Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is an iterative method where a Gaussian process posterior of the underlying function is sequentially updated by new function evaluations. We propose a novel Bayesian optimization framework for situations where the user controls the computational effort and therefore the precision of the function evaluations. This is a common in econometrics where the marginal likelihood is often computed by Markov chain Monte Carlo or importance sampling methods. The new acquisition strategy gives the optimizer the option to explore the function with cheap noisy evaluations and therefore find the optimum faster. The method is applied to estimating the prior hyperparameters in two popular models on US macroeconomic time series data: the steady-state Bayesian vector autoregressive (BVAR) and the time-varying parameter BVAR with stochastic volatility.

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. 

We consider a Gaussian variational approximation of the posterior density in high-dimensional state space models. The number of parameters in the covariance matrix of the variational approximation grows as the square of the number of model parameters, so it is necessary to find simple yet effective parametrisations of the covariance structure when the number of model parame-ters is large. We approximate the joint posterior density of the state vectors by a dynamic factor model, having Markovian time dependence and a factor covariance structure for the states. This gives a reduced description of the dependence struc-ture for the states, as well as a temporal conditional independence structure sim-ilar to that in the true posterior. We illustrate the methodology on two examples. The first is a spatio-temporal model for the spread of the Eurasian collared-dove across North America. Our approach compares favorably to a recently proposed ensemble Kalman filter method for approximate inference in high-dimensional hi-erarchical spatio-temporal models. Our second example is a Wishart-based multi-variate stochastic volatility model for financial returns, which is outside the class of models the ensemble Kalman filter method can handle.

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.

This 2-year longitudinal study compares students’ trajectories for perceived teacher–student relationship quality and students’ selfefficacy (together discussed as students’ school trust) to previously documented teacher-perceived experiences in teacher teams’ collective learning processes. The article’s main contribution is the reflection in students’ perceptions, of their teachers’ perceived quality and attainment in collective learning processes. Comparisons between schools show that trajectories for students belonging to the only teacher team that experienced a more mature and successful learning process in an earlier study, differed significantly from the trajectories for students in compared teams. Differences demonstrated large positive effect sizes (d=0.81–1.14). Individual analysis provides deeper insights about how these students’ perceptions changed. Additionally, the full sample data confirms earlier findings of substantial cross-associations between student-perceived teacher–student relationship quality and student self-efficacy. For example, sustainable associations between supportive teacher–student relationships and students’ global academic self-efficacy and self-efficacy for self-regulative learning were found (r = 0.43–0.51).

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.

In this article, we address the problem of simultaneous testing hypothesis about mean and covariance matrix for repeated measures data when both the mean vector and covariance matrix are patterned. In particular, tests about the mean vector under block circular and doubly exchangeable covariance structures have been considered. The null distributions are established for the corresponding likelihood ratio test statistics, and expressions for the exact or near-exact probability density and cumulative distribution functions are obtained. The application of the results is illustrated by both a simulation study and a real-life data example.

High quality of teacher–student relationships is widely recognized as fundamental part of good education. Moreover, students’ self-efficacy beliefs, or their confidence to succeed within different domains at school, are important impact factors to achievement. Although there is support for an association between student-perceived teacher–student relationship quality and students’ self-efficacy judgements, which mediates achievement, no tool explores this association. This article suggests that two instruments, respectively measuring students’ perceptions of teacher–student relationship quality (TSR) and student’s self-efficacy (SSE), can be used in parallel for a multifaceted exploration of individual students’ perception of TSR quality, in relationship to their self-efficacy. Two well-established instruments were adopted, validated and their factor structures re-confirmed in a Swedish sample, using data from students in five schools (n=382). Factor analysis showed that models with three underlying dimensions of TSR and four underlying dimensions of SSE were the most appropriate. All sub-scales showed good-to-excellent reliability (Cronbach’s α = 0.75–0.94). Findings indicated a lack of multigroup invariance across gender and school level for the TSR-model. Substantial associations were found between student-perceived teacher support, and students’ self-efficacy for self-regulated learning and global academic success. We discuss utility and limitations, need of model improvement, and future potential.   

