Katherine Davies, Debanjan Mitra, William Volterman
In this article, the bivariate exponential distribution proposed by Downton (“Bivariate exponential distributions in reliability theory”, Journal of the Royal Statistical Society Series B, 1970) is extended to a bivariate Weibull distribution, and it is called the Downton’s bivariate Weibull (DBW) distribution. Statistical properties of the DBW distribution are explored and likelihood inference developed based on complete as well as right-censored bivariate data are discussed. Through extensive Monte Carlo
simulations, performance of the point and interval estimates are evaluated. Two real datasets are analyzed for illustrative purposes. It is concluded that the DBW distribution is very useful to model bivariate data.
Introduction
The burden of childhood morbidity and mortality are still huge in most sub-Saharan African countries with West African sub-region contributing largely to the burden. Previous findings have demonstrated strong link between early life events such as low birth weight (LBW) with later events particularly malnutrition. We aim at estimating the specific and shared spatial patterns of LBW and stunting among under-five children in multiple West African countries.
Method
Data set for the study was sourced from the Demographic and Health Surveys conducted in fourteen West African countries. We used a Bayesian shared component model allows us to split the spatial surface into those specific to each of the outcomes and one shared by the two, with inference based on a Bayesian approximation procedure through the integrated nested Laplace approximation.
Results
The findings show spatial clustering in the shared and specific effects of the health outcomes, demonstrating high likelihood in northern Nigeria spanning through Niger and that the spatial pattern for the shared effects are similar to those of the specific effects of stunting. Furthermore, mother’s level of education, attendance in antenatal care and household wealth index are strongly associated with the shared health outcomes.
Conclusion
The study provides insight into the spatial pattern of LBW and stunting among West African children and can be useful in targeted interventions in regions with high burden of LBW and malnutrition which may include more advocacy that promote the use of antenatal care services during pregnancy.
Empirical evidence suggests that the traditional GARCH-type models are unable to accurately estimate the volatility of financial markets. To improve on the accuracy of the traditional GARCH-type models, a hybrid model (BSGARCH (1, 1)) that combines the flexibility of B-splines with the GARCH (1, 1) model has been proposed in the study. The lagged residuals from the GARCH (1, 1) model are fitted with a B-spline estimator and added to the results produced from the GARCH (1, 1) model. The proposed BSGARCH (1, 1) model was applied to simulated data and two real financial time series data (NASDAQ 100 and S&P 500). The outcome was then compared to the outcomes of the GARCH (1, 1), EGARCH (1, 1), GJR-GARCH (1, 1), and APARCH (1, 1) with different error distributions (ED) using the mean absolute percentage error (MAPE), the root mean square error (RMSE), Theil’s inequality coefficient (TIC) and QLIKE. It was concluded that the proposed BSGARCH (1, 1) model outperforms the traditional GARCH-type models that were considered in the study based on the performance metrics, and thus, it can be used for estimating volatility of stock markets.
Nabeela Anwar, Iftikhar Ahmad, Adiqa Kausar Kiani
et al.
The most important factor for increasing crop production is pest and pathogen resistance, which has a major impact on global food security. Pest management also emphasizes the need for farming awareness. A high crop yield is ultimately achieved by protecting crops from pests and raising public awareness of the devastation caused by pests. In this research, we aim to investigate the intricate impacts of nonlinear delayed systems for managing crop pest management (CPM) supervised by Ordinary Differential Equations (ODEs). Our focus will be on highlighting the intricate and often unpredictable relationships that occur over time among crops, pests, strategies for rehabilitation, and environmental factors. The nonlinear delayed CPM model incorporated the four compartments: crop biomass density [B(t)], susceptible pest density [S(t)], infected pest density [I(t)], and population awareness level [A(t)]. The approximate solutions for the four compartments B(t), S(t), I(t), and A(t) are determined by the implementation of sundry scenarios generated with the variation in crop biomass growth rate, rate of pest attacks, pest natural death rate, disease associated death rate and memory loss of aware people, by means of exploiting the strength of the Adams (ADS) and explicit Runge-Kutta (ERK) numerical solvers. Comparative analysis of the designed approach is carried out for the dynamic impacts of the nonlinear delayed CPM model in terms of numerical outcomes and simulations based on sundry scenarios.
