Random field models in image analysis*

Image models are useful in quantitatively specifying natural constraints and general assumptions about the physical world and the imaging process. This review paper explains how Gibbs and Markov random field models provide a unifying theme for many contemporary problems in image analysis. Random field models permit the introduction of spatial context into pixel labeling problems, such as segmentation and restoration. Random field models also describe textured images and lead to algorithms for generating textured images, classifying textures and segmenting textured images. In spite of some impressive model-based image restoration and texture segmentation results reported in the literature, a number of fundamental issues remain unexplored, such as the specification of MRF models, modeling noise processes, performance evaluation, parameter estimation, the phase transition phenomenon and the comparative analysis of alternative procedures. The literature of random field models is filled with great promise, but a better mathematical understanding of these issues is needed as well as efficient algorithms for applications. These issues need to be resolved before random field models will be widely accepted as general tools in the image-processing community.     

Recent trends in mortality in Australia—an analysis of the causes of death through the application of life table techniques

The paper examines the post-1971 reduction in Australian mortality in light of data on causes of death. Multiple-decrement life tables for eleven leading causes of death by sex are calculated and the incidence of each cause of death is presented in terms of the values of the life table functions. The study found that in the overall decline in mortality over the last 20 years significant changes occurred in the contribution of the various causes to total mortality. Among the three leading causes of death, heart disease, malignant neoplasms (cancer), and cerebrovascular disease (stroke), mortality rates due to neoplasms increased and those of the other two causes decreased. The sex-age-cause-specific incidence of mortality changed and the median age at death increased for all causes except for deaths due to motor-vehicle accidents for both sexes and suicide for males. The paper also deciphers the gains in the expectation of life at birth over various time periods and the sex-differentials in the expectation of life at birth at a point in time in terms of the contributions made by the various sex-age-cause-specific mortality rates.     

Random field models in image analysis

Image models are useful in quantitatively specifying natural constraints and general assumptions about the physical world and the imaging process. This review paper explains how Gibbs and Markov random field models provide a unifying theme for many contemporary problems in image analysis. Random field models permit the introduction of spatial context into pixel labeling problems, such as segmentation and restoration. Random field models also describe textured images and lead to algorithms for generating textured images, classifying textures, and segmenting textured images. In spite of some impressive model-based image restoration and texture segmentation results reported in the literature, a number of fundamental issues remain unexplored, such as the specification of MRF models, modeling noise processes, performance evaluation, parameter estimation, the phase transition phenomenon, and the comparative analysis of alternative procedures. The literature of random field models is filled with great promise, but a better mathematical understanding of these issues is needed as well as efficient algorithms for applications. These issues need to be resolved before random field models will be widely accepted as general tools in the image processing community.     

Meta-analysis of Proportions of Rare Events–A Comparison of Exact Likelihood Methods with Robust Variance Estimation

The conventional random effects model for meta-analysis of proportions approximates within-study variation using a normal distribution. Due to potential approximation bias, particularly for the estimation of rare events such as some adverse drug reactions, the conventional method is considered inferior to the exact methods based on binomial distributions. In this article, we compare two existing exact approaches—beta binomial (B-B) and normal-binomial (N-B)—through an extensive simulation study with focus on the case of rare events that are commonly encountered in medical research. In addition, we implement the empirical (“sandwich”) estimator of variance into the two models to improve the robustness of the statistical inferences. To our knowledge, it is the first such application of sandwich estimator of variance to meta-analysis of proportions. The simulation study shows that the B-B approach tends to have substantially smaller bias and mean squared error than N-B for rare events with occurrences under 5%, while N-B outperforms B-B for relatively common events. Use of the sandwich estimator of variance improves the precision of estimation for both models. We illustrate the two approaches by applying them to two published meta-analysis from the fields of orthopedic surgery and prevention of adverse drug reactions.     

