Credibility Weight Research Articles

Evaluating release alternatives for a long-lived bird species under uncertainty about long-term demographic rates

The release of animals to reestablish an extirpated population is a decision problem that is often attended by considerable uncertainty about the probability of success. Annual releases of captive-reared juvenile Whooping Cranes (Grus americana) were begun in 1993 in central Florida, USA, to establish a breeding, non-migratory population. Over a 12-year period, 286 birds were released, but by 2004, the introduced flock had produced only four wild-fledged birds. Consequently, releases were halted over managers’ concerns about the performance of the released flock and uncertainty about the efficacy of further releases. We used data on marked, released birds to develop predictive models for addressing whether releases should be resumed, and if so, under what schedule. To examine the outcome of different release scenarios, we simulated the survival and productivity of individual female birds under a baseline model that recognized age and breeding-class structure and which incorporated empirically estimated stochastic elements. As data on wild-fledged birds from captive-reared parents were sparse, a key uncertainty that confronts release decision-making is whether captive-reared birds and their offspring share the same vital rates. Therefore, we used data on the only population of wild Whooping Cranes in existence to construct two alternatives to the baseline model. The probability of population persistence was highly sensitive to the choice of these three models. Under the baseline model, extirpation of the population was nearly certain under any scenario of resumed releases. In contrast, the model based on estimates from wild birds projected a high probability of persistence under any release scenario, including cessation of releases. Therefore, belief in either of these models suggests that further releases are an ineffective use of resources. In the third model, which simulated a population Allee effect, population persistence was sensitive to the release decision: high persistence probability was achieved only through the release of more birds, whereas extirpation was highly probable with cessation of releases. Despite substantial investment of time and effort in the release program, evidence collected to date does not favor one model over another; therefore, any decision about further releases must be made under considerable biological uncertainty. However, given an assignment of credibility weight to each model, a best, informed decision about releases can be made under uncertainty. Furthermore, if managers can periodically revisit the release decision and collect monitoring data to further inform the models, then managers have a basis for confronting uncertainty and adaptively managing releases through time.

Credible Loss Ratio Claims Reserves: the Benktander, Neuhaus and Mack Methods Revisited

AbstractThe Benktander (1976) and Neuhaus (1992) credibility claims reserving methods are reconsidered in the framework of a credible loss ratio reserving method. As a main contribution we provide a simple and practical optimal credibility weight for combining the chain-ladder or individual loss ratio reserve (grossed up latest claims experience of an origin period) with the Bornhuetter-Ferguson or collective loss ratio reserve (experience based burning cost estimate of the total ultimate claims of an origin period). The obtained simple optimal credibility weights minimize simultaneously the mean squared error and the variance of the claims reserve. We note also that the standard Chain-Ladder, Cape Cod and Bornhuetter-Ferguson methods can be reinterpreted in the credible context and extended to optimal credible standard methods. The new approach is inspired from Mack (2000). Two advantages over the Mack method are worthwhile to be mentioned. First, a pragmatic estimation of the required parameters leads to a straightforward calculation of the optimal credibility weights and mean squared errors of the credible reserves. An advantage of the collective loss ratio claims reserve over the Bornhuetter-Ferguson reserve in Mack (2000) is that different actuaries come always to the same results provided they use the same actuarial premiums.

Correcting for Person Misfit in Aggregated Score Reporting

There has been considerable research regarding the extent to which psychometric sound assessments sometimes yield individual score estimates that are inconsistent with the response patterns of the individual. It has been suggested that individual response patterns may differ from expectations for a number of reasons, including subject motivation, attention, test dimensionality, test bias, or even cheating. Whatever the reason, otherwise sound assessments may yield individual score estimates that are not truly reflective of a subject's underlying trait level. In large-scale testing situations, the extent of individual misfit may materially affect aggregated score reports for relevant subgroups of students. This article investigates the impact of using individual person-fit measures from item response theory (IRT) scored achievement examinations as weighting factors in providing aggregated score reports. About 160,000 students from more than 300 schools completed a mathematics or reading test in a computer adaptive environment. For each subject, a standardized person-fit statistic (Drasgow, Levine, & Williams, 1985) was used to estimate the degree of misfit for each subject. A brief simulation study was done and the results provided cut points for determining misfit in a computer adaptive environment. Step and logistic functions were applied to these person-fit statistics to determine credibility weights for each respondent. Data were then aggregated by using the credibility weights to produce school-level estimates for all students and for each student subgroup. The weighted aggregated estimates were then compared with unweighted estimates to identify the impact of the use of person-fit measures as weighting factors for aggregated score reporting. As expected, weighted group estimates generally produced significantly different group scores than unweighted group estimates but did so differentially across student subgroups (e.g., ethnicity, grade). It is argued that the use of person-fit measures may provide for a useful correction factor for model misfit in generating better aggregated score estimates in large scale testing contexts without jeopardizing relative school standing.

