Bayesian model averaging for mortality forecasting using leave-future-out validation

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Various stochastic frameworks have been developed to model mortality patterns by taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and can lead to some well-documented drawbacks, including model misspecification, parameter uncer-tainty, and overfitting. To address these issues we first consider mortality modeling in a Bayesian negative-binomial framework to account for overdispersion and the uncer-tainty about the parameter estimates in a natural and coherent way. Model averaging techniques are then considered as a response to model misspecifications. In this paper, we propose two methods based on leave-future-out validation and compare them to standard Bayesian model averaging (BMA) based on marginal likelihood. An intensive numerical study is carried out over a large range of simulation setups to compare the performances of the proposed methodologies. An illustration is then proposed on real-life mortality datasets, along with a sensitivity analysis to a Covid-type scenario. Overall, we found that both methods based on an out-of-sample criterion outperform the standard BMA approach in terms of prediction performance and robustness.(c) 2022 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

Testing big data in a big crisis: Nowcasting under COVID-19.

During the COVID-19 pandemic, economists have struggled to obtain reliable economic predictions, with standard models becoming outdated and their forecasting performance deteriorating rapidly. This paper presents two novelties that could be adopted by forecasting institutions in unconventional times. The first innovation is the construction of an extensive data set for macroeconomic forecasting in Europe. We collect more than a thousand time series from conventional and unconventional sources, complementing traditional macroeconomic variables with timely big data indicators and assessing their added value at nowcasting. The second novelty consists of a methodology to merge an enormous amount of non-encompassing data with a large battery of classical and more sophisticated forecasting methods in a seamlessly dynamic Bayesian framework. Specifically, we introduce an innovative "selection prior" that is used not as a way to influence model outcomes, but as a selecting device among competing models. By applying this methodology to the COVID-19 crisis, we show which variables are good predictors for nowcasting Gross Domestic Product and draw lessons for dealing with possible future crises.

Spatiotemporal Bayesian estimation of the number of under-reported COVID-19 cases in Victoria Australia.

Having an estimate of the number of under-reported cases is crucial in determining the true burden of a disease. In the COVID-19 pandemic, there is a great need to quantify the true disease burden by capturing the true incidence rate to establish appropriate measures and strategies to combat the disease. This study investigates the under-reporting of COVID-19 cases in Victoria, Australia, during the third wave of the pandemic as a result of variation in geographic area and time. It is aimed to determine potential under-reported areas and generate the true picture of the disease in terms of the number of cases. A two-tiered Bayesian hierarchical model approach is employed to estimate the true incidence and detection rates through Bayesian model averaging. The proposed model goes beyond testing inequality across areas by looking into other covariates such as weather, vaccination rates, and access to vaccination and testing centres, including interactions and variations between space and time. This model aims for parsimony yet allows a broader range of scope to capture the underlying dynamic of the reported COVID-19 cases. Moreover, it is a data-driven, flexible, and generalisable model to a global context such as cross-country estimation and across time points under strict pandemic conditions.

Bayesian Model Averaging to Account for Model Uncertainty in Estimates of a Vaccine's Effectiveness.

Purpose: Vaccine effectiveness (VE) studies are often conducted after the introduction of new vaccines to ensure they provide protection in real-world settings. Control of confounding is often needed during the analyses, which is most efficiently done through multivariable modeling. When many confounders are being considered, it can be challenging to know which variables need to be included in the final model. We propose an intuitive Bayesian model averaging (BMA) framework for this task. Patients and Methods: Data were used from a matched case-control study that aimed to assess the effectiveness of the Lyme vaccine post-licensure. Cases were residents of Connecticut, 15-70 years of age with confirmed Lyme disease. Up to 2 healthy controls were matched to each case subject by age. All participants were interviewed, and medical records were reviewed to ascertain immunization history and evaluate potential confounders. BMA was used to systematically search for potential models and calculate the weighted average VE estimate from the top subset of models. The performance of BMA was compared to three traditional single-best-model-selection methods: two-stage selection, stepwise elimination, and the leaps and bounds algorithm. Results: The analysis included 358 cases and 554 matched controls. VE ranged between 56% and 73% and 95% confidence intervals crossed zero in <5% of all candidate models. Averaging across the top 15 models, the BMA VE was 69% (95% CI: 18-88%). The two-stage, stepwise, and leaps and bounds algorithm yielded VE of 71% (95% CI: 21-90%), 73% (95% CI: 26-90%), and 74% (95% CI: 27-91%), respectively. Conclusion: This paper highlights how the BMA framework can be used to generate transparent and robust estimates of VE. The BMA-derived VE and confidence intervals were similar to those estimated using traditional methods. However, by incorporating model uncertainty into the parameter estimation, BMA can lend additional rigor and credibility to a well-designed study.

A Novel Layered Learning Approach for Forecasting Respiratory Disease Excess Mortality during the COVID-19 pandemic

Forecasting model selection and model combination are the two contending approaches in the time series forecasting literature. Ensemble learning is useful for addressing a given predictive task by different predictive models when direct mapping from inputs to outputs is inaccurate. We adopt a layered learning approach to an ensemble learning strategy to solve the predictive tasks with improved predictive performance and take advantage of multiple learning processes into an ensemble model. In this proposed strategy, we build each model with a specific holdout and make the ensemble model of time series with a dynamic selection approach. For the experimental section, we studied more than twelve thousand observations in a portfolio of 61-time series of reported respiratory disease deaths to show the amount of improvement in predictive performance of excess mortality. Then we compare the forecasting outcome of our model with the corresponding total deaths of COVID-19 for selected countries. © 2021 Associacao Portuguesa de Sistemas de Informacao. All rights reserved.

