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Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

The focus of the present paper is to forecast mortality rates for small sub-populations that are parts of a larger super-population. In this setting the assumption is that it is possible to produce reliable forecasts for the…

Applications · Statistics 2026-04-22 Mathias Lindholm , Gabriele Pittarello

Survival models are used in various fields, such as the development of cancer treatment protocols. Although many statistical and machine learning models have been proposed to achieve accurate survival predictions, little attention has been…

Machine Learning · Computer Science 2020-03-26 Hrushikesh Loya , Pranav Poduval , Deepak Anand , Neeraj Kumar , Amit Sethi

A new stochastic method for describing mortality is proposed and explored. It is based on differences of observed times series of the transform $\log(-\log x)$ of survival probabilities which seem to follow simple patterns over the years.…

Applications · Statistics 2015-02-26 Meitner Cadena

The missing data problem pervasively exists in statistical applications. Even as simple as the count data in mortality projections, it may not be available for certain age-and-year groups due to the budget limitations or difficulties in…

Methodology · Statistics 2021-03-11 Rui Gong , Xiaoqian Sun , Leping Liu , Yu-Bo Wang

The EU Solvency II directive recommends insurance companies to pay more attention to the risk management methods. The sense of risk management is the ability to quantify risk and apply methods that reduce uncertainty. In life insurance, the…

Econometrics · Economics 2018-04-02 Kamil Jodź

Accurate forecasts of weekly mortality are essential for public health and the insurance industry. We develop a forecasting framework that extends the Lee-Carter model with age- and region-specific seasonal effects and penalized distributed…

Applications · Statistics 2026-05-22 Jens Robben , Karim Barigou

Stock market prediction has been a classical yet challenging problem, with the attention from both economists and computer scientists. With the purpose of building an effective prediction model, both linear and machine learning tools have…

Statistical Finance · Quantitative Finance 2021-08-13 Weiwei Jiang

The predominant way of modelling mortality rates is the Lee-Carter model and its many extensions. The Lee-Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that…

Applications · Statistics 2016-12-14 Eric Beutner , Simon Reese , Jean-Pierre Urbain

Increasingly sophisticated mathematical modelling processes from Machine Learning are being used to analyse complex data. However, the performance and explainability of these models within practical critical systems requires a rigorous and…

Machine Learning · Computer Science 2020-12-08 Xingyu Zhao , Alec Banks , James Sharp , Valentin Robu , David Flynn , Michael Fisher , Xiaowei Huang

Separate modelling of cause specific mortality rates and their projections can yield inconsistent forecasts when the sum of deaths by cause does not match the total observed in a population. We develop a hierarchical probabilistic framework…

Applications · Statistics 2026-03-03 Andrea Nigri , Han Lin Shang , Francesco Ungolo

The aim of this paper is to propose a realistic and operational model to quantify the systematic risk of mortality included in an engagement of retirement. The model presented is built on the basis of model of Lee-Carter. The stochastic…

General Finance · Quantitative Finance 2010-01-13 Frédéric Planchet , Laurent Faucillon , Marc Juillard

Various stochastic models have been proposed to estimate mortality rates. In this paper we illustrate how machine learning techniques allow us to analyze the quality of such mortality models. In addition, we present how these techniques can…

Applications · Statistics 2017-05-10 Philippe Deprez , Pavel V. Shevchenko , Mario V. Wüthrich

Uncertainty estimation bears the potential to make deep learning (DL) systems more reliable. Standard techniques for uncertainty estimation, however, come along with specific combinations of strengths and weaknesses, e.g., with respect to…

Machine Learning · Computer Science 2022-05-02 Joachim Sicking , Maram Akila , Jan David Schneider , Fabian Hüger , Peter Schlicht , Tim Wirtz , Stefan Wrobel

We propose the use of statistical emulators for the purpose of valuing mortality-linked contracts in stochastic mortality models. Such models typically require (nested) evaluation of expected values of nonlinear functionals of…

Statistical Finance · Quantitative Finance 2015-09-15 James Risk , Michael Ludkovski

Deep Learning is a consolidated, state-of-the-art Machine Learning tool to fit a function when provided with large data sets of examples. However, in regression tasks, the straightforward application of Deep Learning models provides a point…

Machine Learning · Computer Science 2018-07-25 Axel Brando , Jose A. Rodríguez-Serrano , Mauricio Ciprian , Roberto Maestre , Jordi Vitrià

A typical trajectory planner of autonomous driving commonly relies on predicting the future behavior of surrounding obstacles. Recently, deep learning technology has been widely adopted to design prediction models due to their impressive…

Artificial Intelligence · Computer Science 2022-07-29 Weitao Zhou , Zhong Cao , Yunkang Xu , Nanshan Deng , Xiaoyu Liu , Kun Jiang , Diange Yang

A multilevel functional data method is adapted for forecasting age-specific mortality for two or more populations in developed countries with high-quality vital registration systems. It uses multilevel functional principal component…

Applications · Statistics 2016-09-30 Han Lin Shang

Predicting future clinical events helps physicians guide appropriate intervention. Machine learning has tremendous promise to assist physicians with predictions based on the discovery of complex patterns from historical data, such as large,…

High-frequency death counts are now widely available and contain timely information about intra-year mortality dynamics, but most stochastic mortality models are still estimated on annual data and therefore update only when annual totals…

Econometrics · Economics 2026-01-12 Runze Li , Rui Zhou , David Pitt