A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting

This paper explores and develops alternative statistical representations and estimation approaches for dynamic mortality models. The framework we adopt is to reinterpret popular mortality models such as the Lee-Carter class of models in a general state-space modelling methodology, which allows modelling, estimation and forecasting of mortality under a unified framework. Furthermore, we propose an alternative class of model identification constraints which is more suited to statistical inference in filtering and parameter estimation settings based on maximization of the marginalized likelihood or in Bayesian inference. We then develop a novel class of Bayesian state-space models which incorporate apriori beliefs about the mortality model characteristics as well as for more flexible and appropriate assumptions relating to heteroscedasticity that present in observed mortality data. We show that multiple period and cohort effect can be cast under a state-space structure. To study long term mortality dynamics, we introduce stochastic volatility to the period effect. The estimation of the resulting stochastic volatility model of mortality is performed using a recent class of Monte Carlo procedure specifically designed for state and parameter estimation in Bayesian state-space models, known as the class of particle Markov chain Monte Carlo methods. We illustrate the framework we have developed using Danish male mortality data, and show that incorporating heteroscedasticity and stochastic volatility markedly improves model fit despite an increase of model complexity. Forecasting properties of the enhanced models are examined with long term and short term calibration periods on the reconstruction of life tables.Comment: 46 page

Unsupervised State-Space Modeling Using Reproducing Kernels

This is the accepted manuscript. The final version is available at http://dx.doi.org/10.1109/TSP.2015.2448527.A novel framework for the design of state-space models (SSMs) is proposed whereby the state-transition function of the model is parametrised using reproducing kernels. The nature of SSMs requires learning a latent function that resides in the state space and for which input-output sample pairs are not available, thus prohibiting the use of gradient-based supervised kernel learning. To this end, we then propose to learn the mixing weights of the kernel estimate by sampling from their posterior density using Monte Carlo methods. We first introduce an offline version of the proposed algorithm, followed by an online version which performs inference on both the parameters and the hidden state through particle filtering. The accuracy of the estimation of the state-transition function is first validated on synthetic data. Next, we show that the proposed algorithm outperforms kernel adaptive filters in the prediction of real-world time series, while also providing probabilistic estimates, a key advantage over standard methods.Felipe Tobar acknowledges financial support from EPSRC grant number EP/L000776/1

Sequential Monte Carlo Methods for System Identification

One of the key challenges in identifying nonlinear and possibly non-Gaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estimation problems arising in SSMs. When combined with additional identification techniques, these algorithms provide solid solutions to the nonlinear system identification problem. We describe two general strategies for creating such combinations and discuss why SMC is a natural tool for implementing these strategies.Comment: In proceedings of the 17th IFAC Symposium on System Identification (SYSID). Added cover pag

State estimation for one-dimensional agro-hydrological processes with model mismatch

The importance of accurate soil moisture data for the development of modern closed-loop irrigation systems cannot be overstated. Due to the diversity of soil, it is difficult to obtain an accurate model for agro-hydrological system. In this study, soil moisture estimation in 1D agro-hydrological systems with model mismatch is the focus. To address the problem of model mismatch, a nonlinear state-space model derived from the Richards equation is utilized, along with additive unknown inputs. The determination of the number of sensors required is achieved through sensitivity analysis and the orthogonalization projection method. To estimate states and unknown inputs in real-time, a recursive expectation maximization (EM) algorithm derived from the conventional EM algorithm is employed. During the E-step, the extended Kalman filter (EKF) is used to compute states and covariance in the recursive Q-function, while in the M-step, unknown inputs are updated by locally maximizing the recursive Q-function. The estimation performance is evaluated using comprehensive simulations. Through this method, accurate soil moisture estimation can be obtained, even in the presence of model mismatch

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area