Improved bridge constructs for stochastic differential equations

We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an Itô stochastic differential equation conditional on an observation taken at a fixed future time-point. Such realisations are typically termed diffusion bridges. Since, in general, no closed form expression exists for the transition densities of the process of interest, a widely adopted solution works with the Euler–Maruyama approximation, by replacing the intractable transition densities with Gaussian approximations. However, the density of the conditioned discrete-time process remains intractable, necessitating the use of computationally intensive methods such as Markov chain Monte Carlo. Designing an efficient proposal mechanism which can be applied to a noisy and partially observed system that exhibits nonlinear dynamics is a challenging problem, and is the focus of this paper. By partitioning the process into two parts, one that accounts for nonlinear dynamics in a deterministic way, and another as a residual stochastic process, we develop a class of novel constructs that bridge the residual process via a linear approximation. In addition, we adapt a recently proposed construct to a partial and noisy observation regime. We compare the performance of each new construct with a number of existing approaches, using three applications.     

Estimating large-scale general linear and seemingly unrelated regressions models after deleting observations

A new numerical method to solve the downdating problem (and variants thereof), namely removing the effect of some observations from the generalized least squares (GLS) estimator of the general linear model (GLM) after it has been estimated, is extensively investigated. It is verified that the solution of the downdated least squares problem can be obtained from the estimation of an equivalent GLM, where the original model is updated with the imaginary deleted observations. This updated GLM has a non positive definite dispersion matrix which comprises complex covariance values and it is proved herein to yield the same normal equations as the downdated model. Additionally, the problem of deleting observations from the seemingly unrelated regressions model is addressed, demonstrating the direct applicability of this method to other multivariate linear models. The algorithms which implement the novel downdating method utilize efficiently the previous computations from the estimation of the original model. As a result, the computational cost is significantly reduced. This shows the great usability potential of the downdating method in computationally intensive problems. The downdating algorithms have been applied to real and synthetic data to illustrate their efficiency.     

Racial/Ethnic Disparities in Mental Health Service Use for Older Foster Youth and Foster Care Alumni

Studies have shown that foster care alumni have disproportionally high rates of poor mental health outcomes compared to the general population. The purpose of this study was to examine differences in mental health service use for Latino, African American, and White youth while in foster care and upon exit from the foster care system. Secondary data were used to identify youth 1 year prior to exiting the foster care system (N?=?934) and 1 year after exit from the foster care system (N?=?433). Racial/ethnic disparities in mental health service use upon exit from the foster care system were found, with Latino youth using the least amount of services after foster care exit. Racial/ethnic service disparities in type of services used were also found. Findings suggest that a lack of support (e.g., mandatory or voluntary) may be significant in overcoming challenges in the continuation or disruption of services.     

Are Daughters Like Mothers: Evidence on Intergenerational Educational Mobility Among Young Females in India

Taking data from the ‘India Youth Survey: Situation and Needs’ the paper examines intergenerational educational mobility for young females (vis-à-vis their mothers) in India. The paper uses transition/mobility matrices and mobility measures widely used in the literature on intergenerational mobility for the examination. The overall intergenerational educational mobility among the young females in India is about 0.69 (the upper limit being 1). The upwards component of the overall intergenerational educational mobility is 0.55 (that is, nearly four-fifth of the overall). Also, the intergenerational educational mobility is slightly higher in the ‘Scheduled Castes and Tribes (SC/ST)’ compared to the ‘Other Backward Castes (OBC)’ as well as ‘Others’ castes. But the upward mobility is substantially higher in the ‘Others’ caste group compared to SC/STs. The upward mobility among the OBCs is higher than that of SC/STs but lower than that of the ‘Others’ category. Also, the overall mobility as well as upward mobility is higher in urban areas. Moreover, there are large inter-state variations with the economically and demographically poorer states having substantially lower overall as well as upward mobility than the economically and demographically advanced states.     

Households,Families and Prospective Economic Mobility in Mexico

The study analyzed poverty as a function of households’ demographic composition using a longitudinal random sample of 4268 urban and rural households that were followed-up from 2005/6 to 2009/12 in Mexico to estimate short-term changes in living conditions. Well-being was measured as the dwelling unit’s number of rooms, water source, sanitary services, garbage disposal, and fuel. Mobility paths included not poor–not poor, poor–poor, not poor–poor, and poor–not poor. Independent variables included household composition, family characteristics, residential changes, schooling, and occupation. Female headship and older adults negatively impacted poverty, whereas economic dependents may be negatively or positively associated. Fertility incentives for low-income populations are not advisable. Working-age adults contribute only if income-generating opportunities exist locally.     

A hierarchical model for ordinal matrix factorization

This paper proposes a hierarchical probabilistic model for ordinal matrix factorization. Unlike previous approaches, we model the ordinal nature of the data and take a principled approach to incorporating priors for the hidden variables. Two algorithms are presented for inference, one based on Gibbs sampling and one based on variational Bayes. Importantly, these algorithms may be implemented in the factorization of very large matrices with missing entries.     

Ex Ante Project Evaluation and the Complexity of Early Decision-Making

This paper looks beyond more traditional evaluation activities to focus primarily on evaluation up front. It suggests that the early appraisal of an investment case or a project should apply essentially the same evaluation criteria that will be used in ex post evaluation, and thus increase the likelihood of a successful project outcome. However, the initial plan might be altered as result of subsequent analysis, assessment, negotiation, positioning, and the exercise of power. The last part of this paper presents an empirical study of 23 projects, which examines the complexity of processes that occur in the idea- and decision phases.     

Is diversity in capabilities desirable when adding decision makers?

When the benefit of making a correct decision is sufficiently high, even a slight increase in the probability of making such a decision justifies an increase in the number of decision makers. Applying a standard uncertain dichotomous choice benchmark setting, this study focuses on the relative desirability of two alternatives: adding individuals with capabilities identical to the existing ones and adding identical individuals with mean-preserving capabilities that depend on the states of nature. Our main result establishes that when the group applies the simple majority rule, variability in the capabilities of the new decision makers under the two states of nature, which is commonly observed in various decision-making settings, is less desirable in terms of the probability of making the correct decision.