Approximating multivariate distributions with vines

In a series of papers, Bedford and Cooke used vine (or pair-copulae) as a graphical tool for representing complex high dimensional distributions in terms of bivariate and conditional bivariate distributions or copulae. In this paper, we show that how vines can be used to approximate any given multivariate distribution to any required degree of approximation. This paper is more about the approximation rather than optimal estimation methods. To maintain uniform approximation in the class of copulae used to build the corresponding vine we use minimum information approaches. We generalised the results found by Bedford and Cooke that if a minimal information copula satis¯es each of the (local) constraints (on moments, rank correlation, etc.), then the resulting joint distribution will be also minimally informative given those constraints, to all regular vines. We then apply our results to modelling a dataset of Norwegian financial data that was previously analysed in Aas et al. (2009)

Association of Serum Leptin with Prognostic Factors in Breast Cancer

Background: Nowadays, cytokines such as Leptin and adiponectin are introduced as prognostic factors which, according to some studies, are also associated with body mass index. This study aimed to determine serum leptin level and its relationship with prognostic factors in breast cancer patients.Methods: This case–control study was conducted in the oncology department of Tohid Hospital, Sanandaj, Iran, between 2019 and 2020. Hundred new cases of breast cancer patients with histological evidence were enrolled in this study. Additionally, 100 age-and BMI-matched healthy individuals were recruited as the control group. The serum leptin level was measured using the ELISA method.Results: Serum leptin levels were significantly higher in breast cancer patients compared to the control group (21.68 ± 9.16 vs 11.89 ± 4.45; p < 0.001). There was no significant relationship between plasma leptin levels with ER, PR, and HER2 expressions (p > 0.05). Also, no significant associations were noted between leptin levels and grading and disease staging (p > 0.05).Conclusion: The study found that leptin is higher in breast cancer patients than in healthy individuals, however, it did not prove that leptin is a predictive or prognostic factor.Keywords: leptin, breast cancer, staging, gradin

A low cost and highly accurate technique for big data spatial-temporal interpolation

The high velocity, variety and volume of data generation by today's systems have necessitated Big Data (BD) analytic techniques. This has penetrated a wide range of industries; BD as a notion has various types and characteristics, and therefore a variety of analytic techniques would be required. The traditional analysis methods are typically unable to analyse spatial-temporal BD. Interpolation is required to approximate the values between the already existing data points, yet since there exist both location and time dimensions, only a multivariate interpolation would be appropriate. Nevertheless, existing software are unable to perform such complex interpolations. To overcome this challenge, this paper presents a layer by layer interpolation approach for spatial-temporal BD. Developing this layered structure provides the opportunity for working with much smaller linear system of equations. Consequently, this structure increases the accuracy and stability of numerical structure of the considered BD interpolation. To construct this layer by layer interpolation, we have used the good properties of Radial Basis Functions (RBFs). The proposed new approach is applied to numerical examples in spatial-temporal big data and the obtained results confirm the high accuracy and low computational cost. Finally, our approach is applied to explore one of the air pollution indices, i.e. daily PM2.5 concentration, based on different stations in the contiguous United States, and it is evaluated by leave-one-out cross validation

Stakeholders’ impact on the reuse potential of structural elements at the end-of-life of a building: A machine learning approach

The construction industry, and at its core the building sector, is the largest consumer of non-renewable resources, which produces the highest amount of waste and greenhouse gas emissions worldwide. Since most of the embodied energy and CO2 emissions during the construction and demolition phases of a building are related to its structure, measures to extend the service life of these components should be prioritised. This study develops a set of easy-to-understand instructions to facilitate the practitioners in assessing the social sustainability and responsibility of reusing the load-bearing structural components within the building sector. The results derived by developing and then employing advanced machine learning techniques indicate that the most significant social factor is the perception of the regulatory authorities. The second and third ranks among the social reusability factors belong to risks. Since there is a strong correlation between perception and risk, the potential risks associated with reusing structural elements affect the stakeholders’ perception of reuse. The Bayesian network developed in this study unveil the complex and non-linear correlation between variables, which means none of the factors could alone determine the reusability of an element. This paper shows that by using the basics of probability theory and combining them with advanced supervised machine learning techniques, it is possible to develop tools that reliably estimate the social reusability of these elements based on influencing variables. Therefore, the authors propose using the developed approach in this study to promote materials' circularity in different construction industry sub-sectors

Copula-based probabilistic assessment of intensity and duration of cold episodes: A case study of Malayer vineyard region

Frost, particularly during the spring, is one of the most damaging weather phenomena for vineyards, causing significant economic losses to vineyards around the world each year. The risk of tardive frost damage in vine-yards due to changing climate is considered as an important threat to the sustainable production of grapes. Therefore, the cold monitoring strategies is one of the criteria with significant impacts on the yields and prosperity of horticulture and raisin factories. Frost events can be characterized by duration and severity. This paper investigates the risk and impacts of frost phenomenon in the vineyards by modeling the joint distribution of duration and severity factors and analyzing the influential parameter’s dependency structure using capabilities of copula functions. A novel mathematical framework is developed within this study to understand the risk and uncertainties associate with frost events and the impacts on yields of vineyards by analyzing the non-linear dependency structure using copula functions as an efficient tool. The developed model was successfully vali-dated for the case study of vineyard in Malayer city of Iran. The copula model developed in this study was shown to be a robust tool for predicting the return period of the frost events

Using Machine Learning Algorithms to Develop a Clinical Decision-Making Tool for COVID-19 Inpatients.

BACKGROUND: Within the UK, COVID-19 has contributed towards over 103,000 deaths. Although multiple risk factors for COVID-19 have been identified, using this data to improve clinical care has proven challenging. The main aim of this study is to develop a reliable, multivariable predictive model for COVID-19 in-patient outcomes, thus enabling risk-stratification and earlier clinical decision-making. METHODS: Anonymised data consisting of 44 independent predictor variables from 355 adults diagnosed with COVID-19, at a UK hospital, was manually extracted from electronic patient records for retrospective, case-control analysis. Primary outcomes included inpatient mortality, required ventilatory support, and duration of inpatient treatment. Pulmonary embolism sequala was the only secondary outcome. After balancing data, key variables were feature selected for each outcome using random forests. Predictive models were then learned and constructed using Bayesian networks. RESULTS: The proposed probabilistic models were able to predict, using feature selected risk factors, the probability of the mentioned outcomes. Overall, our findings demonstrate reliable, multivariable, quantitative predictive models for four outcomes, which utilise readily available clinical information for COVID-19 adult inpatients. Further research is required to externally validate our models and demonstrate their utility as risk stratification and clinical decision-making tools