Longevity risk is putting more and more financial pressure on governments and pension plans worldwide due to pensioners’ increasing trend of life expectancy and the growing numbers of people reaching retirement age. Lee and Carter (1992, Journal of the American Statistical Association, 87(419), 659–671.) applied a one-factor dynamic factor model to forecast the trend of mortality improvement, and the model has since become the field’s workhorse. It is, however, well known that their model is subject to the limitation of overlooking cross-dependence between different age groups. We introduce Factor-Augmented Vector Autoregressive (FAVAR) models to the mortality modelling literature. The model, obtained by adding an unobserved factor process to a Vector Autoregressive (VAR) process, nests VAR and Lee–Carter models as special cases and inherits both frameworks’ advantages. A Bayesian estimation approach, adapted from the Minnesota prior, is proposed. The empirical application to the US and French mortality data demonstrates our proposed method’s efficacy in both in-sample and out-of-sample performance.

We consider a queueing loss system with heterogeneous skill based servers with arbitrary service distributions. We assume Poisson arrivals, with each arrival having a vector indicating which of the servers are eligible to serve it. An arrival can only be assigned to a server that is both idle and eligible. Assuming exchangeable eligibility vectors and an idle time ordering assignment policy, the limiting distribution of the system is derived. It is shown that the limiting probabilities of the set of idle servers depend on the service time distributions only through their means. Moreover, conditional on the set of idle servers, the remaining service times of the busy servers are independent and have their respective equilibrium service distributions.

We consider Markov chain Monte Carlo algorithms which combine Gibbs updates with Metropolis-Hastings updates, resulting in a conditional Metropolis-Hastings sampler (CMH sampler). We develop conditions under which the CMH sampler will be geometrically or uniformly ergodic. We illustrate our results by analysing a CMH sampler used for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon discrete observations.

Oil prices rose sharply prior to the onset of the 2007–2009 recession. Hamilton [in the Palgrave Dictionary of Macroeconomics (2008)] noted that nine of the last ten recessions in the United States were preceded by a substantial increases in the price of oil. In this paper, we consider whether oil price shocks significantly increase the probability of recessions in a number of countries. Because business cycle turning points generally are not available for other countries, we estimate the turning points together with oil's effect in a Markov-switching model with time-varying transition probabilities. We find that, for most countries, oil shocks do affect the likelihood of entering a recession. In particular, for a constant, zero-term spread, an average-sized shock to WTI oil prices increases the probability of recession in the United States by nearly 50 percentage points after one year and nearly 90 percentage points after two years.

The objective of this study was to apply factor analysis to describe lactation curves in dairy buffaloes in order to estimate the phenotypic and genetic association between common latent factors and cumulative milk yield. A total of 31 257 monthly test-day milk yield records from buffaloes belonging to herds located in the state of São Paulo were used to estimate two common latent factors, which were then analysed in a multi-trait animal model for estimating genetic parameters. Estimates of (co)variance components for the two common latent factors and cumulated 270-d milk yield were obtained by Bayesian inference using a multiple trait animal model. Contemporary group, number of milkings per day (two levels) and age of buffalo cow at calving (linear and quadratic) as covariate were included in the model as fixed effects. The additive genetic, permanent environmental and residual effects were included as random effects. The first common latent factor (F1) was associated with persistency of lactation and the second common latent factor (F2) with the level of production in early lactation. Heritability estimates for F1 and F2 were 0·12 and 0·07, respectively. Genetic correlation estimates between F1 and F2 with cumulative milk yield were positive and moderate (0·63 and 0·52). Multivariate statistics employing factor analysis allowed the extraction of two variables (latent factors) that described the shape of the lactation curve. It is expected that the response to selection to increase lactation persistency is higher than the response obtained from selecting animals to increase lactation peak. Selection for higher total milk yield would result in a favourable correlated response to increase the level of production in early lactation and the lactation persistency.

We consider a set of workers' compensation insurance claim data where the aggregate number of losses (claims) reported to insurers are classified by year of occurrence of the event causing loss, the US state in which the loss event occurred and the occupation class of the insured workers to which the loss count relates. An exposure measure, equal to the total payroll of observed workers in each three-way classification, is also included in the dataset. Data are analysed across ten different states, 24 different occupation classes and seven separate observation years. A multiple linear regression model, with only predictors for main effects, could be estimated in 223 + 9 + 1 + 1 = 234 ways, theoretically more than 17 billion different possible models! In addition, one might expect that the number of claims recorded in each year in the same state and relating to the same occupation class, are positively correlated. Different modelling assumptions as to the nature of this correlation should also be considered. On the other hand it may reasonably be assumed that the number of losses reported from different states and from different occupation classes are independent. Our data can therefore be modelled using the statistical techniques applicable to panel data and we work with generalised estimating equations (GEE) in the paper. For model selection, Pan (2001) suggested the use of an alternative to the AIC, namely the quasi-likelihood under independence model criterion (QIC), for model comparison. This paper develops and applies a Gibbs sampling algorithm for efficiently locating, out of the more than 17 billion possible models that could be considered for the analysis, that model with the optimal (least) QIC value. The technique is illustrated using both a simulation study and using workers' compensation insurance claim data.

