On representation of monotone preference orders in a sequence space

In this paper we investigate the relation between scalar continuity and representability of monotone preference orders in a sequence space. Scalar continuity is shown to be sufficient for representability of a monotone preference order and easy to verify in concrete examples. Generalizing this result, we show that a condition, which restricts the extent of scalar discontinuity of a monotone preference order, ensures representability. We relate this condition to the well-known order dense property, which is both necessary and sufficient for representability.     

A Bayesian hierarchical model for inference across related reverse phase protein arrays experiments

We consider inference for functional proteomics experiments that record protein activation over time following perturbation under different dose levels of several drugs. The main inference goal is the dependence structure of the selected proteins. A critical challenge is the lack of sufficient data under any one drug and dose level to allow meaningful inference on dependence structure. We propose a hierarchical model to implement the desired inference. The key element of the model is a shared dependence structure on (latent) binary indicators of protein activation.     

A short note on the taeuber paradox

When the force of mortality is reduced by a constant fraction 0 at every age, the relative increase in life expectancy e(0) can be measured by δH, where H is determined by the l(a) values of the life table. Although H is not easily reducible in terms of the well-known life table parameters, it has been shown that it can be approximately estimated by 2 – e(0)/à in which d is the average age of the stationary population. It has been found that, for a given value of 0, the relative gain in life expectancy is less appreciable in countries with larger values of e(0).     

On the continuity of ethical social welfare orders on infinite utility streams

In this paper we study the extent to which ethical social welfare orders on infinite utility streams can be continuous. For a class of metrics, we show that ethical preferences can be continuous if and only if the continuity requirement is in terms of a metric which satisfies a simplex condition. This condition requires that the distance from the origin to the unit simplex in the space of utility streams be positive. We use this characterization result to establish that the metric used by Svensson (Econometrica 48:1251–1256, 1980) induces the smallest topology for which there exist continuous ethical preferences. We thank an associate editor and two referees of this journal for their comments and suggestions.     

On the efficiency of the estimates of life table functions

Expected values and variances of several life table functions have been obtained by converting the sample estimates of age-specific mortality rates to probabilities of dying by Reed-Merrell’s approximation. The expressions also permit the development of a procedure that will enable the researcher, constrained usually by his limited resources, to maximize the efficiency of his sampling technique. Needless to say, these results will be particularly useful for countries where national vital statistics are not adequate for construction of life tables, and also for countries where such tables are usually obtained by comparing age distributions of successive censuses.     

On the derivation of a two-sex stable population model

It is well known that the intrinsic rates of growth derived separately for the males and females in a population, when one assumes the continuation of their respective mortality and fertility experiences, usually turn out to be different. Noting that the phenomenon of human reproduction is a product of the cooperation between the two sexes, we have attempted in this paper to define the sex-age-specific fertility rates as a function not only of age but also of time, where the latter is implicitly introduced in the model through the sex composition of the reproductive population. It has been shown that a stable model can then be defined based on such changing sex-age-specific fertility rates and given sets of unchanging mortality rates. The fertility rates stabilize with time, and the common intrinsic rates of growth for the two sexes are found to lie in the interval generated by the corresponding rates of the two one-sex models. Several other interesting relationships among the parameters of this model have been presented in the paper. Among other alternatives, a least square solution has been presented for the values of sex-age-specific fertility rates that are minimally discrepant with the observed rates but are consistent in terms of the parametric estimates they generate. It is interesting to note that a relatively modest adjustment in the sex-age-specific fertility rates is all that it takes to eliminate the inconsistencies generated by the separate one-sex models.     

Influence of instantaneous fertility decline to replacement level on population growth: An alternative model

If age-specific birth rates m, of a stable population drop abruptly tom _x/R ₀, whereR ₀ is the net reproduction rate, then, according to Keyfitz, the size of the ultimate stationary population relative to.that at the beginning of the process is given byI =be ⁰ ₀ R ₀ ? 1)/(rμR ₀, whereb andr are the birth rate and the rate of growth, respectively, of the stable population,e ₀ ⁰ the life expectancy at birth, andμ the average age at childbirth in the resulting stationary population. Noting that the decline inm _x need not necessarily be uniform, investigation has been carried out to examine the effect on Iwhen fertility decline is more rapid at higher ages. In particular, the effect of the reduced age-specific rates such asm _xe^? rx (which also produces a stationary population) has been analyzed, and simplifications of the results carried out separately for three different models of the net maternity function. It has also been shown that when m, drops abruptly to somem _x ^*, where the form ofm _x ^* need not be specified except for the restriction that the resulting population will be stationary, the value of the index can be approximately obtained fromI ^* =be ₀ ⁰ (1 -rμ/2), whereμ is the average age at childbearing of the initial stable population.     

Rationalizing Policy Functions by Dynamic Optimization

We derive necessary and sufficient conditions for a pair of functions to be the optimal policy function and the optimal value function of a dynamic maximization problem with convex constraints and concave objective functional. It is shown that every Lipschitz continuous function can be the solution of such a problem. If the maintained assumptions include free disposal and monotonicity, then we obtain a complete characterization of all optimal policy and optimal value functions. This is the case, e.g., in the standard aggregative optimal growth model.