Based on agent opinion analysis theory, Bayesian predictive synthesis (BPS) is a framework for combining predictive distributions in the face of model uncertainty. In this article, we generalize existing parametric implementations of BPS by showing how to combine competing probabilistic forecasts using interpretable Bayesian tree‐based machine learning methods. We demonstrate the advantages of our approach—in terms of improved forecast accuracy and interpretability—via two macroeconomic forecasting applications. The first uses density forecasts for GDP growth from the euro area's Survey of Professional Forecasters. The second combines density forecasts of U.S. inflation produced by many simple regression models.

This paper develops a mixed frequency vector autoregressive (MF-VAR) model to produce nowcasts and historical estimates of monthly real state-level GDP for the 50 U.S. states, plus Washington DC, from 1964 through the present day. The MF-VAR model incorporates state and U.S. data at the monthly, quarterly, and annual frequencies. Temporal and cross-sectional constraints are imposed to ensure that the monthly state-level estimates are consistent with official estimates of quarterly GDP at the U.S. and state-levels. We illustrate the utility of the historical estimates in better understanding state business cycles and cross-state dependencies. We show how the model produces accurate nowcasts of state GDP three months ahead of the BEA's quarterly estimates, after conditioning on the latest estimates of U.S. GDP.

Surges in Party MembershipThis book presents a comprehensive analysis of a remarkable and unexpected outcome of the 2014 referendum on Scottish independence.Despite defeat in the Scottish referendum, the two leading parties in the Yes campaign -the Scottish National Party and Scottish Green Party -experienced an extraordinary surge in membership.The book explains these events, examining the relationship between political parties and social movements, and it assesses the longterm consequences of the surge.Based on surveys of members and interviews with party and movement actors since the referendum, the book analyses the members' involvement in the 2014 referendum, their motives for joining a party, their backgrounds and political attitudes, and their behaviour as party members.A key component of the book is how the surge changed the parties -socio-demographically, ideologically and organisationally.This book will appeal to scholars, students and observers of electoral politics, political participation, social and political movements, and political parties and their members, and more broadly to those interested in the debate on Scottish independence, British politics and comparative politics.

Vicarious liability is the treatment, regardless of fault, of one defender as liable for another defender's wrong. The basic inquiry involves examination of whether (i) the defenders stand in a relationship capable of giving rise to vicarious liability; and (ii) the wrongdoing is relevantly linked to that relationship. Unsatisfactory though the reality and its results may be, the contours of these core components are sculpted as new fact patterns come before the courts, and judges emphasise differently and compromise between various policy goals. The elementary principles are quite well-settled, especially given a relative paucity of case law and literature. But room for refinement remains. We here further analyse issues of interest in Scotland and beyond concerning the basic inquiry, and clarify the unimportance in this context of the distinctiveness of Scots law, before summarising our conclusions.

In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper proposes a nonparametric TVP-VAR model using Bayesian additive regression trees (BART). The novelty of this model stems from the fact that the law of motion driving the parameters is treated nonparametrically. This leads to great flexibility in the nature and extent of parameter change, both in the conditional mean and in the conditional variance. In contrast to other nonparametric and machine learning methods that are black box, inference using our model is straightforward because, in treating the parameters rather than the variables nonparametrically, the model remains conditionally linear in the mean. Parsimony is achieved through adopting nonparametric factor structures and use of shrinkage priors. In an application to US macroeconomic data, we illustrate the use of our model in tracking both the evolving nature of the Phillips curve and how the effects of business cycle shocks on inflationary measures vary nonlinearly with movements in uncertainty.

In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper proposes a nonparametric TVP-VAR model using Bayesian additive regression trees (BART) that models the TVPs as an unknown function of effect modifiers. The novelty of this model arises from the fact that the law of motion driving the parameters is treated nonparametrically. This leads to great flexibility in the nature and extent of parameter change, both in the conditional mean and in the conditional variance. Parsimony is achieved through adopting nonparametric factor structures and use of shrinkage priors. In an application to US macroeconomic data, we illustrate the use of our model in tracking both the evolving nature of the Phillips curve and how the effects of business cycle shocks on inflation measures vary nonlinearly with changes in the effect modifiers.

Output growth data for the UK regions are available at only annual frequency and are released with significant delay. Regional policy makers would benefit from more frequent and timely data. We develop a stacked, mixed frequency vector auto-regression to provide, each quarter, nowcasts of annual output growth for the UK regions. The information that we use to update our regional nowcasts includes output growth data for the UK as a whole, as these aggregate data are released in a more timely and frequent (quarterly) fashion than the regional disaggregates which they comprise. We show how entropic tilting methods can be adapted to exploit the restriction that UK output growth is a weighted average of regional growth. In our realtime nowcasting application we find that the stacked mixed frequency vector-autoregressive model, with entropic tilting, provides an effective means of nowcasting the regional disaggregates exploiting known information on the aggregate.

Uncertainty is an inherent part of knowledge, and yet in an era of contested expertise, many shy away from openly communicating their uncertainty about what they know, fearful of their audience's reaction. But what effect does communication of such epistemic uncertainty have? Empirical research is widely scattered across many disciplines. This interdisciplinary review structures and summarizes current practice and research across domains, combining a statistical and psychological perspective. This informs a framework for uncertainty communication in which we identify three objects of uncertainty—facts, numbers and science—and two levels of uncertainty: direct and indirect. An examination of current practices provides a scale of nine expressions of direct uncertainty. We discuss attempts to codify indirect uncertainty in terms of quality of the underlying evidence. We review the limited literature about the effects of communicating epistemic uncertainty on cognition, affect, trust and decision-making. While there is some evidence that communicating epistemic uncertainty does not necessarily affect audiences negatively, impact can vary between individuals and communication formats. Case studies in economic statistics and climate change illustrate our framework in action. We conclude with advice to guide both communicators and future researchers in this important but so far rather neglected field.

Local elections were held across Scotland in May 2017, the third set using single transferable vote (see Chapter 2.3), during the early run-up to the snap general election of June 2017.There were some boundary changes, and though the SNP won the greatest percentage of seats overall (30%), after the elections all 32 councils in Scotland were now under 'no overall control'.Much the biggest recent challenges facing Scottish local authorities are financial pressures from UK and Scottish government austerity policies, combined with increased demands for services, especially with an ageing population, and some increasing staff costs including pensions.As Figure 1 from Audit Scotland makes clear, all local authorities face funding gaps and either need to make further savings or make more use of their reserves.Some authorities are better placed than others to address these challenges.

If any trend can be confidently associated with 21st century Europe, it is the increasingly multicultural character of its constituent nationstates. The European Union (EU), the embodiment of the continental idea, is comprised of 28 nations, which originally had as their core raison d’etre a cultural community. Among the defining characteristics of those cultures were shared language, history, traditions, ethnicity and, yes, racial identity.

Density forecast combinations are becoming increasingly popular as a means of improving forecast ‘accuracy’, as measured by a scoring rule. In this paper we generalise this literature by letting the combination weights follow more general schemes. Sieve estimation is used to optimise the score of the generalised density combination where the combination weights depend on the variable one is trying to forecast. Specific attention is paid to the use of piecewise linear weight functions that let the weights vary by region of the density. We analyse these schemes theoretically, in Monte Carlo experiments and in an empirical study. Our results show that the generalised combinations outperform their linear counterparts.