Patterns and dynamics of population heterogeneity in mixtures models

Mixtures of distributions are a common modelling tool for durations of social phenomena, especially when the population is believed to be heterogeneous. We discuss heterogeneity patterns which can be captured by various mixing distributions in continuous and discrete time. Particular attention is given to recidivism data which Kaplan modeled by beta-mixtures of geometric distributions. We also investigate the dynamics of heterogeneity, measured via the variance of the mixing distribution, over the duration. It is shown that not all mixture models display decreasing heterogeneity over time.     

On allocating R&D budgets among and within projects

Choosing how to allocate resources to R&D projects is challenging, due to their uncertain success rates and achievement levels. We address the issue of allocating a given R&D budget among projects, and to parallel teams within each project. The achievement level of each team is assumed to be stochastically increasing in its funding level. We consider the objectives of maximizing: 1. the weighted sum of the probabilities that best team in each project achieves a threshold; 2. the weighted sum of expected achievement levels; and 3. the weighted sum of the expected number of teams attaining their threshold. Numerical results for a particular family of distributions are provided. The nature of the objective is seen to have a substantial impact on the optimal allocation.     

Profitable Advice: the Value of Information Provided by Canada's Inventor's Assistance Program

Inventors who are considering whether and how to commercialize their inventions. can often avail themselves to evaluations and advice provided by government supported programs initiated to encourage innovation. In Canada. such a service is provided by the Canadian Innovation Centre. through its Inventor's Assistance Program. In its twenty years of operations the IAP has evaluated 11,000 inventions. The fee charged for an invention evaluation was Cdn. $262 in 1995, and these fees covered about half the program's expenses. We compute the expected value of the information the IAP's evaluation provides under different assumptions and scenarios. Under plausible conditions, the value of the information to the inventor is found to be higher than both the fee and the social cost of the program. The implications of some inventors not following the advice given to them by the IAP are briefly explored.     

Estimating Arbitrator's Hidden Judgement in Final Offer Arbitration

In Final Offer Arbitration the arbitrator has to choose between two prices – salary offer a and demand b, presented by two negotiating sides. This situation is common e.g., in Major League Baseball since 1974, for players with at least three years experience. We model the arbitrator's decision process as follows. First, the arbitrator chooses an appropriate sum Z. Then he selects the one among a and b which is closer to the ‘proper sum’Z. The final amount selected is Y . Based on the history of n cases, the information available is the triplets {(Y _i, a _i, b _i) : i= 1, 2, . . . n}(the {Z _i} are hidden). It is assumed that the {Z _i} are random variables with a distribution which depends on an unknown parameter q and the challenge is to estimate q. Furthermore, since each case had different merits and characteristics, the resulting distribution is case-specific. Thus, our model allows the inclusion of explanatory variables. The statistical algorithm which we shall use is the Expectation-Maximization(EM) algorithm. In the paper, the statistical model is introduced in detail and the application of the EM algorithm to the available data is explained. Two numerical examples illustrate the use of the EM algorithm in estimating the arbitrator's hidden judgements.     

How should a principal reward and support agents when firm performance is characterized by success or failure?

Principal‐agent models with multiple agents typically assume that the principal wishes to maximize the sum of the agents' achievements (net of the rewards paid to them). But in many settings, like R&D, all that the principal “needs” is that at least one agent will be “successful.” We identify settings where the principal actually wants agents to refrain from exerting high effort in order to save expected compensation. We show that the number of agents can decrease in the project's value for the principal. We also consider sequential efforts and investigate settings where the principal can provide support to agents.     

Optimal Rationing Policies and Production Quantities for Products with Several Demand Classes

This paper considers a situation in which several distinct classes of customers exist for a single product or service in a fixed, finite planning period. If such a product is also perishable and if backlogging is not permitted, it may sometimes be worthwhile to reject “low-revenue customers” upon arrival, depending on the number of units on hand and time left until the end of the period. The objectives of this study are to derive optimal rationing policies at any state of the planning period and to formulate a procedure for calculating the optimal production quantity at the beginning of the period for various cost (production) functions, given that an optimal rationing policy is to be followed. The approach used is backward-recursion dynamic programming. Résumé Ce mémoire examine une situation dans laquelle plusieurs classes distinctes de clients existent pour un seul produit ou service au cours d'une période de planification déterminée. Si cette denrée est également périssable et que le stockage n'est pas permis, il est parfois avantageux de rejeter les “clients à bas revenus,” tout dépendant du nombre d'unités en main et du temps qui reste avant la fin de la période. Les objectifs de l'éude visent à créer des politiques de rationnement optimal au cours de la période de planification et de formuler une méthode de calcul des quantités optimales de production en début de période relativement à plusieurs fonctions relatives au coǔt (production), compte tenu de l'application d'une politique de rationnement optimal. Il s'agit ici de programmation dynamique à récursivité rétrograde.