The Indian buffet process (IBP) and phylogenetic Indian buffet process (pIBP) can be used as prior models to infer latent features in a data set. The theoretical properties of these models are under-explored, however, especially in high dimensional settings. In this paper, we show that under mild sparsity condition, the posterior distribution of the latent feature matrix, generated via IBP or pIBP priors, converges to the true latent feature matrix asymptotically. We derive the posterior convergence rate, referred to as the contraction rate. We show that the convergence results remain valid even when the dimensionality of the latent feature matrix increases with the sample size, therefore making the posterior inference valid in high dimensional settings. We demonstrate the theoretical results using computer simulation, in which the parallel-tempering Markov chain Monte Carlo method is applied to overcome computational hurdles. The practical utility of the derived properties is demonstrated by inferring the latent features in a reverse phase protein arrays (RPPA) dataset under the IBP prior model.
Properties of catenation of sequences of finite (words) and infinite ( lengths are largely studied in formal language theory. These operations are derived from the mechanism how they are accepted or generated by the corresponding devices. Finite automata accept structures containing only words, automata accept only words. Structures containing both words and words (∞ - words) are mostly generated by various types of ∞ - automata(∞- machines). The aim of the paper is to investigate algebraic properties of operations on ∞ - words generated by IGk –automata, where k is to model the depth of memory. It has importance in many applications (shift registers, discrete systems with memory,…). It is shown that resulting algebraic structures are of „pure“ groupoid or partial groupoid type.
Evangelos Georganas, Dhiraj Kalamkar, Sasikanth Avancha
et al.
During the past decade, novel Deep Learning (DL) algorithms, workloads and hardware have been developed to tackle a wide range of problems. Despite the advances in workload and hardware ecosystems, the programming methodology of DL systems is stagnant. DL workloads leverage either highly-optimized, yet platform-specific and inflexible kernels from DL libraries, or in the case of novel operators, reference implementations are built via DL framework primitives with underwhelming performance. This work introduces the Tensor Processing Primitives (TPP), a programming abstraction striving for efficient, portable implementation of DL workloads with high-productivity. TPPs define a compact, yet versatile set of 2D-tensor operators [or a virtual Tensor Instruction Set Architecture (ISA)], which subsequently can be utilized as building-blocks to construct complex operators on high-dimensional tensors. The TPP specification is platform-agnostic, thus, code expressed via TPPs is portable, whereas the TPP implementation is highly-optimized and platform-specific. We demonstrate the efficacy and viability of our approach using standalone kernels and end-to-end DL & High Performance Computing (HPC) workloads expressed entirely via TPPs that outperform state-of-the-art implementations on multiple platforms.
Eleni Boumpa, Vasileios Tsoukas, Vasileios Chioktour
et al.
In this survey, the issues of urban routing are analyzed, and critical considerations for smart and cost-effective delivery services are highlighted. Smart cities require intelligent services and solutions to address their routing issues. This article gives a brief description of current services that either apply classical methods or services that employ machine learning approaches. Furthermore, a comparison of the most promising research options in regard to VRP is provided. Finally, an initial design of a holistic scheme that would optimally combine several tools and approaches to serve the needs of different users with regard to the VRP is presented.
Khalil Shafie, Mohammad Reza Faridrohani, Siamak Noorbaloochi
et al.
Functional Magnetic Resonance Imaging (fMRI) is a fundamental tool in advancing our understanding of the brain's functionality. Recently, a series of Bayesian approaches have been suggested to test for the voxel activation in different brain regions. In this paper, we propose a novel definition for the global Bayes factor to test for activation using the Radon-Nikodym derivative. Our proposed method extends the definition of Bayes factor to an infinite dimensional Hilbert space. Using this extended definition, a Bayesian testing procedure is introduced for signal detection in noisy images when both signal and noise are considered as an element of an infinite dimensional Hilbert space. This new approach is illustrated through a real data analysis to find activated areas of Brain in an fMRI data.
