In the traditional multidimensional credibility models developed by Jewell ((1973) Operations Research Center, pp. 73–77.), the estimation of the hypothetical mean vector involves complex matrix manipulations, which can be challenging to implement in practice. Additionally, the estimation of hyperparameters becomes even more difficult in high-dimensional risk variable scenarios. To address these issues, this paper proposes a new multidimensional credibility model based on the conditional joint distribution function for predicting future premiums. First, we develop an estimator of the joint distribution function of a vector of claims using linear combinations of indicator functions based on past observations. By minimizing the integral of the expected quadratic distance function between the proposed estimator and the true joint distribution function, we obtain the optimal linear Bayesian estimator of the joint distribution function. Using the plug-in method, we obtain an explicit formula for the multidimensional credibility estimator of the hypothetical mean vector. In contrast to the traditional multidimensional credibility approach, our newly proposed estimator does not involve a matrix as the credibility factor, but rather a scalar. This scalar is composed of both population information and sample information, and it still maintains the essential property of increasingness with respect to the sample size. Furthermore, the new estimator based on the joint distribution function can be naturally extended and applied to estimate the process covariance matrix and risk premiums under various premium principles. We further illustrate the performance of the new estimator by comparing it with the traditional multidimensional credibility model using bivariate exponential-gamma and multivariate normal distributions. Finally, we present two real examples to demonstrate the findings of our study.

Must rational thinkers have consistent sets of beliefs? I shall argue that it can be rational for a thinker to believe a set of propositions known to be inconsistent. If this is right, an important test for a theory of rational belief is that it allows for the right kinds of inconsistency. One problem we face in trying to resolve disagreements about putative rational requirements is that parties to the disagreement might be working with different conceptions of the relevant attitudes. My aim is modest. I hope to show that there is at least one important notion of belief such that a thinker might rationally hold a collection of beliefs (so understood) even when the thinker knows their contents entail a contradiction.

Choices made in risky scenarios are considered fundamentally noisy because decisions have often been found to be inconsistent when repeated. Past measures of noise may, however, be confounded by the use of randomized contextual factors that are known to influence choice, in particular, the order of trials. In two experiments, we control trial order to test the extent to which inconsistent choice is attributable to changes in experimental context. Both tasks find strong evidence that trial order has no effect on choice consistency, indicating such experimental factors have little influence on behavior compared with internal noise. Choices also showed an increase in consistency across multiple repetitions, suggesting a fall in noise with experience, but this increase was not associated with any improvement in performance, with choices showing no greater adherence to either expected value or expected utility across repetitions. Instead, choices increasingly adhered to simplistic heuristic decision rules, possibly indicating greater reliance on such strategies as the tasks progressed. These results carry implications for a number of decision-making theories, including true-and-error models, rank-based methods, and strategy shift approaches.

Bilingualism is a multifaceted experience that researchers have examined using various questionnaires to gain insights and characterize the experience. However, there are several issues related to questionnaire choice. To address this, we applied Content Overlap Analysis to seven prevalent bilingualism questionnaires, assessing their affinity. We found little overlap in these questionnaires; most had fewer than 15% of items in common, suggesting they capture different aspects of the bilingual experience and provide complementary rather than redundant data for researchers. Our investigation highlights the importance of choosing a bilingualism assessment tool to carefully fit research questions and sample language experiences.

In this paper we study the drift parameter estimation for reflected stochastic linear differential equations of a large signal. We discuss the consistency and asymptotic distributions of trajectory fitting estimator (TFE).

This article considers the rule that a claimant who has been wronged will be denied recovery where the damage flowed from a sanction imposed as a result of their own illegal acts such that compensating the claimant would divert a sanction intended to be imposed on the claimant to the defendant. The article has two purposes. The first aim is to provide a counterweight to the overwhelming body of academic literature critical of Gray v Thames Trains Ltd. in which the House of Lords, in applying the illegality bar found it unnecessary to examine the purpose of the criminal sanction against the claimant, preferring to treat its existence as sufficient to lead to a denial of recovery. The article argues that academic support for adoption of an alternative test of “significant personal responsibility” rests on precarious grounds, depending, as it does, on the “unsatisfactory state of law” and “different policies” arguments. This article reconceptualises the rule in Gray and systematically examines the role played by the theme of consistency between the civil law and criminal law in judicial decision-making. The second aim is to evaluate Gray in light of Patel v Mirza. The article critiques the Supreme Court's inconsistent treatment of deterrence in Henderson v Dorset University NHS Foundation Trust and Stoffel v Grondona, and argues that the way the court in Henderson conceptualised the relationship between Gray and Patel discloses an approach which is more closely aligned with that adopted by the minority in Patel.