A framework for multi-source data fusion

A general view of the multi-source data fusion process is presented. Some of the considerations and information that must go into the development of a multi-source data fusion algorithm are described. Features that play a role in expressing user requirements are also described. We provide a general framework for data fusion based on a voting like process that tries to adjudicate conflict among the data. We discuss idea of a compatibility relationship and introduce several important examples of these relationships. We show that our formulation results in some conditions on the fused value implying that the fusion process has the nature of a mean type aggregation. Situations in which the sources have different credibility weights are considered. We present a concept of reasonableness as a means for including in the fusion process any information available other then that provided by the sources. We consider the situation where we allow our fused values to be granular objects such as linguistic terms or subsets.

A framework for multi-source data fusion

A general view of the multi-source data fusion process is presented. Some of the considerations and information that must go into the development of a multi-source data fusion algorithm are described. Features that play a role in expressing user requirements are also described. We provide a general framework for data fusion based on a voting like process that tries to adjudicate conflict among the data. We discuss idea of a compatibility relationship and introduce several important examples of these relationships. We show that our formulation results in some conditions on the fused value implying that the fusion process has the nature of a mean type aggregation. Situations in which the sources have different credibility weights are considered. We present a concept of reasonableness as a means for including in the fusion process any information available other then that provided by the sources. We consider the situation where we allow our fused values to be granular objects such as linguistic terms or subsets.

Equity and Exact Credibility

AbstractWe consider an alternative to the usual credibility premium that arises from squared-error loss, namely, a so-called equitable credibility premium (Promislow and Young, 1999). We derive formulas for the credibility weight in certain cases and give sufficient conditions for exact credibility.

Equity and Credibility

We build on previous work concerned with measuring equity and consider the problem of using observed claim data or other information to calculate premiums which maximize equity. When these optimal premiums are used, we show that gathering more information or refining the risk classification always increases equity. We study the case for which the premium is constrained to be an affine function of the claim data and obtain results analogous to classical credibility theory, including the inhomogeneous and homogeneous cases of the Bu¨hlmann-Straub model. We derive formulas for the credibility weights in certain cases.

A self-evaluating expert system for X-ray rocking curve analysis

X-ray rocking curve analysis is widely used in research and industry to investigate the perfection of a variety of natural and synthetic crystals. In this article a method is demonstrated for the effective self-evaluation of an expert system for x-ray rocking curve analysis. the method uses a combination of fuzzy logic and machine learning, the latter defined as a self-adaptive system that improves system performance over time. the heuristics of several experts are combined using rules, frames, and connection matrices. Each expert is weighted on the basis of experience and these credibility weights are used to influence the decision processes of the expert system. All weights are evaluated over time and the basis for evaluation is successful or unsuccessful expert system decisions. Individual rules are also evaluated and whenever a rule is shown to be ineffective it is hidden from the reasoning processes of the expert system. When new situations occur that have not been allowed for in the rules of the expert system, then existing rules are fine-tuned and changed to deal with these new facts. New rules are inferred and evaluated in the same way as the heuristics of the human experts. © 1994 John Wiley & Sons, Inc.

