.