Models that capture symmetries present in the data have been widely used in different applications, with early examples from psychometric and medical research. The aim of this article is to study a random effects model focusing on the covariance structure that is block circular symmetric. Useful results are obtained for the spectra of these structured matrices.

The general unbalanced mixed linear model with two variance components is considered. Through resampling it is demonstrated how the fixed effects can be estimated explicitly. It is shown that the obtained nonlinear estimator is unbiased and its variance is also derived. A condition is given when the proposed estimator is recommended instead of the ordinary least squares estimator.

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.

Bilinear models with three types of effects are considered: fixed effects, random effects and latent variable effects. In the literature, bilinear models with random effects and bilinear models with latent variables have been discussed but there are no results available when combining random effects and latent variables. It is shown, via appropriate vector space decompositions, how to remove the random effects so that a well-known model comprising only fixed effects and latent variables is obtained. The spaces are chosen so that the likelihood function can be factored in a convenient and interpretable way. To obtain explicit estimators, an important standardization constraint on the random effects is assumed to hold. A theorem is presented where a complete solution to the estimation problem is given.

In this paper, we make use of Bayesian VAR (BVAR) models to conduct an out-of-sample forecasting exercise for CPIF inflation, the inflation target variable at the Riksbank in Sweden. The proposed BVAR models generally outperform simple benchmark models, the BVAR model used by the Riksbank as presented in Iversen et al. (Real-time forecasting for monetary policy analysis: the case of Sveriges Riksbank, Working Paper 16/318, Sveriges riksbank, Stockhol, 2016) and professional forecasts made by the National Institute of Economic Research in Sweden. Moreover, the BVAR models proposed in the present paper have better forecasting precision than both survey forecasts and the method suggested by Faust and Wright (in: Elliott, Timmermann (eds) Handbook of forecasting, 2013). The findings in this paper might be of value to analysts, policymakers and forecasters of the inflation in Sweden (and possibly other small open economies alike).

Small area estimation techniques have got a lot of attention during the last decades due to their important applications in survey studies. Mixed linear models and reduced rank regression analysis are jointly used when considering small area estimation. Estimates of parameters are presented as well as prediction of random effects and unobserved area measurements.

Time-dependent volatility clustering (or heteroscedasticity) in macroeconomic and financial time series has been analyzed for more than half a century. The inefficiencies it causes in various inference procedures are well known and understood. Despite this, heteroscedasticity is surprisingly often neglected in practical work. The correct way is to model the variance jointly with the other properties of the time series by using some of the many methods available in the literature. In the first two papers of this thesis, we explore a third option, that is rarely used in the literature, in which we first remove the heteroscedasticity and only then fit a simpler model to the homogenized data.

In the first paper, we introduce a filter that removes heteroscedasticity from simulated data without affecting other time series properties. We show that filtering the data leads to efficiency gains when estimating parameters in ARMA models, and in some cases to higher forecast precision for US GDP growth.

The work of the first paper is extended to the case of multivariate time series in Paper II. In this paper, the stochastic volatility model is used for tracking the latent evolution of the time series variances. Also in this scenario variance stabilization offers efficiency gains when estimating model parameters.

During the last decade, there has been an increasing interest in using large-scale VARs together with Bayesian shrinkage methods. The rich parameterization together with the need for simulations methods results in a computational bottleneck that either force concessions regarding the flexibility of the model or the size of the data set. In the last two papers, we address these issues with methods from the machine learning literature.  

In Paper III, we develop a new Bayesian optimization strategy for finding optimal hyperparameters for econometric models via maximization of the marginal likelihood. We illustrate that the algorithm finds optimal values fast compared to conventional methods. 

Finally, in Paper IV we present a fast variational inference (VI) algorithm for approximating the parameter posterior and predictive distribution of the steady-state BVAR. We show that VI produces results that are very close to those of the conventional Gibbs sampler but are obtained at a much lower computational cost. This is illustrated in both a simulation study and on US macroeconomic data.