Socio-economic correlates of fecundability in a sample of taiwanese women

Estimates of fecundability (monthly probability of conception) in the absence of contraception are derived from the frequency distribution of conceptive delays immediately following marriage, reported by 2,443 married women aged 20 to 39 included in the Taichung (Taiwan) Intensive Fertility Survey of 1962. Average fecundability of women is positively associated with their socio-economic status. These differentials are not accounted for by differences among socio-economic groups with respect to memory and truncation biases (associated with the marriage duration), wife’s age at marriage, or unreported premarital conceptions. A Multiple Classification Analysis suggests that among the socio-economic characteristics, husband’s education, rural background, and modern family type are the more important predictors of fecundability. The importance of genetic factors as opposed to cultural factors in producing these socio-economic differences in fecundability can not be evaluated systematically. Moreover, the relation of a couple’s privacy, their attitude toward family building, and patterns of mate selection to their socioeconomic status would have to be taken into account before the differences in fecundability could be attributed to factors such as nutrition, health, or infections which might directly influence their physiological ability to conceive.     

Mortality in Ghana: Evidence from the cape coast project data

Abstract This paper deals with the estimation of mortality for a rural community of about 20,000 persons in the rain-forest area of south-west Ghana. Specifically, infant, child and adult mortality estimates have been obtained by the application of a wide range of direct and indirect methods of measuring mortality from the different statistics collected by a longitudinal mortality and fertility project conducted during 1974-7. It was noted that infant and childhood mortality rates obtained from death registrations were consistent with those rates yielded by pregnancy histories and child survival statistics. However, the adult mortality estimates derived from orphanhood statistics tended to be lower than those suggested by death registrations. The analysis revealed an infant mortality rate of 100 for boys and 84 for girls, equal childhood mortality rates for boys and girls (85-6), a lower expectation of life at birth for men (45.8 years) than for women (52.8), and a much more severe incidence of mortality among men aged over 40 than for women at the corresponding ages.     

Net delay of next conception by contraception: A highly simplified case

Abstract A probability model, building on the work of Perrin and Sheps, is presented and applied. The model makes it possible to follow a cohort of women from a pregnancy outcome to next conception. Principal simplifying assumptions are homogeneity among women and constant fecundity. Cases treated include no contraception; a single contraceptive method practised; and a second contraceptive method practised following a first one. Expected durations to next conception may be calculated in relation to the following factors: outcome of previous pregnancy, length of anovulation, natural fecundability, time first contraceptive method is initiated, characteristics of first contraceptive (effectiveness and continuation rate), characteristics of second contraceptive, and gap between termination of first and commencing second contraceptive. By suitably pairing runs of the model, one can construct experiments in which the only differentiating factor is use and non-use of a specified contraceptive, and, by differencing the corresponding mean durations to next conception, compute the net delay of next conception produced by that contraceptive.     

Distributed Development and Product Line Decisions

Distributed product development is becoming increasingly prevalent in a number of industries. We study how the global distribution of product development impacts the profit‐maximizing product line that a firm offers. Specifically, we formulate a model to understand the linkage between cost arbitrage as a driver of distributed development and consequent market implications such as customer perceived quality loss to remotely developed products. Analysis of the model reveals that a firm should expand the product line for a development‐intensive good only at intermediate values of cost advantage and quality loss. We modify the base model to include development capacity constraints as a driver of distributed development and find that the results are robust to this change. Our analysis affirms the need for product managers to incorporate the implications of distributed development in making their product line design decision.     

Comparison of confidence intervals of traffic intensity forM/E k/1 queueing systems

This paper compares the width of confidence intervals for the traffic intensity inM/E _k/1 queueing systems with three methods-Lilliefors' method, a second method based on the number of arrivals during the service period, and a third method using censored observations, in which only those service periods with no arrivals are observed. It is shown that the width of confidence intervals, based on the number of arrivals during the service period, is narrower than for other methods.     

Demographic aspects of lactation and postpartum amenorrhea

Interrelations between lactation and post-partum amenorrhea are studied from the reports of about 5,000 married women included in a 1966 Follow-up Survey of Acceptors of an Intrauterine Device (IUD) in Taiwan. The length of post-partum amenorrhea and of breastfeeding are positively associated. On an average, breastfeeding delayed the resumption of menstruation by about 7 months. The association between lactation and amenorrhea is not accounted for by differences in mother’s age, parity, education and her place of residence. A multiple regression analysis suggests that (1) age affects amenorrhea both directly and through lactation, (2) parity has no independent effect on either lactation or amenorrhea, and (3) education and place of residence affect amenorrhea mainly through the cultural variations in the practice of breastfeeding.