Abstract:In this study we develop a multi-factor extension of the family of Lee-Carter stochastic mortality models. We build upon the time, period and cohort stochastic model structure to extend it to include exogenous observable demographic features that can be used as additional factors to improve model fit and forecasting accuracy. We develop a dimension reduction feature extraction framework which (a) employs projection based techniques of dimensionality reduction; in doing this we also develop (b) a robust feature extraction framework that is amenable to different structures of demographic data; (c) we analyse demographic data sets from the patterns of missingness and the impact of such missingness on the feature extraction, and (d) introduce a class of multi-factor stochastic mortality models incorporating time, period, cohort and demographic features, which we develop within a Bayesian state-space estimation framework; finally (e) we develop an efficient combined Markov chain and filtering framework for sampling the posterior and forecasting. We undertake a detailed case study on the Human Mortality Database demographic data from European countries and we use the extracted features to better explain the term structure of mortality in the UK over time for male and female populations when compared to a pure Lee-Carter stochastic mortality model, demonstrating our feature extraction framework and consequent multi-factor mortality model improves both in sample fit and importantly out-off sample mortality forecasts by a non-trivial gain in performance.

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A novel class of dimension reduction methods is combined with a stochastic multi-factor panel regression-based state-space model in order to model the dynamics of yield curves whilst incorporating regression factors. This is achieved via Probabilistic Principal Component Analysis (PPCA) in which new statistically-robust variants are derived also treating missing data. We embed the rank reduced feature extractions into a stochastic representation for state-space models for yield curve dynamics and compare the results to classical multi-factor dynamic Nelson-Siegel state-space models. This leads to important new representations of yield curve models that can be practically important for addressing questions of financial stress testing and monetary policy interventions, which can incorporate efficiently financial big data. We illustrate our results on various financial and macroeconomic datasets from the Euro Zone and international market.

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Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is of interest to select a parsimonious subset of those being effectively relevant for predicting the response variable. Variational approximations facilitate fast approximate Bayesian inference for the parameters of a variety of statistical models, including linear mixed models. However, for models having a high number of fixed or random effects, simple application of standard variational inference principles does not lead to fast approximate inference algorithms, due to the size of model design matrices and inefficient treatment of sparse matrix problems arising from the required approximating density parameters updates. We illustrate how recently developed streamlined variational inference procedures can be generalized to make fast and accurate inference for the parameters of linear mixed models with nested random effects and global-local priors for Bayesian fixed effects selection. Our variational inference algorithms achieve convergence to the same optima of their standard implementations, although with significantly lower computational effort, memory usage and time, especially for large numbers of random effects. Using simulated and real data examples, we assess the quality of automated procedures for fixed effects selection that are free from hyperparameters tuning and only rely upon variational posterior approximations. Moreover, we show high accuracy of variational approximations against model fitting via Markov Chain Monte Carlo sampling.

Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is of interest to select a parsimonious subset of those being effectively relevant for predicting the response variable. Variational approximations facilitate fast approximate Bayesian inference for the parameters of a variety of statistical models, including linear mixed models. However, for models having a high number of fixed or random effects, simple application of standard variational inference principles does not lead to fast approximate inference algorithms, due to the size of model design matrices and inefficient treatment of sparse matrix problems arising from the required approximating density parameters updates.We illustrate how recently developed streamlined variational inference procedures can be generalized to make fast and accurate inference for the parameters of linear mixed models with nested random effects and globallocal priors for Bayesian fixed effects selection. Our variational inference algorithms achieve convergence to the same optima of their standard implementations, although with significantly lower computational effort, memory usage and time, especially for large numbers of random effects. Using simulated and real data examples, we assess the quality of automated procedures for fixed effects selection that are free from hyperparameters tuning and only rely upon variational posterior approximations. Moreover, we show high accuracy of variational approximations against model fitting via Markov Chain Monte Carlo sampling.

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