Abstract. In this paper we introduce the notion of Algebraic (Trapdoor) One Way Functions, which, roughly speaking, captures and formalizes many of the properties of number-theoretic one-way functions. Informally, a (trapdoor) one way function F : X → Y is said to be algebraic if X and Y are (finite) abelian cyclic groups, the function is homomor-, and is ring-homomorphic, meaning that it is possible to compute linear operations "in the exponent" over some ring (which may be different from Zp where p is the order of the underlying group X) without knowing the bases. Moreover, algebraic OWFs must be flexibly one-way in the sense that given y = F (x), it must be infeasible to compute (x , d) such that F (x ) = y d (for d = 0). Interestingly, algebraic one way functions can be constructed from a variety of standard number theoretic assumptions, such as RSA, Factoring and CDH over bilinear groups.As a second contribution of this paper, we show several applications where algebraic (trapdoor) OWFs turn out to be useful. These include publicly verifiable secure outsourcing of polynomials, linearly homomorphic signatures and batch execution of Sigma protocols.

We propose a generalised framework for Bayesian Structural Equation Modelling (SEM) that can be applied to a variety of data types. The introduced framework focuses on the approximate zero approach, according to which a hypothesised structure is formulated with approximate rather than exact zero. It extends previously suggested models by Muthén and Asparouhov ( 2012) and can handle continuous, binary, and ordinal data. Moreover, we propose a novel model assessment paradigm aiming to address shortcomings of posterior predictive p−values, which provide the default metric of fit for Bayesian SEM. The introduced model assessment procedure monitors the out-of-sample predictive performance of the model in question, and draws from a list of principles to answer whether the hypothesised theory is supported by the data. We incorporate scoring rules and cross-validation to supplement existing model assessment metrics for Bayesian SEM. The methodology is illustrated in continuous and categorical data examples via simulation experiments as well as real-world applications on the 'Big-5' personality scale and the Fagerstrom test for nicotine dependence.

Field studies in many domains have found evidence of decision fatigue, a phenomenon describing how decision quality can be impaired by the act of making previous decisions. Debate remains, however, over posited psychological mechanisms underlying decision fatigue, and the size of effects in high-stakes settings. We examine an extensive set of pretrial arraignments in a large, urban court system to investigate how judicial release and bail decisions are influenced by the time an arraignment occurs. We find that release rates decline modestly in the hours before lunch and before dinner, and these declines persist after statistically adjusting for an extensive set of observed covariates. However, we find no evidence that arraignment time affects pretrial release rates in the remainder of each decision-making session. Moreover, we find that release rates remain unchanged after a meal break even though judges have the opportunity to replenish their mental and physical resources by resting and eating. In a complementary analysis, we find that the rate at which judges concur with prosecutorial bail requests does not appear to be influenced by either arraignment time or a meal break. Taken together, our results imply that to the extent that decision fatigue plays a role in pretrial release judgments, effects are small and inconsistent with previous explanations implicating psychological depletion processes.

The process of approving and assessing new drugs is often quite complicated, mainly due to the fact that multiple criteria need to be considered. A standard way to proceed is with benefit risk analysis, often under the Bayesian paradigm to account for uncertainty and combine data with expert judgement, which is operationalised via multi-criteria decision analysis (MCDA) scores. The procedure is based on a suitable model to accommodate key features of the data, which are typically of mixed type and potentially depended, with factor models providing a standard choice. The contribution of this paper is threefold: first, we extend the family of existing structured factor models. Second, we provide a framework for choosing between them, which combines fit and out-of-sample predictive performance. Third, we present a sequential estimation framework that can offer multiple benefits: (i) it allows us to efficiently re-estimate MCDA scores of different drugs each time new data become available, thus getting an idea on potential fluctuations in differences between them, (ii) it can provide information on potential early stopping in cases of evident conclusions, thus reducing unnecessary further exposure to undesirable treatments; (iii) it can potentially allow to assign treatment groups dynamically based on research objectives. A drawback of sequential estimation is the increased computational time, but this can be mitigated by efficient sequential Monte Carlo schemes which we tailor in this paper to the context of Bayesian benefit risk analysis. The devel-

Abstract-This work began when the two authors met at a software development meeting. Konstantinos was building Bayesian models in his research and wanted to learn how to better manage his research process. Marianne was working on data analysis workflows in industry and wanted to learn more about Bayesian statistics. In this paper, the authors present a Bayesian scientific research workflow for statistical analysis. Drawing on a case study in clinical trials, they demonstrate lessons that other scientists, not necessarily Bayesian, could find useful in their own work. Notably, they can be used to improve productivity and reproducibility in any computational research project.