A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

Effects of sampling opportunities on preference for adults with severe disabilities

A variable that appears to affect preference development is the exposure to a variety of options. Providing opportunities for systematically sampling different options is one procedure that can facilitate the development of preference, which is indicated by the consistency of selections. The purpose of this study was to evaluate the effects of providing sampling opportunities on the preference development for two adults with severe disabilities. Opportunities for sampling a variety of drink items were presented, followed by choice opportunities for selections at the site where sampling occurred and at a non-sampling site (a grocery store). Results show that the participants developed a definite response consistency in selections at both sites. Implications for sampling practices are discussed.

Chest pain in the dental surgery: A brief review and practical points in diagnosis and management

If a dental patient develops chest pain it must always be managed promptly and properly, i.e., the practitioner immediately stops the procedure and, being aware of the patients's medical history, questions the patient regarding the nature of the pain to help determine the likely diagnosis. It will most likely be a manifestation of coronary artery disease (synonymous with ischaemic heart disease), i.e., angina pectoris or acute myocardial infarction, most usually the former. Angina will usually resolve with proper intervention whereas up to about one-half of myocardial infarction cases will develop cardiac arrest, mostly in the first few hours, and this will be fatal in up to two-thirds of cases. As health care professions, dental practitioners have an inherent duty of care to be able to initiate appropriate care if such a medical emergency occurs.

Low-density koala (Phascolarctos cinereus) populations in the mulgalands of south-west Queensland. I. Faecal pellet sampling protocol

Koala (Phascolarctos cinereus) populations in eastern Australia are threatened by land clearing for agricultural and urban development. At the same time, conservation efforts are hindered by a dearth of information about inland populations. Faecal deposits offer a source of information that is readily available and easily collected non-invasively. We detail a faecal pellet sampling protocol that was developed for use in a large rangeland biogeographic region. The method samples trees in belt transects, uses a thorough search at the tree base to quickly identify trees with koala pellets under them, then estimates the abundance of faecal pellets under those trees using 1-m(2) quadrats. There was a strong linear relationship between these estimates and a complete enumeration of pellet abundance under the same trees. We evaluated the accuracy of our method in detecting trees where pellets were present by means of a misclassification index that was weighed more heavily for missed trees that had high numbers of pellets under them. This showed acceptable accuracy in all landforms except riverine, where some trees with large numbers of pellets were missed. Here, accuracy in detecting pellet presence was improved by sampling with quadrats, rather than basal searches. Finally, we developed a method to reliably age pellets and demonstrate how this protocol could be used with the faecal-standing-crop method to derive a regional estimate of absolute koala abundance.

The number of rational points of a class of Artin-Schreier curves

We determine the number of F-q-rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound. (C) 2002 Elsevier Science (USA).

Two-dimensional balanced sampling plans excluding contiguous units

A balanced sampling plan excluding contiguous units (or BSEC for short) was first introduced by Hedayat, Rao and Stufken in 1988. These designs can be used for survey sampling when the units are arranged in one-dimensional ordering and the contiguous units in this ordering provide similar information. In this paper, we generalize the concept of a BSEC to the two-dimensional situation and give constructions of two-dimensional BSECs with block size 3. The existence problem is completely solved in the case where lambda = 1.

Monitoring the composition and form of urban environments based on the vegetation-impervious surface-soil (VIS) model by sub-pixel analysis techniques

The majority of the world's population now resides in urban environments and information on the internal composition and dynamics of these environments is essential to enable preservation of certain standards of living. Remotely sensed data, especially the global coverage of moderate spatial resolution satellites such as Landsat, Indian Resource Satellite and Systeme Pour I'Observation de la Terre (SPOT), offer a highly useful data source for mapping the composition of these cities and examining their changes over time. The utility and range of applications for remotely sensed data in urban environments could be improved with a more appropriate conceptual model relating urban environments to the sampling resolutions of imaging sensors and processing routines. Hence, the aim of this work was to take the Vegetation-Impervious surface-Soil (VIS) model of urban composition and match it with the most appropriate image processing methodology to deliver information on VIS composition for urban environments. Several approaches were evaluated for mapping the urban composition of Brisbane city (south-cast Queensland, Australia) using Landsat 5 Thematic Mapper data and 1:5000 aerial photographs. The methods evaluated were: image classification; interpretation of aerial photographs; and constrained linear mixture analysis. Over 900 reference sample points on four transects were extracted from the aerial photographs and used as a basis to check output of the classification and mixture analysis. Distinctive zonations of VIS related to urban composition were found in the per-pixel classification and aggregated air-photo interpretation; however, significant spectral confusion also resulted between classes. In contrast, the VIS fraction images produced from the mixture analysis enabled distinctive densities of commercial, industrial and residential zones within the city to be clearly defined, based on their relative amount of vegetation cover. The soil fraction image served as an index for areas being (re)developed. The logical match of a low (L)-resolution, spectral mixture analysis approach with the moderate spatial resolution image data, ensured the processing model matched the spectrally heterogeneous nature of the urban environments at the scale of Landsat Thematic Mapper data.

Empirical evidence for ultrametric structure in multi-layer perceptron error surfaces

Combinatorial optimization problems share an interesting property with spin glass systems in that their state spaces can exhibit ultrametric structure. We use sampling methods to analyse the error surfaces of feedforward multi-layer perceptron neural networks learning encoder problems. The third order statistics of these points of attraction are examined and found to be arranged in a highly ultrametric way. This is a unique result for a finite, continuous parameter space. The implications of this result are discussed.

Evaluation of line-transect sampling for estimating koala abundance in the Pine Rivers Shire, south-east Queensland

Distance sampling using line transects has not been previously used or tested for estimating koala abundance. In July 2001, a pilot survey was conducted to compare the use of line transects with strip transects for estimating koala abundance. Both methods provided a similar estimate of density. On the basis of the results of the pilot survey, the distribution and abundance of koalas in the Pine Rivers Shire, south-east Queensland, was determined using line-transect sampling. In total, 134 lines (length 64 km) were used to sample bushland areas. Eighty-two independent koalas were sighted. Analysis of the frequency distribution of sighting distances using the software program DISTANCE enabled a global detection function to be estimated for survey sites in bushland areas across the Shire. Abundance in urban parts of the Shire was estimated from densities obtained from total counts at eight urban sites that ranged from 26 to 51 ha in size. Koala abundance in the Pine Rivers Shire was estimated at 4584 (95% confidence interval, 4040-5247). Line-transect sampling is a useful method for estimating koala abundance provided experienced koala observers are used when conducting surveys.

More on exact bicoverings of 12 points

The minimum number of incomplete blocks required to cover, exactly lambda times, all t-element subsets from a set V of cardinality v (v > t) is denoted by y(lambda, t; v). The value of g(2, 2; v) is known for v = 3, 4,..., 11. It was previously known that 14 less than or equal to g(2, 2; 12) less than or equal to 16. We prove that g(2, 2; 12) greater than or equal to 15.