Equivalence of truncated count mixture distributions and mixtures of truncated count distributions

This article is about modeling count data with zero truncation. A parametric count density family is considered. The truncated mixture of densities from this family is different from the mixture of truncated densities from the same family. Whereas the former model is more natural to formulate and to interpret, the latter model is theoretically easier to treat. It is shown that for any mixing distribution leading to a truncated mixture, a (usually different) mixing distribution can be found so. that the associated mixture of truncated densities equals the truncated mixture, and vice versa. This implies that the likelihood surfaces for both situations agree, and in this sense both models are equivalent. Zero-truncated count data models are used frequently in the capture-recapture setting to estimate population size, and it can be shown that the two Horvitz-Thompson estimators, associated with the two models, agree. In particular, it is possible to achieve strong results for mixtures of truncated Poisson densities, including reliable, global construction of the unique NPMLE (nonparametric maximum likelihood estimator) of the mixing distribution, implying a unique estimator for the population size. The benefit of these results lies in the fact that it is valid to work with the mixture of truncated count densities, which is less appealing for the practitioner but theoretically easier. Mixtures of truncated count densities form a convex linear model, for which a developed theory exists, including global maximum likelihood theory as well as algorithmic approaches. Once the problem has been solved in this class, it might readily be transformed back to the original problem by means of an explicitly given mapping. Applications of these ideas are given, particularly in the case of the truncated Poisson family.

Maximizing revenue in Grid markets using an economically enhanced resource manager

Traditional resource management has had as its main objective the optimization of throughput, based on parameters such as CPU, memory, and network bandwidth. With the appearance of Grid markets, new variables that determine economic expenditure, benefit and opportunity must be taken into account. The Self-organizing ICT Resource Management (SORMA) project aims at allowing resource owners and consumers to exploit market mechanisms to sell and buy resources across the Grid. SORMA's motivation is to achieve efficient resource utilization by maximizing revenue for resource providers and minimizing the cost of resource consumption within a market environment. An overriding factor in Grid markets is the need to ensure that the desired quality of service levels meet the expectations of market participants. This paper explains the proposed use of an economically enhanced resource manager (EERM) for resource provisioning based on economic models. In particular, this paper describes techniques used by the EERM to support revenue maximization across multiple service level agreements and provides an application scenario to demonstrate its usefulness and effectiveness. Copyright © 2008 John Wiley & Sons, Ltd.

On the equivalence between radiance and retrieval assimilation

The need for consistent assimilation of satellite measurements for numerical weather prediction led operational meteorological centers to assimilate satellite radiances directly using variational data assimilation systems. More recently there has been a renewed interest in assimilating satellite retrievals (e.g., to avoid the use of relatively complicated radiative transfer models as observation operators for data assimilation). The aim of this paper is to provide a rigorous and comprehensive discussion of the conditions for the equivalence between radiance and retrieval assimilation. It is shown that two requirements need to be satisfied for the equivalence: (i) the radiance observation operator needs to be approximately linear in a region of the state space centered at the retrieval and with a radius of the order of the retrieval error; and (ii) any prior information used to constrain the retrieval should not underrepresent the variability of the state, so as to retain the information content of the measurements. Both these requirements can be tested in practice. When these requirements are met, retrievals can be transformed so as to represent only the portion of the state that is well constrained by the original radiance measurements and can be assimilated in a consistent and optimal way, by means of an appropriate observation operator and a unit matrix as error covariance. Finally, specific cases when retrieval assimilation can be more advantageous (e.g., when the estimate sought by the operational assimilation system depends on the first guess) are discussed.

Equivalence of weak formulations of the steady water waves equations

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.

Efficiency, enforcement and revenue tradeoffs in participatory forest management: an example from Tanzania

Where joint forest management has been introduced into Tanzania, ‘volunteer’ patrollers take responsibility for enforcing restrictions over the harvesting of forest resources, often receiving as an incentive a share of the collected fine revenue. Using an optimal enforcement model, we explore how that share, and whether villagers have alternative sources of forest products, determines the effort patrollers put into enforcement and whether they choose to take a bribe rather than honestly reporting the illegal collection of forest resources. Without funds for paying and monitoring patrollers, policy makers face tradeoffs over illegal extraction, forest protection and revenue generation through fine collection.

