A mixture of experts models the conditional density of a response variable using a mixture of regression models with covariate-dependent mixture weights. We extend the finite mixture of experts model by allowing the parameters in both the mixture components and the weights to evolve in time by following random walk processes. Inference for time-varying parameters in richly parameterized mixture of experts models is challenging. We propose a sequential Monte Carlo algorithm for online inference based on a tailored proposal distribution built on ideas from linear Bayes methods and the EM algorithm. The method gives a unified treatment for mixtures with time-varying parameters, including the special case of static parameters. We assess the properties of the method on simulated data and on industrial data where the aim is to predict software faults in a continuously upgraded large-scale software project. 

As global average temperatures rise, so does the frequency and intensity of El Niño-induced droughts, which in turn threaten the reliability of hydropower. 1.4 billion people live in countries where hydropower constitutes more than a quarter of the electricity production and which have experienced El Niño droughts, meaning many more power outages can be expected around the world. Little research has been conducted on the impact of power outages on mental health. This study takes Zambia as its case study to examine the impact that El Niño droughts have had on the lives of householders connected to a highly hydropower-dependant electricity grid, and includes the impact it has had on their physical and self-reported mental health. Using 54 online responses to a survey, we found that the greatest impacts of outages spoiled food, compromised entertainment, compromised ability to work and limitation in cooking options. More than a fifth of respondents reported experiencing self-reported depression to a major degree or all of the time due to power outages, with individuals writing their own responses that they felt debilitated, experienced reduced communication and reduced activities, and stress. Using Bayesian inference, we found that changes in sleeping patterns arising from power outages was a statistically significant predictor of self-reported depression. 63% of surveyed households were willing to pay approximately USD 0.10/kWh as of the end of 2019, about double the tariff that they did, to ensure reliable electricity supply. Household income was a statistically significant predictor of willingness to pay more.

We address a problem in inference from retrospective studies where the value of a variable is measured at the date of the survey but is used as covariate to events that have occurred long before the survey. This causes problem because the value of the current-date (anticipatory) covariate does not follow the temporal order of events. We propose a dynamic Bayesian approach for modelling jointly the anticipatory covariate and the event of interest, and allowing the effects of the anticipatory covariate to vary over time. The issues are illustrated with data on the effects of education attained by the survey-time on divorce risks among Swedish men. The overall results show that failure to adjust for the anticipatory nature of education leads to elevated relative risks of divorce across educational levels. The results are partially in accordance with previous findings based on analyses of the same data set. More importantly, our findings provide new insights in that the bias due to anticipatory covariates varies over marriage duration.

We propose a dynamic Bayesian survival model for analyzing differentials in the timing of family initiation. Such formulation relaxes the strong assumption of constant hazard ratio in conventional proportional hazards models and allows covariate effects to vary over time. Inference is fully Bayesian, and efficient sequential Monte Carlo (particle filter) is used to sample from the posterior distribution. We illustrate the proposed model with data on entry into first marriage among Eritrean men and women surveyed in the 2010 Eritrean Population and Health Survey. Results from the conventional proportional hazards model indicate significant differences in family initiation among all educational and residential groups. In the dynamic model, on the other hand, only one educational and one residential group among the women and only one residential group among the men differ from their respective baseline groups. Since the empirical relative intensities of entry into first marriage vary across respondents’ ages, we argue that the proposed dynamic model captures differentials in family initiation more accurately.

We examine the effects of the 3-points-for-a-win (3pfaw) rule in the football world. Data that form the basis of our analyses come from seven leagues around the world (Albania, Brazil, England, Germany, Poland, Romania, and Scotland) and consist of mean goals and proportions of decided matches over a period of about six years before- and about seven years after the introduction of the rule in the respective leagues. Bayesian change-point analyses and Shiryaev-Roberts tests show that the rule had no effects on the mean goals but, indeed, had increasing effects on the proportions of decided matches in most of the leagues studied. This, in turn, implies that while the rule has given teams the incentive to aim at winning matches, such aim was not achieved by scoring excess goals. Instead, it was achieved by scoring enough goals in order to win and, at the same time, defending enough in order not to lose. Our results are in accordance with recent findings on comparing the values of attack and defense - that, in top-level football, not conceding a goal is more valuable than scoring a single goal.

Many processes evolve over time and statistical models need to be adaptive to change. This thesis proposes flexible models and statistical methods for inference about a data generating process that varies over time. The models considered are quite general dynamic predictive models with parameters linked to a set of covariates via link functions. The dynamics can arise from time-varying regression coefficients and from changes in the link function over time. The covariates can be time-varying and may also have incomplete information.

An efficient Bayesian inference methodology is developed for analyzing the posterior of dynamic regression models sequentially, with a particular focus on online learning and real-time prediction. The core inferential algorithm belongs to a family of sequential Monte Carlo methods commonly known as particle filters, and a key contribution is the development of a tailored proposal distribution. The algorithm is shown to outperform a state-of-the-art Markov Chain Monte Carlo method and is also extended to mixture-of-experts models.

The performance of the inference methodology is assessed through various simulation experiments and real data from clinical and social-demographic studies, as well as from an industrial software development project.

We address a problem in causal inference from retrospective surveys where the value of a covariate is measured at the date of the survey but is used to explain behaviour that has occurred long before the survey. This causes bias because the anticipatory covariate does not follow the temporal order of events. We propose a Bayesian dynamic modelling approach that allows effects of the anticipatory covariate to vary over time and, thereby, restore its value at the event of interest. The issues are illustrated with data on the effects of anticipatory educational level on divorce risks among Swedish men. The overall results show that failure to adjust for the anticipatory nature of education leads to underestimation of the relative risks of divorce across educational levels. The results build, in part, on previous analyses of the same data set but also reveal that the degree of underestimation varies over marriage durations.

We examine the e⁄ects of the 3-point-for-a-win (3pfaw) rule in the football (soccer) world. Data on mean goals and proportions of decided matches from seven leagues around the world form the basis of our analyses. Bayesian change-point analysis shows that the rule had no e⁄ects on the mean goals in any of the leagues but, indeed, had increasing e⁄ects on the proportions of decided matches in most of the leagues studied. This, in turn, implies that while the rule has given teams the incentive to aim at winning matches, such aim was achieved not by scoring excess goals. Instead, it was achieved by scoring enough goals in order to win and, at the same, defending enough in order not to lose.

This article proposes an efficient Bayesian inference for piecewise exponential hazard (PEH) models, which allow the effect of a covariate to change over time. The proposed inference methodology is based on a particle smoothing (PS) algorithm that depends on three particle filters. Efficient proposal (importance) distributions for the particle filters tailored to the nature of survival data and PEH models are developedusing the Laplace approximation of the posterior distribution and linear Bayes theory. The algorithm is applied to both simulated and real data, and the results show that it generates an effective sample sizethat is more than two orders of magnitude larger than a state-of-the-art MCMC sampler for the samecomputing time, and scales well in high-dimensional and relatively large data.