Pitfalls of the Current Experience Rating Plan

Introduction Workers' compensation insurance is the largest line of commercial casualty insurance in the United States and the oldest for which standard rating approaches have been developed. The principal statistical and ratemaking body, the National Council on Compensation Insurance (NCCI), uses similar experience rating techniques for individual states with variations by state, depending on unique classes or individual state requirements. The rather complex rate development process can be summarized as follows: (1) The premiums and losses for a state are collected totally; separately by manufacturing, contracting, and all other classes; and individual classification. (2) Rates are determined by class using credibility factors and adjusting total rate levels in accordance with permissible levels and state increase parameters. The insurance rates developed through this process may be modified under the regulatory process in each state. The results of the ratemaking process are known as class rates. The premium for an individual risk is the result of applying class rates to the applicable number of payroll units ($100 of payroll) subject to a premium discount based on the size of the overall premium. Experience rating is a supplemental procedure that utilizes the individual risk's past loss experience to forecast future losses. It is an effort to modify the ratemaking process by recognizing an individual risk's potential for incurring claims. An effective experience rating plan surcharges poor risks and credits good risks in proportion to relative exposure to loss. In other words, experience rating adjusts the class premium to provide all policy holders with relatively equal expected loss ratios. However, when basic assumptions involving firm ownership are violated, the appropriateness of the method comes into question. For example, significant rating differences may exist depending on whether Company A buys Company B or Company B buys Company A. The experience rating procedure utilizes three years of loss history (second through fourth prior) as an indicator of future losses. A policy rated on January 1, 1993, would therefore utilize the loss experience of 1989, 1990, and 1991 to develop an experience modification factor. (Losses for the immediate prior year are considered too green and generally are not available for use in the experience rating process.) The process used to calculate an experience modification factor is a form of rating. The incurred loss value for each claim is split between a value and an value. The rationale is to give more weight to the frequency than to the severity of claims. This is intuitively reasonable as the size of the loss is more subject to chance than the number of losses. Perryman (1937) developed the generally accepted formula for experience modification factors: M = |A.sub.p~ + B + W|A.sub.e~ + (1 - W)|E.sub.e~/E + B, (1) where |A.sub.p~ = actual primary losses, B = ballast (stabilizing) value. W = credibility weight assigned to actual excess losses, |A.sub.e~ = actual excess losses, |E.sub.e~ = expected excess losses, and E = total expected losses. The values B and W vary according to the size of the risk. At one extreme, a small risk will have no credibility assigned to historical excess losses (W = 0) and will have a ballast (stabilizing) value of $20,000 added to the numerator and denominator of the experience modification formula. The use of a low W-value and a high B-value gives lower credibility to actual loss experience and thus reduces the difference from the rate. A large, self-rated risk, however, could have full credibility for its loss experience (W = 1) with no ballast. In such a case, the individual risk's own loss experience is weighted 100 percent. Thus, the experience modification formula for a self-rated risk reduces to the formula M = A/E. …

Fuzzy knowledge combination

A general answer is given to what one should conclude from disagreeing experts. the answer is generalized further to incorporate the experts' credibility weights. the answer rests on a wide range of intuitively based epistemic axioms, scientific and philosophical conjectures, and formal mathematical relationships. A recurring theme is the making of Bellman - Zadeh fuzzy decisions, wherein a decision is the intersection of fuzzy goal and fuzzy constraint subsets of some space of alternatives. Another result is that measures of central tendency, such as the arithmetic mean, make poor knowledge combination operators. Formally, fuzzy knowledge combination operators are sought. the function space of knowledge combination operators ø: K″ → K is shrunk by imposing successive axioms. the final shrunken set is said to consist of admissible knowledge combination operators. Some of its mathematical properties are explored and a simple admissible operator is finally chosen. Knowledge sources Xi: S → K are mappings from epistemic stimuli or questions into a knowledge response set K. the uncertainty of the underlying epistemic situations is captured by the cardinality of K and by the fuzziness of its partial ordering. Admissible knowledge combination operators Aggregate knowledge responses in some desirable way. the arithmetic mean is not admissible. Nor in general is a probabilistic framework even definable in the abstract poset setting employed by this theory. the fuzzy knowledge combination theory is extended by associating general credibility weights with the knowledge sources. A new set of weighting axioms is required to satisfy certain intuitions and to satisfy the admissibility axioms. General weighting functions are obtained and thereby weighted admissible operators are obtained. the weighted mean still proves inadmissible. Appendix I contains a technical glossary and summary of the proposed fuzzy knowledge combination theory. Appendix II contains proofs of the probabilistic uncertainty theorems required for the uncertainty testbed used in the theory.

Operations analysis during the underwater search for Scorpions

AbstractThis paper discusses the operations analysis in the underwater search for the remains of the submarine ScorpionThe a priori target location probability distribution for the search was obtained by monte‐carlo procedures based upon nine different scenarios concerning the Scorpion loss and associated credibility weights. These scenarios and weights were postulated by others. Scorpion was found within 260 yards of the search grid cell having the largest a priori probabilityFrequent computations of local effectiveness probabilities (LEPs) were carried out on scene during the search and were used to determine an updated (a posteriori) target location distribution. This distribution formed the basis for recommendation of the current high probability areas for searchThe sum of LEPs weighted by the a priori target location probabilities is called search effectiveness probability (SEP) and was used as the overall measure of effectiveness for the operation. SEP and LEPs were used previously in the Mediterranean H‐bomb searchOn‐scene and stateside operations analysis are discussed and the progress of the search is indicated by values of SEP for various periods during the operation.