An ensemble learning strategy for panel time series forecasting of excess mortality during the COVID-19 pandemic.

Quantifying and analyzing excess mortality in crises such as the ongoing COVID-19 pandemic is crucial for policymakers. Traditional measures fail to take into account differences in the level, long-term secular trends, and seasonal patterns in all-cause mortality across countries and regions. This paper develops and empirically investigates the forecasting performance of a novel, flexible and dynamic ensemble learning with a model selection strategy (DELMS) for the seasonal time series forecasting of monthly respiratory disease death data across a pool of 61 heterogeneous countries. The strategy is based on a Bayesian model averaging (BMA) of heterogeneous time series methods involving both the selection of the subset of best forecasters (model confidence set), the identification of the best holdout period for each contributed model, and the determination of optimal weights using out-of-sample predictive accuracy. A model selection strategy is also developed to remove the outlier models and to combine the models with reasonable accuracy in the ensemble. The empirical outcomes of this large set of experiments show that the accuracy of the BMA approach is significantly improved with DELMS when selecting a flexible and dynamic holdout period and removing the outlier models. Additionally, the forecasts of respiratory disease deaths for each country are highly accurate and exhibit a high correlation (94%) with COVID-19 deaths in 2020.

Modeling the contribution of Nitrogen Dioxide, Vertical pressure velocity and PM2.5 to COVID-19 fatalities.

The COVID-19 caused by the severe acute respiratory syndrome coronavirus was reported in China in December 2019. The severity and lethality of this disease have been linked to poor air quality indicators such as tropospheric nitrogen dioxide (NO2) and dust surface mass concentration particulate matter (PM2.5) as possible contributors. The Arab League has 22 member countries and is home to almost 420 million people. The primary objective of this study is to assess the relationship between NO2, PM2.5 and vertical pressure velocity (hereafter: OMEGA) (extracted from the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) database), socio-economic factors (the population and geographic area of each member country) and COVID-19 deaths using Bayesian model averaging. The total plausible models (25) were estimated. The results show that the posterior inclusion probability (PIP), which indicates the probability that a particular indicator is included in the best model, was 0.69, 0.94, 0.68, 0.47, and 0.61 for OMEGA, PM2.5, NO2, geographical area, and population, respectively, meaning that these variables are important contributors in predicting COVID-19 fatalities in the Arab League states. This study shows that atmospheric satellite measurements from MERRA-2 datasets are capable of being used to quantify trace gases in pandemic studies.

Bayesian model averaging for mortality forecasting using leave-future-out validation

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Various stochastic frameworks have been developed to model mortality patterns by taking into account the main stylized facts driving these patterns. However, relying on the prediction of one specific model can be too restrictive and can lead to some well-documented drawbacks, including model misspecification, parameter uncertainty, and overfitting. To address these issues we first consider mortality modeling in a Bayesian negative-binomial framework to account for overdispersion and the uncertainty about the parameter estimates in a natural and coherent way. Model averaging techniques are then considered as a response to model misspecifications. In this paper, we propose two methods based on leave-future-out validation and compare them to standard Bayesian model averaging (BMA) based on marginal likelihood. An intensive numerical study is carried out over a large range of simulation setups to compare the performances of the proposed methodologies. An illustration is then proposed on real-life mortality datasets, along with a sensitivity analysis to a Covid-type scenario. Overall, we found that both methods based on an out-of-sample criterion outperform the standard BMA approach in terms of prediction performance and robustness.

Modeling the spread of COVID-19 in New York City.

This paper proposes an ensemble predictor for the weekly increase in the number of confirmed COVID-19 cases in the city of New York at zip code level. Within a Bayesian model averaging framework, the baseline is a Poisson regression for count data. The set of covariates includes autoregressive terms, spatial effects, and demographic and socioeconomic variables. Our results for the second wave of the coronavirus pandemic show that these regressors are more significant to predict the number of new confirmed cases as the pandemic unfolds. Both pointwise and interval forecasts exhibit strong predictive ability in-sample and out-of-sample.

Este artículo propone un predictor de conjunto para el aumento semanal del número de casos confirmados de COVID­19 en la ciudad de Nueva York a nivel de código postal. Dentro de un marco de promediación de modelo bayesiano, la línea de base es una regresión de Poisson para datos de recuento. El conjunto de covariables incluye términos autorregresivos, efectos espaciales y variables demográficas y socioeconómicas. Los resultados para la segunda ola de la pandemia de coronavirus muestran que estos regresores son más significativos para predecir el número de nuevos casos confirmados a medida que se desarrolla la pandemia. Tanto las previsiones puntuales como las de intervalo muestran una fuerte capacidad de predicción, tanto dentro como fuera de la muestra.

The determinants of output losses during the Covid-19 pandemic.

The global recession in the wake of the Covid-19 pandemic was accompanied by a significant degree of heterogeneity in the economic contraction across countries. We use a rich data set and Bayesian model averaging techniques to identify the factors shaping the extent of heterogeneity. The results highlight the importance of adverse initial conditions (large contact-intensive service sector) and behavioural changes (increased voluntary spatial distancing) relative to the extent of public containment measures.

The COVID-19 shock and long-term interest rates in emerging market economies.

Motivated by a divergent behavior of long-term sovereign bond yields across emerging market economies in the onset of the COVID-19 pandemic, we employ the Bayesian model averaging to uncover the country-specific factors that explain those differences. The most pronounced determinants of a country's vulnerability to the COVID-19 shock were: (a) low GDP dynamics and (b) high sensitivity of bond yields to VIX in the period preceding the pandemic. Our results speak to the role of growth fundamentals in building-up the exposure to crises in emerging markets. They also signify a persistent differentiation of emerging economies by international investors.