It was the purpose of this study to assess the consistency of selected animal-based welfare parameters for dairy cattle throughout a one-year period. Eight cubicle-housed dairy herds were visited five times, at two-monthly intervals. At each visit, lameness, injuries to the carpal and tarsal joints, cleanliness, social behaviour and the avoidance distance towards an unknown person were assessed by the same observer in a random sample.

At herd level, lesions of the carpal joints, udder cleanliness and frequencies of agonistic and cohesive behaviour showed low consistency. However, correlations between consecutive recordings as well as between single visits and the average were moderate to satisfactory for lameness prevalence, lesions of the tarsal joints, cleanliness of the hind leg and avoidance distances towards an unknown person in two different locations. The integration of these parameters into on-farm welfare assessment protocols seems to be justified.

Consistency over time is a basic requirement for welfare assessment schemes since consistency must not depend, for example, on the day it is carried out. This study analysed the consistency of the indicators of the Animal Welfare Indicators (AWIN) protocol for horses (Equus caballus) over time. Given the multi-dimensionality of animal welfare, the AWIN protocol includes a variety of indicators evaluating, eg the health status or the behaviour of the animals. Fourteen establishments keeping horses in Germany were visited four times each (day 0, day 3, day 42, day 90). For the evaluation of reliability and agreement between the different visits, ie across time, the reference visit on day 0 was compared to the other visits via calculation of Spearman's rank correlation (RS), intra-class correlation (ICC), smallest detectable change (SDC) and limits of agreement (LoA). The indicator, Qualitative Behaviour Assessment (QBA) was analysed by Principal Component Analysis (PCA). Most of the indicators demonstrated sufficient consistency over time. Indicators that were inconsistent included parts of the Horse Grimace Scale, outcomes of behavioural tests, the presence of swollen joints as well as the indicators hoof neglect, alopecia on the legs and water cleanliness. The QBA was consistent for the period of 42 days, but not for 90 days. Overall, those indicators with insufficient consistency over time require to be revised or replaced in future welfare assessment schemes.

Answer set programs used in real-world applications often require that the program is usable with different input data. This, however, can often lead to contradictory statements and consequently to an inconsistent program. Causes for potential contradictions in a program are conflicting rules. In this paper, we show how to ensure that a program $\mathcal{P}$ remains non-contradictory given any allowed set of such input data. For that, we introduce the notion of conflict-resolving ${\lambda}$-extensions. A conflict-resolving ${\lambda}$-extension for a conflicting rule r is a set ${\lambda}$ of (default) literals such that extending the body of r by ${\lambda}$ resolves all conflicts of r at once. We investigate the properties that suitable ${\lambda}$-extensions should possess and building on that, we develop a strategy to compute all such conflict-resolving ${\lambda}$-extensions for each conflicting rule in $\mathcal{P}$. We show that by implementing a conflict resolution process that successively resolves conflicts using ${\lambda}$-extensions eventually yields a program that remains non-contradictory given any allowed set of input data.

Equality before the law is a foundational principle of the common law and is of particular importance for administrative law, given the connection between judicial review and the rule of law. Analysis as to the precise requirements of this principle can help us better to understand the role that obligations to act consistently play within judicial review. This article will examine whether consistency ought to be classed as a separate ground of review and argue that this is unnecessary. Examination of the role that legal equality plays within common law reason generally will shed light on the role that it plays within administrative law in particular. Consistency is best conceived as a background principle, informed by the value of legal equality, housed within reasonableness review and not as a separate ground of review that could elide the distinction between review and appeal.