Exploring unanticipated consequences of strategy amongst stakeholder segments: the case of a European Revenue Service

This article applies FIMIX-PLS segmentation methodology to detect and explore unanticipated reactions to organisational strategy among stakeholder segments. For many large organisations today, the tendency to apply a “one-size-fits-all” strategy to members of a stakeholder population, commonly driven by a desire for simplicity, efficiency and fairness, may actually result in unanticipated consequences amongst specific subgroups within the target population. This study argues that it is critical for organisations to understand the varying and potentially harmful effects of strategic actions across differing, and previously unidentified, segments within a stakeholder population. The case of a European revenue service that currently focuses its strategic actions on building trust and compliant behaviour amongst taxpayers is used as the context for this study. FIMIX-PLS analysis is applied to a sample of 501 individual taxpayers, while a novel PLS-based approach for assessing measurement model invariance that can be applied to both reflective and formative measures is also introduced for the purpose of multi-group comparisons. The findings suggest that individual taxpayers can be split into two equal-sized segments with highly differentiated characteristics and reactions to organisational strategy and communications. Compliant behaviour in the first segment (n = 223), labelled “relationships centred on trust,” is mainly driven through positive service experiences and judgements of competence, while judgements of benevolence lead to the unanticipated reaction of increasing distrust among this group. Conversely, compliant behaviour in the second segment (n = 278), labelled “relationships centred on distrust,” is driven by the reduction of fear and scepticism towards the revenue service, which is achieved through signalling benevolence, reduced enforcement and the lower incidence of negative stories. In this segment, the use of enforcement has the unanticipated and counterproductive effect of ultimately reducing compliant behaviour.

Revenue-neutral tax policy under price uncertainty

The firm's response to revenue-neutral taxation is investigated under price uncertainty. Revenue-neutral policies adjust simultaneously the marginal tax rate and the level of exemptions while keeping expected tax receipts constant. Nonincreasing absolute risk aversion is sufficient to sign the firm's response: a reduction in the marginal rate causes the firm to contract output. Implications are established for the equilibrium level of treasury receipts.

Revenue-neutral tax policies under price uncertainty: reply

In their comment on my 1990 article, Yeh, Suwanakul, and Mai extend my analysis-which focused attention exclusively on firm output-to allow for simultaneous endogeneity of price, aggregate output, and numbers of firms. They show that, with downward- sloping demand, industry output adjusts positively to revenue-neutral changes in the marginal rate of taxation. This result is significant for two reasons. First, we are more often interested in predictions about aggregate phenomena than we are in predictions about individual firms. Indeed, firm-level predictions are frequently irrefutable since firm data are often unavailable. Second, the authors derive their result under a set of conditions that appear to be more general than those invoked in my 1990 article. In particular, they circumvent the need to invoke specific assumptions about the nature of firms' aversions toward risk. I consider this a useful extension and I appreciate the careful scrutiny of my paper.

Natural disaster accounting bias and its equivalence across genetic resource stocks

Two sources of bias arise in conventional loss predictions in the wake of natural disasters. One source of bias stems from neglect of accounting for animal genetic resource loss. A second source of bias stems from failure to identify, in addition to the direct effects of such loss, the indirect effects arising from implications impacting animal-human interactions. We argue that, in some contexts, the magnitude of bias imputed by neglecting animal genetic resource stocks is substantial. We show, in addition, and contrary to popular belief, that the biases attributable to losses in distinct genetic resource stocks are very likely to be the same. We derive the formal equivalence across the distinct resource stocks by deriving an envelope result in a model that forms the mainstay of enquiry in subsistence farming and we validate the theory, empirically, in a World-Society-for-the-Protection-of-Animals application

Strangely dual orbifold equivalence I

In this brief note we prove orbifold equivalence between two potentials described by strangely dual exceptional unimodular singularities of type K14 and Q10 in two different ways. The matrix factorizations proving the orbifold equivalence give rise to equations whose solutions are permuted by Galois groups which differ for different expressions of the same singularity.