An integrated epidemic modelling framework for the real-time forecast of COVID-19 outbreaks in current epicentres

Various studies have provided a wide variety of mathematical and statistical models for early epidemic prediction of the COVID-19 outbreaks in Mainland China and other epicentres worldwide. In this paper, we present an integrated modelling framework, which incorporates typical exponential growth models, dynamic systems of compartmental models and statistical approaches, to depict the trends of COVID-19 spreading in 33 most heavily suffering countries. The dynamic system of SIR-X plays the main role for estimation and prediction of the epidemic trajectories showing the effectiveness of containment measures, while the other modelling approaches help determine the infectious period and the basic reproduction number. The modelling framework has reproduced the subexponential scaling law in the growth of confirmed cases and adequate fitting of empirical time-series data has facilitated the efficient forecast of the peak in the case counts of asymptomatic or unidentified infected individuals, the plateau that indicates the saturation at the end of the epidemic growth, as well as the number of daily positive cases for an extended period

Bayesian Framework for Multi-Wave COVID-19 Epidemic Analysis Using Empirical Vaccination Data

The COVID-19 pandemic has highlighted the necessity of advanced modeling inference using the limited data of daily cases. Tracking a long-term epidemic trajectory requires explanatory modeling with more complexities than the one with short-time forecasts, especially for the highly vaccinated scenario in the latest phase. With this work, we propose a novel modeling framework that combines an epidemiological model with Bayesian inference to perform an explanatory analysis on the spreading of COVID-19 in Israel. The Bayesian inference is implemented on a modified SEIR compartmental model supplemented by real-time vaccination data and piecewise transmission and infectious rates determined by change points. We illustrate the fitted multi-wave trajectory in Israel with the checkpoints of major changes in publicly announced interventions or critical social events. The result of our modeling framework partly reflects the impact of different stages of mitigation strategies as well as the vaccination effectiveness, and provides forecasts of near future scenarios

Bayesian Framework for Multi-Wave COVID-19 Epidemic Analysis Using Empirical Vaccination Data

The COVID-19 pandemic has highlighted the necessity of advanced modeling inference using the limited data of daily cases. Tracking a long-term epidemic trajectory requires explanatory modeling with more complexities than the one with short-time forecasts, especially for the highly vaccinated scenario in the latest phase. With this work, we propose a novel modeling framework that combines an epidemiological model with Bayesian inference to perform an explanatory analysis on the spreading of COVID-19 in Israel. The Bayesian inference is implemented on a modified SEIR compartmental model supplemented by real-time vaccination data and piecewise transmission and infectious rates determined by change points. We illustrate the fitted multi-wave trajectory in Israel with the checkpoints of major changes in publicly announced interventions or critical social events. The result of our modeling framework partly reflects the impact of different stages of mitigation strategies as well as the vaccination effectiveness, and provides forecasts of near future scenarios

Reference analysis for Birnbaum-Saunders distribution

In this paper we consider the Bayesian estimators for the unknown parameters of the Birnbaum-Saunders distribution under the reference prior. The Bayesian estimators cannot be obtained in closed forms. An approximate Bayesian approach is proposed using the idea of Lindley and Gibbs sampling procedure is also used to obtain the Bayesian estimators. These results are compared using Monte Carlo simulations with the maximum likelihood method and another approximate Bayesian approach Laplace's approximation. Two real data sets are analyzed for illustrative purposes.

Bayesian Estimation of Gumbel Type-II Distribution

In this paper we consider the Bayesian estimators for the unknown parameters of Gumbel type-II distribution. The Bayesian estimators cannot be obtained in closed forms. Approximate Bayesian estimators are computed using the idea of Lindley’s approximation under different loss functions. The approximate Bayes estimates obtained under the assumption of non-informative priors are compared with their maximum likelihood counterparts using Monte Carlo simulation. A real data set is analyzed for illustrative purpose

Robust Sparse Reduced-Rank Regression with Response Dependency

In multiple response regression, the reduced rank regression model is an effective method to reduce the number of model parameters and it takes advantage of interrelation among the response variables. To improve the prediction performance of the multiple response regression, a method for the sparse robust reduced rank regression with covariance estimation(Cov-SR4) is proposed, which can carry out variable selection, outlier detection, and covariance estimation simultaneously. The random error term of this model follows a multivariate normal distribution which is a symmetric distribution and the covariance matrix or precision matrix must be a symmetric matrix that reduces the number of parameters. Both the element-wise penalty function and row-wise penalty function can be used to handle different types of outliers. A numerical algorithm with a covariance estimation method is proposed to solve the robust sparse reduced rank regression. We compare our method with three recent reduced rank regression methods in a simulation study and real data analysis. Our method exhibits competitive performance both in prediction error and variable selection accuracy

Semiparametric estimation for accelerated failure time mixture cure model allowing non-curable competing risk

The mixture cure model is the most popular model used to analyse the major event with a potential cure fraction. But in the real world there may exist a potential risk from other non-curable competing events. In this paper, we study the accelerated failure time model with mixture cure model via kernel-based nonparametric maximum likelihood estimation allowing non-curable competing risk. An EM algorithm is developed to calculate the estimates for both the regression parameters and the unknown error densities, in which a kernel-smoothed conditional profile likelihood is maximised in the M-step, and the resulting estimates are consistent. Its performance is demonstrated through comprehensive simulation studies. Finally, the proposed method is applied to the colorectal clinical trial data

Statistical inference for zero-and-one-inflated poisson models

In this paper, a zero-and-one-inflated Poisson (ZOIP) model is studied. The maximum likelihood estimation and the Bayesian estimation of the model parameters are obtained based on data augmentation method. A simulation study based on proposed sampling algorithm is conducted to assess the performance of the proposed estimation for various sample sizes. Finally, two real data-sets are analysed to illustrate the practicability of the proposed method

Research on three-step accelerated gradient algorithm in deep learning

Gradient descent (GD) algorithm is the widely used optimisation method in training machine learning and deep learning models. In this paper, based on GD, Polyak's momentum (PM), and Nesterov accelerated gradient (NAG), we give the convergence of the algorithms from an initial value to the optimal value of an objective function in simple quadratic form. Based on the convergence property of the quadratic function, two sister sequences of NAG's iteration and parallel tangent methods in neural networks, the three-step accelerated gradient (TAG) algorithm is proposed, which has three sequences other than two sister sequences. To illustrate the performance of this algorithm, we compare the proposed algorithm with the three other algorithms in quadratic function, high-dimensional quadratic functions, and nonquadratic function. Then we consider to combine the TAG algorithm to the backpropagation algorithm and the stochastic gradient descent algorithm in deep learning. For conveniently facilitate the proposed algorithms, we rewite the R package ‘neuralnet’ and extend it to ‘supneuralnet’. All kinds of deep learning algorithms in this paper are included in ‘supneuralnet’ package. Finally, we show our algorithms are superior to other algorithms in four case studies