Sequential Truncation of R-Vine Copula Mixture Model for High-Dimensional Datasets

Uncovering hidden mixture dependencies among variables has been investigated in the literature using mixture R-vine copula models. They provide considerable flexibility for modeling multivariate data. As the dimensions increase, the number of the model parameters that need to be estimated is increased dramatically, which comes along with massive computational times and efforts. This situation becomes even much more complex and complicated in the regular vine copula mixture models. Incorporating the truncation method with a mixture of regular vine models will reduce the computation difficulty for the mixture-based models. In this paper, the tree-by-tree estimation mixture model is joined with the truncation method to reduce computational time and the number of parameters that need to be estimated in the mixture vine copula models. A simulation study and real data applications illustrated the performance of the method. In addition, the real data applications show the effect of the mixture components on the truncation level.

Reservoir Sizing at Draft Level of 75% of Mean Annual Flow Using Drought Magnitude Based Method on Canadian Rivers

On a global basis, there is trend that a majority of reservoirs are sized using a draft of 75% of the mean annual flow (0.75 MAF). The reservoir volumes based on the proposed drought magnitude (DM) method and the sequent peak algorithm (SPA) at 0.75 MAF draft were compared at the annual, monthly and weekly scales using the flow sequences of 25 Canadian rivers. In our assessment, the monthly scale is adequate for such analyses. The DM method, although capable of using flow data at any time scale, has been demonstrated using monthly standardized hydrological index (SHI) sequences. The moving average (MA) smoothing of the monthly SHI sequences formed the basis in the DM method for estimating the reservoir volume through the use of the extreme number theorem, and the hypothesis that drought magnitude is equal to the product of the drought intensity and drought length. The truncation level in the SHI sequences was found as SHIo [ = (0.75 ‒ 1) µo/σo], where µo and σo are the overall mean and standard deviation of the monthly flows. The DM-based estimates for the deficit volumes and the SPA-based reservoir volumes were found comparable within an error margin of ±18%.

Truncation Mixture R-Vine Copulas

Uncovering hidden mixture correlation among variables have been investigating in the literature using mixture R-vine copula models. These models are hierarchical in nature. They provides a huge flexibility for modelling multivariate data. As the dimensions increases, the number of the model parameters that need to be estimated is increased dramatically, which becomes along with huge computational times and efforts. This situation becomes even much more harder and complicated in the mixture Regular vine models. Incorporating truncation method with mixture Regular vine models will reduce the computation difficulty for the mixture based models. In this paper, tree-by-tree estimation mixture model is joined with the truncation method, in order to reduce the computational time and the number of the parameters that need to be estimated in the mixture vine copula models. A simulation study and a real data applications illustrated the performance of the method. In addition, the real data applications show the affect of the mixture components on the truncation level.

HYPOTHESIS TESTING FOR THE PARAMETERS OF LOG-LOGISTIC REGRESSION MODEL WITH LEFT-TRUNCATED AND RIGHT-CENSORED SURVIVAL DATA

Left-truncation and right-censoring (LTRC) arise naturally in lifetime data. Data may be left-truncated due to a limitation in the study design. Failure of a unit is observed only if it fails after a certain period. Usually, the units under study may not be followed until all of them have failed but the study has to be stopped at a certain time. This introduces the right censoring into the survival data. Log-logistic model is extended to accommodate the left-truncated and right-censored survival data. The bias, standard error (SE), and root mean square error (RMSE) of the parameter estimates are computed to evaluate the performance of the model at different sample sizes, censoring proportion (CP), and truncation level (TL). The results show that the SE of the parameter estimates increase as the truncation level (TL) and censoring proportion (CP) increase. Having low and high TL (5% and 15%) in the data, the graphs clearly show that the empirical power of both tests increases with the increase of TL for parameter and . The SE and RMSE also decrease as the sample size increases. Following that, power analysis is conducted via simulation to compare the performance of hypothesis tests based on the Wald and Likelihood Ratio (LR) for the parameters. The results clearly indicate that the Wald performs slightly better than the LR when dealing with the proposed model.

The Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0

This paper describes a reduced-order quasi-geostrophic coupled ocean–atmosphere model that allows for an arbitrary number of atmospheric and oceanic modes to be retained in the spectral decomposition. The modularity of this new model allows one to easily modify the model physics. Using this new model, coined the "Modular Arbitrary-Order Ocean-Atmosphere Model" (MAOOAM), we analyse the dependence of the model dynamics on the truncation level of the spectral expansion, and unveil spurious behaviour that may exist at low resolution by a comparison with the higher-resolution configurations. In particular, we assess the robustness of the coupled low-frequency variability when the number of modes is increased. An "optimal" configuration is proposed for which the ocean resolution is sufficiently high, while the total number of modes is small enough to allow for a tractable and extensive analysis of the dynamics.

A Modular Arbitrary-Order Ocean-Atmosphere Model: MAOOAM v1.0

This paper describes a reduced-order quasi-geostrophic coupled ocean-atmosphere model that allows for an arbitrary number of atmospheric and oceanic modes to be retained in the spectral decomposition. The modularity of this new model allows one to easily modify the model physics. Using this new model, coined "Modular Arbitrary-Order Ocean-Atmosphere Model" (MAOOAM), we analyse the dependence of the model dynamics on the truncation level of the spectral expansion, and unveil spurious behaviour that may exist at low resolution by a comparison with the higher resolution versions. In particular, we assess the robustness of the coupled low-frequency variability when the number of modes is increased. An "optimal" version is proposed for which the ocean resolution is sufficiently high while the total number of modes is small enough to allow for a tractable and extensive analysis of the dynamics.

Influence of segmented vessel size due to limited imaging resolution on coronary hyperemic flow prediction from arterial crown volume

Computational predictions of the functional stenosis severity from coronary imaging data use an allometric scaling law to derive hyperemic blood flow (Q) from coronary arterial volume (V), Q = αVβ. Reliable estimates of α and β are essential for meaningful flow estimations. We hypothesize that the relation between Q and V depends on imaging resolution. In five canine hearts, fluorescent microspheres were injected into the left anterior descending coronary artery during maximal hyperemia. The coronary arteries of the excised heart were filled with fluorescent cast material, frozen, and processed with an imaging cryomicrotome to yield a three-dimensional representation of the coronary arterial network. The effect of limited image resolution was simulated by assessing scaling law parameters from the virtual arterial network at 11 truncation levels ranging from 50 to 1,000 μm segment radius. Mapped microsphere locations were used to derive the corresponding relative Q using a reference truncation level of 200 μm. The scaling law factor α did not change with truncation level, despite considerable intersubject variability. In contrast, the scaling law exponent β decreased from 0.79 to 0.55 with increasing truncation radius and was significantly lower for truncation radii above 500 μm vs. 50 μm ( P < 0.05). Hyperemic Q was underestimated for vessel truncation above the reference level. In conclusion, flow-crown volume relations confirmed overall power law behavior; however, this relation depends on the terminal vessel radius that can be visualized. The scaling law exponent β should therefore be adapted to the resolution of the imaging modality.