This study proposes a bivariate index vector to concurrently analyze both the degree and direction of departure from the quasi-symmetry (QS) model for ordinal square contingency tables. The QS model and extended QS (EQS) models identify the symmetry and asymmetry between the probabilities of normal circulation and reverse circulation when the order exists for arbitrary three categories. The asymmetry parameter of the EQS model implies the degree of departure from the QS model; the EQS model is equivalent to the QS model when the asymmetry parameter equals to one. The structure of the EQS model differs depending on whether the asymmetry parameter approaches zero or infinity. Thus, the asymmetry parameter of the EQS model also implies the direction of departure from the QS model. The proposed bivariate index vector is constructed by combining existing and original sub-indexes that represent the degree of departure from the QS model and its direction. These sub-indexes are expressed as functions of the asymmetry parameter under the EQS model. We construct an estimator of the proposed bivariate index vector and an approximate confidence region for the proposed bivariate index vector. Using real data, we show that the proposed bivariate index vector is important to compare degrees of departure from the QS model for plural data sets.
We prove a simple criterion of exponential tightness for sequences of Gaussian r.v.’s with values in a separable Banach space from which we deduce a general result of Large Deviations which allows easily to obtain LD estimates in various situations.
Christopher M Sabillon, Christina I Guzman, Golam Kibria
Introduction: Coronavirus disease 2019 (COVID-19), a respiratory disease caused by the coronavirus SARSCoV-2, has had an immense impact on a variety of sectors both worldwide and nationwide. Vast differences are observed among states within the United States of America in terms of COVID-19 cases and deaths.
Objective: The objective of this paper is to present a means through which we can compare deaths between multiple states, using the index date approach applied by Middelburg and Rosendaal.
Materials and Methods: Using the CDC COVID-19 tracker, we created two sets of ten states focusing on states with (1) the highest number of deaths and (2) the highest number of deaths per 100,000. We applied features of the authors’ technique in order to compare deaths between certain states through visualizations. We referred to the cumulative number of deaths on each day from January 21st, 2020 to September 30th, 2020, as a percentage of the cumulative deaths 40 days after the first death.
Results and Discussion: Comparability was established by synchronizing each state to a baseline date, which allows us to adjust for issues that arise from the scales used within a standard cumulative deaths graph, such as a tendency to be driven by the states with the highest cumulative number of deaths. This technique also normalized each state to a standard start date.
Conclusion: This paper shows the application of a technique that allows for clearer comparisons of COVID19 related deaths between states, as opposed to the use of a standard cumulative deaths graphs.
Finite field is a wide topic in mathematics. Consequently, none can talk about the whole contents of finite fields. That is why this research focuses on small content of finite fields such as polynomials computational, ring of integers modulo p where p is prime or a power of prime. Most of the times, books which talk about finite fields are rarely to be found, therefore one can know how arithmetic computational on small finite fields works and be able to extend to the higher order. This means how integer and polynomial arithmetic operations are done for Z p such as addition, subtraction, division and multiplication in Z p followed by reduction of p (modulo p). Since addition is the same as subtraction and division is treated as the inverse of the multiplication, thus in this paper, only addition and multiplication arithmetic operations are applied for the considered small finite fields (Z 2 − Z 17 ). With polynomials, one can learn from this paper how arithmetic computational through polynomials over finite fields are performed since these polynomials have coefficients drawn from finite fields. The paper includes also construction of polynomials over finite fields as an extension of finite fields with polynomials. This lead to arithmetic computational tables for the finite fields F q [x]/f(x), where f(x) is irreducible over F q . From the past decades, many researchers complained about the applications of some topics in pure mathematics and therefore the finite fields play more important role in coding theory, which involves error-coding detection and error-correction as well as cyclic codes. As a result, this research paper shows these applications among others.
Average biosimilarity is investigated under a three-arm parallel design: one arm corresponds to the test drug T , and the other two arms correspond to two versions of the reference drug, say R1 and R2. The hypothesis of interest is the equivalence of the population average response for T with the mean of the population average responses for R_1 and R_2. The parameter of interest is formulated as the absolute difference of the above two averages, scaled by the absolute difference between the population means corresponding to R_1 and R_2. A difference parameter is also proposed. For the ratio parameter, a test can be derived using the asymptotic normality of an appropriate test statistic; however, the test is not satisfactory in terms of type I error probabilities. Improved tests are derived by applying a bootstrap calibration, and by using the idea of a generalized pivotal quantity (gpq). The tests are developed under equal variance and unequal variance scenarios. Sample size determination is also addressed. For the difference parameter, a satisfactory test is developed using the gpq idea. The proposed methods result in tests that are satisfactory in terms of type I error performance.