In this paper non-normal distributions via scale mixtures are introduced into insurance applications. The symmetric distributions of interest are the Student-t and exponential power (EP) distributions. A Bayesian approach is adopted with the aid of simulation to obtain posterior summaries. We shall show that the computational burden for the Bayesian calculations is alleviated via the scale mixtures representations. Illustrative examples are given.

The paper proves the statement of the title, and shows that it has useful applications in evaluating the convergence of queueing models and Gibbs samplers with deterministic and random scans.

We consider Markov processes of DNA sequence evolution in which the instantaneous rates of substitution at a site are allowed to depend upon the states at the sites in a neighbourhood of the site at the instant of the substitution. We characterize the class of Markov process models of DNA sequence evolution for which the stationary distribution is a Gibbs measure, and give a procedure for calculating the normalizing constant of the measure. We develop an MCMC method for estimating the transition probability between sequences under models of this type. Finally, we analyse an alignment of two HIV-1 gene sequences using the developed theory and methodology.

Financial time series data are typically found to possess leptokurtic frequency distributions, time varying volatilities, outliers and correlation structures inconsistent with linear generating processes, nonlinear dependence, and dependencies between series that are not stable over time. Regime Switching Vector Autoregressions are of interest because they are capable of explaining the observed features of the data, can capture a variety of interactions between series, appear intuitively reasonable, are vector processes, and are now tractable.

This paper considers a vector autoregression subject to periodic structural changes. The parameters of a vector autoregression are modelled as the outcome of an unobserved discrete Markov process with unknown transition probabilities. The unobserved regimes, one for each time point, together with the regime transition probabilities, are determined in addition to the vector autoregression parameters within each regime.

A Bayesian Markov Chain Monte Carlo estimation procedure is developed which efficiently generates the posterior joint density of the parameters and the regimes. The complete likelihood surface is generated at the same time, enabling estimation of posterior model probabilities for use in non-nested model selection. The procedure can readily be extended to produce joint prediction densities for the variables, incorporating both parameter and model uncertainty.

Results using simulated and real data are provided. A clear separation of the variance between a stable and an unstable regime was observed. Ignoring regime shifts is very likely to produce misleading volatility estimates and is unlikely to be robust to outliers. A comparison with commonly used models suggests that Regime Switching Vector Autoregressions provide a particularly good description of the observed data.

Recently Propp and Wilson [14] have proposed an algorithm, called coupling from the past (CFTP), which allows not only an approximate but perfect (i.e. exact) simulation of the stationary distribution of certain finite state space Markov chains. Perfect sampling using CFTP has been successfully extended to the context of point processes by, amongst other authors, Häggström et al. [5]. In [5] Gibbs sampling is applied to a bivariate point process, the penetrable spheres mixture model [19]. However, in general the running time of CFTP in terms of number of transitions is not independent of the state sampled. Thus an impatient user who aborts long runs may introduce a subtle bias, the user impatience bias. Fill [3] introduced an exact sampling algorithm for finite state space Markov chains which, in contrast to CFTP, is unbiased for user impatience. Fill's algorithm is a form of rejection sampling and similarly to CFTP requires sufficient monotonicity properties of the transition kernel used. We show how Fill's version of rejection sampling can be extended to an infinite state space context to produce an exact sample of the penetrable spheres mixture process and related models. Following [5] we use Gibbs sampling and make use of the partial order of the mixture model state space. Thus we construct an algorithm which protects against bias caused by user impatience and which delivers samples not only of the mixture model but also of the attractive area-interaction and the continuum random-cluster process.

This paper gives a method for premium rating by postcode area. The method is based on spatial models in a Bayesian framework and uses the Gibbs sampler for estimation. A summary of the theory of Bayesian spatial methods is given and the data which was analysed by Taylor (1989) is reanalysed. An indication is given of the wide range of models within this class which would be suitable for insurance data. The aim of the paper is to introduce the models and to show how they can be utilised in an insurance setting.