Choice with imprecise information: an experimental approach

This article provides an experimental analysis of attitude toward imprecise and variable information. Imprecise information is provided in the form of a set of possible probability values, such that it is virtually impossible for the subjects to guess or estimate, which one in the set is true or more likely to be true. We investigate how geometric features of such information pieces affect choices. We find that the subjects care about more features than the pairs of best-case and worst-case, which is a counter-evidence to the well-known models, maximin and α-maximin. We find that presence of nonextreme points in the set affects choice, which suggests that attitude toward imprecision is ‘nonlinear.’ We also obtain an observation, though not significant, that information pieces have a complementarity that may not be explained by the Bayesian view.     

On flexible product-mix decision problems under randomness and fuzziness

This paper considers several models of product-mix decision problems and production planning problems under uncertain conditions, and shows that these are extensional and versatile models for resolving previous product-mix problems. These proposed models include randomness derived from statistical analysis based on historical data, ambiguity of decision maker's intuition and the quality of received information, and flexibility in accomplishing the original plan. Furthermore, given that the upper limit values of some constraints have flexibility, and given a decision maker's level of satisfaction, we propose a flexible product mix of problems using the theory of constraints (TOC), and develop an efficient solution method. We then provide a numerical example that compares our models with some previous basic models. Efficiency of flexibility is obtained when our proposed models are applied to several conditions, such as measurable changes from the expected value of future returns.     

The measurement of transient poverty: Theory and application to Pakistan

The present paper investigates the measurement of transient poverty when each person's welfare level fluctuates due to exogenous risk. The paper namely characterizes the sensitivity of transient/chronic poverty decomposition with respect to the poverty line and to the expected welfare level so that the decomposition analysis will be based on solid theoretical foundations and be robust empirically. Theoretical results show that poverty measures associated with prudent risk preferences perform better than other measures in assuring that the value of transient poverty increases with the depth of chronic poverty and that the decomposition is not highly sensitive to the poverty line. Poverty measures such as those associated with constant relative risk aversion are thus superior to popular Foster–Greer–Thorbecke (FGT) measures such as headcount, poverty gap, and squared poverty gap indices. These theoretical arguments are confirmed empirically by the application of the decomposition to a two-period household panel dataset from rural Pakistan. The relative magnitudes of transient versus chronic poverty are more robust to changes in the poverty line when poverty measures associated with constant relative risk aversion are used than when FGT poverty measures are used.     

On the conservative simultaneous confidence procedures for multiple comparisons among mean vectors

In this paper, conservative simultaneous confidence intervals for multiple comparisons among mean vectors in multivariate normal distributions are considered. Some properties of the multivariate Tukey–Kramer procedure for pairwise comparisons and the conservative simultaneous confidence procedure for comparisons with a control are presented. Particularly, the upper bound for the conservativeness of the simultaneous confidence procedure for comparisons with a control is obtained. Finally, numerical results by Monte Carlo simulations and an example to illustrate the procedure are given.     

Social organization of the voleClethrionomys rufocanus and its demographic and genetic consequences: A review

Recent findings on the relationship between social interaction and demographic process in the gray-sided voleClethrionomys rufocanus are reviewed with reference to the findings in other microtine rodents. Social behavior was particularly focused on spacing and dispersal, and their effects on population dynamics are discussed. Female territoriality can limit a population abundance as a density-dependent factor, although its regulatory effect is controversial. Female philopatry and male-biased dispersal should bring about the clumped distribution of female relatives and genetically random distribution of males during the breeding season. The sexual difference in dispersal patterns can contribute to the mating behavior of the vole; promiscuous mating and low frequency of incestuous mating. However, effects of social structure, including kinship, on reproduction and survival of individuals still remains to be clarified. Molecular markers may help to solve these issues and provide new field of population ecology in microtine rodents.     

Small grid drawings of planar graphs with balanced partition

In a grid drawing of a planar graph, every vertex is located at a grid point, and every edge is drawn as a straight-line segment without any edge-intersection. It is known that every planar graph G of n vertices has a grid drawing on an (n?2)×(n?2) or (4n/3)×(2n/3) integer grid. In this paper we show that if a planar graph G has a balanced partition then G has a grid drawing with small grid area. More precisely, if a separation pair bipartitions G into two edge-disjoint subgraphs G ₁ and?G ₂, then G has a max?{n ₁,n ₂}×max?{n ₁,n ₂} grid drawing, where n ₁ and n ₂ are the numbers of vertices in G ₁ and?G ₂, respectively. In particular, we show that every series-parallel graph G has a (2n/3)×(2n/3) grid drawing and a grid drawing with area smaller than 0.3941n ² (<(2/3)² n ²).     

On the leximin and utilitarian overtaking criteria with extended anonymity

We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S{\mathcal{S}}-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S{\mathcal{S}}-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S{\mathcal{S}}-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.     

General upper bound for the number of blocks having a given number of treatments common with a given block

The purpose of this paper is systematically to derive the general upper bound for the number of blocks having a given number of treatments common with a given block of certain incomplete block designs. The approach adopted here is based on the spectral decomposition of N′N for the incidence matrix N of a design, where N' is the transpose of the matrix N. This approach will lead us to upper bounds for incomplete block designs, in particular for a large number of partially balanced incomplete block (PBIB) designs, which are not covered with the standard approach (Shah 1964, 1966), Kapadia (1966)) of using well known relations between blocks of the designs and their association schemes. Several results concerning block structure of block designs are also derived from the main theorem. Finally, further generalizations of the main theorem are discussed with some illustrations.     

The Mean Squared Error Optimum Design Criterion for Parameter Estimation in Nonlinear Regression Models

In the context of nonlinear regression models, we propose an optimal experimental design criterion for estimating the parameters that account for the intrinsic and parameter-effects nonlinearity. The optimal design criterion proposed in this article minimizes the determinant of the mean squared error matrix of the parameter estimator that is quadratically approximated using the curvature array. The design criterion reduces to the D-optimal design criterion if there are no intrinsic and parameter-effects nonlinearity in the model, and depends on the scale parameter estimator and on the reparameterization used. Some examples, using a well known nonlinear kinetics model, demonstrate the application of the proposed criterion to nonsequential design of experiments as compared with the D-optimal criterion.