We introduce a flexible model for multivariate time-series exhibiting heterogeneous sampling frequencies, where time-varying unobservable heterogeneity is captured by a finite number of latent regimes. The latent unobservable process evolves over time according to a semi-Markov chain. The inference is based on a Bayesian approach involving reversible jump Markov chain Monte Carlo (RJ-MCMC), which allows us to avoid specifying the number of latent regimes in advance. In a simulation study we show how our approach correctly recovers the true configuration of latent regimes with high probability, and that the proposed model can be seen as advantageous with respect to possible competitors. We illustrate through an analysis of two major polluting agents recorded daily at the Danmarksplass site (Norway) in 2022, and their association with certain mixed-frequency weather variables.

Overweight and obesity in adults are known to be associated with increased risk of metabolic and cardiovascular diseases. Obesity has now reached epidemic proportions, increasingly affecting children. Therefore, it is important to understand if this condition persists from early life to childhood and if different patterns can be detected to inform intervention policies. Our motivating application is a study of temporal patterns of obesity in children from South Eastern Asia. Our main focus is on clustering obesity patterns after adjusting for the effect of baseline information. Specifically, we consider a joint model for height and weight over time. Measurements are taken every six months from birth. To allow for data-driven clustering of trajectories, we assume a vector autoregressive sampling model with a dependent logit stick-breaking prior. Simulation studies show good performance of the proposed model to capture overall growth patterns, as compared to other alternatives. We also fit the model to the motivating dataset, and discuss the results, in particular highlighting cluster differences. We have found four large clusters, corresponding to children sub-groups, though two of them are similar in terms of both height and weight at each time point. We provide interpretation of these clusters in terms of combinations of predictors.

Actuaries have long been interested in the forecasting of mortality for the purpose of the pricing and reserving of pensions and annuities. Most models of mortality in age and year of death, and often year of birth, are not identifiable so actuaries worried about what constraints should be used to give sensible estimates of the age and year of death parameters, and, if required, the year of birth parameters. These parameters were then forecast with an ARIMA model to give the required forecasts of mortality. A recent article showed that, while the fitted parameters were not identifiable, both the fitted and forecast mortalities were. This result holds if the age term is smoothed with P-splines. The present article deals with generalized linear models with a rank deficient regression matrix. We have two aims. First, we investigate the effect that different constraints have on the estimated regression coefficients. We show that it is possible to fit the model under different constraints in R without imposing any explicit constraints. R does all the necessary booking-keeping ‘under the bonnet’. The estimated regression coefficients under a particular set of constraints can then be recovered from the invariant fitted values. We have a black box approach to fitting the model subject to any set of constraints.

Over the course of the COVID-19 pandemic, Generalized Additive Models (GAMs) have been successfully employed on numerous occasions to obtain vital data-driven insights. In this article we further substantiate the success story of GAMs, demonstrating their flexibility by focusing on three relevant pandemic-related issues. First, we examine the interdepency among infections in different age groups, concentrating on school children. In this context, we derive the setting under which parameter estimates are independent of the (unknown) case-detection ratio, which plays an important role in COVID-19 surveillance data. Second, we model the incidence of hospitalizations, for which data is only available with a temporal delay. We illustrate how correcting for this reporting delay through a nowcasting procedure can be naturally incorporated into the GAM framework as an offset term. Third, we propose a multinomial model for the weekly occupancy of intensive care units (ICU), where we distinguish between the number of COVID-19 patients, other patients and vacant beds. With these three examples, we aim to showcase the practical and ‘off-the-shelf’ applicability of GAMs to gain new insights from real-world data.

