Bayesian computational methods for state-space models with application to SIR model

The state-space model is a powerful statistical tool to estimate linear or non-linear discrete-time dynamic systems. This model naturally leads to the estimation problem of the time-varying parameters of the discovery-time demographic version of the susceptible-infected-recovered (SIR) model that we consider. In this paper, we consider computational methods to perform Bayesian inference on state-space models for analysing time-series data. We compare the three popular Bayesian computational methods for state-space models: the adaptive Metropolis-within-Gibbs algorithm, Liu and West's algorithm and variational approximation method based on Gaussian distributions. The performances of the three methods are compared based on synthetic datasets. Furthermore, we analyse the trend of the spread of COVID-19 in South Korea to point out the limitations of existing methods and derive meaningful results. [ FROM AUTHOR] Copyright of Journal of Statistical Computation & Simulation is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

Bayesian Inference and Data Analysis of the Unit–Power Burr X Distribution

The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysis of its key characteristics is performed, including shape analysis of the primary functions, analytical expression for moments, quantile function, incomplete moments, stochastic ordering, and stress–strength reliability. Rényi, Havrda and Charvat, and d-generalized entropies, which are measures of uncertainty, are also obtained. The model's parameters are estimated using a Bayesian estimation approach via symmetric and asymmetric loss functions. The Bayesian credible intervals are constructed based on the marginal posterior distribution. Monte Carlo simulation research is intended to test the accuracy of various estimators based on certain measures, in accordance with the complex forms of Bayesian estimators. Finally, we show that the new distribution is more appropriate than certain other competing models, according to their application for COVID-19 in Saudi Arabia and the United Kingdom. © 2023 by the authors.

Effectiveness analysis of multiple epidemic prevention measures in the context of COVID-19 using the SVIRD model and ensemble Kalman filter.

The ability to accurately forecast the spread of coronavirus disease 2019 (COVID-19) is of great importance to the resumption of societal normality. Existing methods of epidemic forecasting often ignore the comprehensive analysis of multiple epidemic prevention measures. This paper aims to analyze various epidemic prevention measures through a compound framework. Here, a susceptible-vaccinated-infected-recovered-deceased (SVIRD) model is constructed to consider the effects of population mobility among origin and destination, vaccination, and positive retest populations. And we further use real-time observations to correct the model trajectory with the help of data assimilation. Seven prevention measures are used to analyze the short-term trend of active cases. The results of the synthetic scene recommended that four measures-improving the vaccination protection rate (IVPR), reducing the number of contacts per person per day (RNCP), selecting the region with less infected people as origin A (SES-O) and limiting population flow entering from A to B per day (LAIP-OD)-are the most effective in the short-term, with maximum reductions of 75%, 53%, 35% and 31%, respectively, in active cases after 150 days. The results of the real-world experiment with Hong Kong as the origin and Shenzhen as the destination indicate that when the daily vaccination rate increased from 5% to 9.5%, the number of active cases decreased by only 7.35%. The results demonstrate that reducing the number of contacts per person per day after productive life resumes is more effective than increasing vaccination rates.

Spatiotemporal disease case prediction using contrastive predictive coding

Time series prediction models have played a vital role in guiding effective policymaking and response during the COVID-19 pandemic by predicting future cases and deaths at the country, state, and county levels. However, for emerging diseases, there is not sufficient historic data to fit traditional supervised prediction models. In addition, such models do not consider human mobility between regions. To mitigate the need for supervised models and to include human mobility data in the prediction, we propose Spatial Probabilistic Contrastive Predictive Coding (SP-CPC) which leverages Contrastive Predictive Coding (CPC), an unsupervised time-series representation learning approach. We augment CPC to incorporate a covariate mobility matrix into the loss function, representing the relative number of individuals traveling between each county on a given day. The proposal distribution learned by the algorithm is then sampled by the Metropolis-Hastings algorithm to give a final prediction of the number of COVID-19 cases. We find that the model applied to COVID-19 data can make accurate short-term predictions, more accurate than ARIMA and simple time-series extrapolation methods, one day into the future. However, for longer-term prediction windows of seven or more days into the future, we find that our predictions are not as competitive and require future research. © 2022 ACM.

Calibrating deterministic compartmental models of infection dynamics using neural network and data sampling approaches

Pandemics caused by the new coronavirus has spread globally with a strong contagion rate and death rate. In this paper the deterministic SEIR model is calibrated with Metropolis Hasting algorithm, physics-informed neural network (PINN) and latin hypercube sampling (LHS) method to identify the optimal hyper parameters of SEIR model and to forecast the dynamics of COVID-19 incidence in Saint-Petersburg, Russia, its retrospective analysis and evaluation of the effectiveness of control measures. © 2022 IEEE.

Coronavirus disease 2019 epidemic prediction in Shanghai under the "dynamic zero-COVID policy" using time-dependent SEAIQR model.

It's urgently needed to assess the COVID-19 epidemic under the "dynamic zero-COVID policy" in China, which provides a scientific basis for evaluating the effectiveness of this strategy in COVID-19 control. Here, we developed a time-dependent susceptible-exposed-asymptomatic-infected-quarantined-removed (SEAIQR) model with stage-specific interventions based on recent Shanghai epidemic data, considering a large number of asymptomatic infectious, the changing parameters, and control procedures. The data collected from March 1st, 2022 to April 15th, 2022 were used to fit the model, and the data of subsequent 7 days and 14 days were used to evaluate the model performance of forecasting. We then calculated the effective regeneration number (R t) and analyzed the sensitivity of different measures scenarios. Asymptomatic infectious accounts for the vast majority of the outbreaks in Shanghai, and Pudong is the district with the most positive cases. The peak of newly confirmed cases and newly asymptomatic infectious predicted by the SEAIQR model would appear on April 13th, 2022, with 1963 and 28,502 cases, respectively, and zero community transmission may be achieved in early to mid-May. The prediction errors for newly confirmed cases were considered to be reasonable, and newly asymptomatic infectious were considered to be good between April 16th to 22nd and reasonable between April 16th to 29th. The final ranges of cumulative confirmed cases and cumulative asymptomatic infectious predicted in this round of the epidemic were 26,477 âˆ¼ 47,749 and 402,254 âˆ¼ 730,176, respectively. At the beginning of the outbreak, R t was 6.69. Since the implementation of comprehensive control, R t showed a gradual downward trend, dropping to below 1.0 on April 15th, 2022. With the early implementation of control measures and the improvement of quarantine rate, recovery rate, and immunity threshold, the peak number of infections will continue to decrease, whereas the earlier the control is implemented, the earlier the turning point of the epidemic will arrive. The proposed time-dependent SEAIQR dynamic model fits and forecasts the epidemic well, which can provide a reference for decision making of the "dynamic zero-COVID policy".

Exact and computationally efficient Bayesian inference for generalized Markov modulated Poisson processes.

Statistical modeling of temporal point patterns is an important problem in several areas. The Cox process, a Poisson process where the intensity function is stochastic, is a common model for such data. We present a new class of unidimensional Cox process models in which the intensity function assumes parametric functional forms that switch according to a continuous-time Markov chain. A novel methodology is introduced to perform exact (up to Monte Carlo error) Bayesian inference based on MCMC algorithms. The reliability of the algorithms depends on a variety of specifications which are carefully addressed, resulting in a computationally efficient (in terms of computing time) algorithm and enabling its use with large data sets. Simulated and real examples are presented to illustrate the efficiency and applicability of the methodology. A specific model to fit epidemic curves is proposed and used to analyze data from Dengue Fever in Brazil and COVID-19 in some countries.