Holistic trajectories: a study of combined employment, housing and family careers by using multiple-sequence analysis

Summary.  Social science applications of sequence analysis have thus far involved the development of a typology on the basis of an analysis of one or two variables which have had a relatively low number of different states. There is a yet unexplored potential for sequence analysis to be applied to a greater number of variables and thereby a much larger state space. The development of a typology of employment experiences, for example, without reference to data on changes in housing, marital and family status is arguably inadequate. The paper demonstrates the use of sequence analysis in the examination of multivariable combinations of status as they change over time and shows that this method can provide insights that are difficult to achieve through other analytic methods. The data that are examined here provide support to intuitive understandings of clusters of common experiences which are both life course specific and related to socio-economic factors. Housing tenure is found to be of key importance in understanding the holistic trajectories that are examined. This suggests that life course trajectories are sharply differentiated by experience of social housing.     

On calculating the fisher information in order statistics

This article gives a simple result for the expression of the Fisher information in order statistics. This result enables us to calculate easily the Fisher information in any set of order statistics whose details have been known to be messy and complicated. We consider here its application in the optimal spacing problem where the exact Fisher information in order statistics has been approximated with the asymptotic information or the reciprocal of the variance of a suitable estimator. This work was supported by Korea Research Foundation Grant(KRF-2000-015-DP0056)     

SHOULD WE ESTIMATE THE PROBABILITY OF CORRECT SELECTION?

Various authors, given k location parameters, have considered lower confidence bounds on (standardized) dserences between the largest and each of the other k - 1 parameters. They have then used these bounds to put lower confidence bounds on the probability of correct selection (PCS) in the same experiment (as was used for finding the lower bounds on differences). It is pointed out that this is an inappropriate inference procedure. Moreover, if the PCS refers to some later experiment it is shown that if a non-trivial confidence bound is possible then it is already possible to conclude, with greater confidence, that correct selection has occurred in the first experiment. The short answer to the question in the title is therefore ‘No’, but this should be qualified in the case of a Bayesian analysis.     

Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?

This article introduces a new model for transaction prices in the presence of market microstructure noise in order to study the properties of the price process on two different time scales, namely, transaction time where prices are sampled with every transaction and tick time where prices are sampled with every price change. Both sampling schemes have been used in the literature on realized variance, but a formal investigation into their properties has been lacking. Our empirical and theoretical results indicate that the return dynamics in transaction time are very different from those in tick time and the choice of sampling scheme can therefore have an important impact on the properties of realized variance. For RV we find that tick time sampling is superior to transaction time sampling in terms of mean-squared-error, especially when the level of noise, number of ticks, or the arrival frequency of efficient price moves is low. Importantly, we show that while the microstructure noise may appear close to IID in transaction time, in tick time it is highly dependent. As a result, bias correction procedures that rely on the noise being independent, can fail in tick time and are better implemented in transaction time.     

A regression-based smoothing spline Monte Carlo algorithm for pricing American options in discrete time

American options in discrete time can be priced by solving optimal stopping problems. This can be done by computing so-called continuation values, which we represent as regression functions defined recursively by using the continuation values of the next time step. We use Monte Carlo to generate data, and then we apply smoothing spline regression estimates to estimate the continuation values from these data. All parameters of the estimate are chosen data dependent. We present results concerning consistency and the estimates’ rate of convergence.     

Uncertain Numbers and Uncertainty in the Selection of Input Distributions—Consequences for a Probabilistic Risk Assessment of Contaminated Land

Risks from exposure to contaminated land are often assessed with the aid of mathematical models. The current probabilistic approach is a considerable improvement on previous deterministic risk assessment practices, in that it attempts to characterize uncertainty and variability. However, some inputs continue to be assigned as precise numbers, while others are characterized as precise probability distributions. Such precision is hard to justify, and we show in this article how rounding errors and distribution assumptions can affect an exposure assessment. The outcome of traditional deterministic point estimates and Monte Carlo simulations were compared to probability bounds analyses. Assigning all scalars as imprecise numbers (intervals prescribed by significant digits) added uncertainty to the deterministic point estimate of about one order of magnitude. Similarly, representing probability distributions as probability boxes added several orders of magnitude to the uncertainty of the probabilistic estimate. This indicates that the size of the uncertainty in such assessments is actually much greater than currently reported. The article suggests that full disclosure of the uncertainty may facilitate decision making in opening up a negotiation window. In the risk analysis process, it is also an ethical obligation to clarify the boundary between the scientific and social domains.     

Sample selection in radiocarbon dating

Archaeologists working on the island of O'ahu, Hawai'i, use radiocarbon dating of samples of organic matter found trapped in fish-pond sediments to help them to learn about the chronology of the construction and use of the aquicultural systems created by the Polynesians. At one particular site, Loko Kuwili, 25 organic samples were obtained and funds were available to date an initial nine. However, on calibration to the calendar scale, the radiocarbon determinations provided date estimates that had very large variances. As a result, major issues of chronology remained unresolved and the archaeologists were faced with the prospect of another expensive programme of radiocarbon dating. This paper presents results of research that tackles the problems associated with selecting samples from those which are still available. Building on considerable recent research that utilizes Markov chain Monte Carlo methods to aid archaeologists in their radiocarbon calibration and interpretation, we adopt the standard Bayesian framework of risk functions, which allows us to assess the optimal samples to be sent for dating. Although rather computer intensive, our algorithms are simple to implement within the Bayesian radiocarbon framework that is already in place and produce results that are capable of direct interpretation by the archaeologists. By dating just three more samples from Loko Kuwili the expected variance on the date of greatest interest could be substantially reduced.     

One-dimensional optimal bounded-shape partitions for Schur convex sum objective functions

Consider the problem of partitioning n nonnegative numbers into p parts, where part i can be assigned n_i numbers with n_i lying in a given range. The goal is to maximize a Schur convex function F whose ith argument is the sum of numbers assigned to part i. The shape of a partition is the vector consisting of the sizes of its parts, further, a shape (without referring to a particular partition) is a vector of nonnegative integers (n₁,..., n_p) which sum to n. A partition is called size-consecutive if there is a ranking of the parts which is consistent with their sizes, and all elements in a higher-ranked part exceed all elements in the lower-ranked part. We demonstrate that one can restrict attention to size-consecutive partitions with shapes that are nonmajorized, we study these shapes, bound their numbers and develop algorithms to enumerate them. Our study extends the analysis of a previous paper by Hwang and Rothblum which discussed the above problem assuming the existence of a majorizing shape. This research is partially supported by ROC National Science grant NSC 92-2115-M-009-014.     

Layouts for ocean wave energy farms: Models,properties, and optimization

Renewable energy, such as wave energy, plays a significant role in sustainable energy development. Wave energy represents a large untapped source of energy worldwide and potentially offers a vast source of sustainable energy. We present models and a heuristic algorithm for choosing optimal locations of wave energy conversion (WEC) devices within an array, or wave farm. The location problem can have a significant impact on the total power of the farm due to the interactions among the incident ocean waves and the scattered and radiated waves produced by the WECs. Depending on the nature of the interference (constructive or destructive) among these waves, the wave energy entering multiple devices, and thus the power output of the farm, may be significantly larger or smaller than the energy that would be seen if the devices were operating in isolation. Our algorithm chooses WEC locations to maximize the performance of a wave farm as measured by a well known performance measure called the q-factor, which is the ratio of the power from an array of N WECs to the power from N WECs operating independently, under the point absorber approximation. We prove an analytical optimal solution for the 2-WEC problem and, based on the properties of the 2-WEC solution, we propose an iterative heuristic optimization algorithm for the general problem.