We propose a novel Bayesian model framework for discrete ordinal and count data based on conditional transformations of the responses. The conditional transformation function is estimated from the data in conjunction with an a priori chosen reference distribution. For count responses, the resulting transformation model is novel in the sense that it is a Bayesian fully parametric yet distribution-free approach that can additionally account for excess zeros with additive transformation function specifications. For ordinal categoric responses, our cumulative link transformation model allows the inclusion of linear and non-linear covariate effects that can additionally be made category-specific, resulting in (non-)proportional odds or hazards models and more, depending on the choice of the reference distribution. Inference is conducted by a generic modular Markov chain Monte Carlo algorithm where multivariate Gaussian priors enforce specific properties such as smoothness on the functional effects. To illustrate the versatility of Bayesian discrete conditional transformation models, applications to counts of patent citations in the presence of excess zeros and on treating forest health categories in a discrete partial proportional odds model are presented.

This article studies long-term, short-term volatility and co-volatility in stock markets by introducing modelling strategies to the multivariate data analysis that deal with serially correlated innovations and cross-section dependence. In particular, it presents an innovative mixed-effects model through a GARCH process, allowing for heterogeneity effects and time-series dynamics. We propose a non-parametric regression model of the penalized low-rank smoothing spline to present time trends into the variance and covariance equations. The strategy provides flexible modelling of the low-frequency volatility and co-volatility in equity markets. The decomposed low-frequency matrix was modelled using the modified Cholesky factorization. The Hamiltonian Monte Carlo technique is implemented as a Bayesian computing process for estimating parameters and latent factors. The advantage of our modelling strategy in empirical studies is highlighted by examining the effect of latent financial factors on a panel across 10 equities over 110 weekly series. The model can differentiate non-parametrically dynamic patterns of high and low frequencies of variance–covariance structural equations and incorporate economic features to predict variabilities in stock markets regarding time-series evidence.

In many settings, data acquisition generates outliers that can obscure inference. Therefore, practitioners often either identify and remove outliers or accommodate outliers using robust models. However, identifying and removing outliers is often an ad hoc process that affects inference, and robust methods are often too simple for some applications. In our motivating application, scientists drill snow cores and measure snow density to infer densification rates that aid in estimating snow water accumulation rates and glacier mass balances. Advanced measurement techniques can measure density at high resolution over depth but are sensitive to core imperfections, making them prone to outliers. Outlier accommodation is challenging in this setting because the distribution of outliers evolves over depth and the data demonstrate natural heteroscedasticity. To address these challenges, we present a two-component mixture model using a physically motivated snow density model and an outlier model, both of which evolve over depth. The physical component of the mixture model has a mean function with normally distributed depth-dependent heteroscedastic errors. The outlier component is specified using a semiparametric prior density process constructed through a normalized process convolution of log-normal random variables. We demonstrate that this model outperforms alternatives and can be used for various inferential tasks.

Quantile regression (QR) has gained popularity during the last decades, and is now considered a standard method by applied statisticians and practitioners in various fields. In this work, we applied QR to investigate climate change by analysing historical temperatures in the Arctic Circle. This approach proved very flexible and allowed to investigate the tails of the distribution, that correspond to extreme events. The presence of quantile crossing, however, prevented using the fitted model for prediction and extrapolation. In search of a possible solution, we first considered a different version of QR, in which the QR coefficients were described by parametric functions. This alleviated the crossing problem, but did not eliminate it completely. Finally, we exploited the imposed parametric structure to formulate a constrained optimization algorithm that enforced monotonicity. The proposed example showed how the relatively unexplored field of parametric quantile functions could offer new solutions to the long-standing problem of quantile crossing. Our approach is particularly convenient in situations, like the analysis of time series, in which the fitted model may be used to predict extreme quantiles or to perform extrapolation. The described estimator has been implemented in the R package qrcm.

There is an increasing interest in models for discrete valued time series. Among them, the integer autoregressive conditional heteroscedastic (INGARCH) is a model that has found several applications. In the present article, we study the problem of model selection for this family of models. Namely we consider that an observation conditional on the past follows a Poisson distribution where its mean depends on its past mean values and on past observations. We consider both linear and log-linear models. Our purpose is to select the most appropriate order of such models, using a trans-dimensional Bayesian approach that allows jumps between competing models. A small simulation experiment supports the usage of the method. We apply the methodology to real datasets to illustrate the potential of the approach.