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Unbiased cross-validation (UCV) is a commonly-used method to calculate the optimal bandwidth for the kernel density estimator (KDE), which estimates the underlying probability density function (PDF) for a given data set. Since the UCV method was proposed, there have been few studies that have pointed out its instability when determining the KDE bandwidth. Following the principle of stability improvement, this paper presents a novel ensemble UCV based KDE (EUCV-KDE), which determines the expectation of an estimated PDF using an ensemble of data-block based UCVs rather than a single data-point based UCV. To derive the optimal bandwidth, a novel objective function is designed for EUCV-KDE by considering the empirical and structural risk of KDE together. We validate the rationality and effectiveness of EUCV-KDE on 10 probability distributions. The experimental results show that EUCV-KDE is convergent as the number of data-block based UCVs increases and can obtain a more stable and better prediction performance than the classical UCV-KDE and the revisited cross-validation (RCV) based KDE (RCV-KDE). In addition, a real-world application based on UK climate data is provided to further validate the effectiveness of EUCV-KDE by determining the optimal bandwidth for Nadaraya-Watson kernel regression estimator. [ABSTRACT FROM AUTHOR]

• Refining crude oil is a highly complex industrial process, subject to a large number of variables. • We propose a novel preprocessing methodology for obtaining quality data and extracting information from the data involved in the crude oil refining process. • The methodology incorporates dynamic knowledge, treatment of noise, reduction of the dimensionality, feature selection and introduction of slopes. • The proposal is validated through optimization of three state-of-the-art regressors: GB, RF and SVR. • This methodology along with SVR offer useful information for the expert of the refining process. This paper proposes a novel preprocessing methodology, framed within the field of time series forecasting. The aim is to get quality data and to extract information on the most important variables involved in a real-world crude oil refining process. To achieve this objective, the methodology incorporates the addition of dynamic knowledge, treatment of the noise present in the data, reduction of the dimensionality, feature selection and the introduction of slopes in the variables. Predictions are made for each step of the methodology and evaluated based on four measures: MAE, MSE, SMAPE and the delay in the prediction as compared to the original variable. The final solution is chosen based on these four measures and delivered to the experts so that they can optimize the crude oil refining process. [ABSTRACT FROM AUTHOR]

Abstract: Since the introduction of the Autoregressive Conditional Heteroscedasticity (ARCH) model of Engle [R. Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica 50 (1982) 987–1007], the literature of modelling the conditional second moment has become increasingly popular in the last two decades. Many extensions and alternate models of the original ARCH have been proposed in the literature aiming to capture the dynamics of volatility more accurately. Interestingly, the Quasi Maximum Likelihood Estimator (QMLE) with normal density is typically used to estimate the parameters in these models. As such, the higher moments of the underlying distribution are assumed to be the same as those of the normal distribution. However, various studies reveal that the higher moments, such as skewness and kurtosis of the distribution of financial returns are not likely to be the same as the normal distribution, and in some cases, they are not even constant over time. These have significant implications in risk management, especially in the calculation of Value-at-Risk (VaR) which focuses on the negative quantile of the return distribution. Failed to accurately capture the shape of the negative quantile would produce inaccurate measure of risk, and subsequently lead to misleading decision in risk management. This paper proposes a solution to model the distribution of financial returns more accurately by introducing a general framework to model the distribution of financial returns using maximum entropy density (MED). The main advantage of MED is that it provides a general framework to estimate the distribution function directly based on a given set of data, and it provides a convenient framework to model higher order moments up to any arbitrary finite order k. However this flexibility comes with a high cost in computational time as k increases, therefore this paper proposes an alternative model that would reduce computation time substantially. Moreover, the sensitivity of the parameters in the MED with respect to the dynamic changes of moments is derived analytically. This result is important as it relates the dynamic structure of the moments to the parameters in the MED. The usefulness of this approach will be demonstrated using 5min intra-daily returns of the Euro/USD exchange rate. [Copyright &y& Elsevier]

The COVID-19 epidemic continues to rage in many parts of the world. In the UK alone, an array of mathematical models have played a prominent role in guiding policymaking. Whilst considerable pedagogical material exists for understanding the basics of transmission dynamics modelling, there is a substantial gap between the relatively simple models used for exposition of the theory and those used in practice to model the transmission dynamics of COVID-19. Understanding these models requires considerable prerequisite knowledge and presents challenges to those new to the field of epidemiological modelling. In this paper, we introduce an open-source R package, comomodels, which can be used to understand the complexities of modelling the transmission dynamics of COVID-19 through a series of differential equation models. Alongside the base package, we describe a host of learning resources, including detailed tutorials and an interactive web-based interface allowing dynamic investigation of the model properties. We then use comomodels to illustrate three key lessons in the transmission of COVID-19 within R Markdown vignettes. • Compartmental models of transmission dynamics have been important determinants of public health policy for COVID-19. • Many important characteristics of the spread of COVID-19 can be deduced from relatively simple models. • The comomodels package and its associated GUI allow users to learn the characteristics of complex compartmental models in incremental fashion. • Estimating model parameters from data is generally difficult, and sensitivity analyses are key. [ABSTRACT FROM AUTHOR]

Abstract: Vaccination against the human papillomavirus (HPV) is a recent development in the UK. This paper uses an optimal control model to explore how best to target vaccination. We find that the vaccination of sexually active individuals has a greater impact on disease control than the vaccination of sexually non-active individuals. Extending the model to include male vaccination, we find that including males in a vaccination strategy is cost-effective. We compare the optimal control solution to that from a constant control model and show that the optimal control model is more efficient at forcing the system to a disease-controlled steady state. [Copyright &y& Elsevier]

Abstract: This paper estimates stochastic differential equation models for the interest rate dynamics of the United Kingdom bond market using Gaussian estimation econometric methods and monthly data over the period 1970–2010 using a range of maturities. Gaussian estimates of single and two equation models indicate that there is a relationship between the level of rates and the volatility of rates across the maturities. In addition, there is some evidence of feedback effects. [Copyright &y& Elsevier]

Abstract: The Transmission Disequilibrium Test (TDT) detects linkage between a marker and a disease-susceptibility locus in the presence of linkage disequilibrium. The TDT requires data on the genotypes of affected offspring and their parents, which might not always be available. For example, for late onset diseases it might be difficult to find parents still alive, or genotypes of offspring might not be available. Genotyping unaffected siblings, combining different genotype data sets, or assuming a model mechanism for missing parents have all been proposed to deal with missing genotypes in parents but not in offspring. In this paper, we propose a Mendel Inheritance-Transmission Disequilibrium Test (MI-TDT) to impute missing genotypes in any members of a family with two affected offspring. Our method does not require any of the remedies mentioned above but simply utilizes the fundamental property of Mendel Inheritance on the transmission of alleles from parents to offspring. Most importantly, the MI-TDT reassures researchers about the declared significant genes when incomplete data is ignored. We illustrate the MI-TDT by identifying significant genes in type 1 diabetes from the Warren families in the United Kingdom. [ABSTRACT FROM AUTHOR]