Travel-Time Constraints on Destination-Choice Sets

The importance of travel-time constraints in spatial choice is widely recognized in the literature of geography and related disciplines, but little work has been done toward developing operational models of spatial choice wherein these constraints and their effects are made explicit. The purpose of the paper is to test the accuracy of predictions produced by a destination choice model that does not take explicit account of travel constraints under the assumption that observed choices are made from choice sets delineated by a constraint of maximum travel time. Observed choices are generated by simulation from a new random utility model consistent with the constrained nature of individual choice sets. Results show that the characteristics of constraints are a decisive factor in the accuracy of the unconstrained choice model. Choice probabilities of the constrained reality are predicted with a reasonably good accuracy in some instances, but predictions are less impressive, and even poor, in many others.     

Calibration and Test of a Discrete Choice Model with Endogenous Choice Sets

Conventional discrete choice models assume implicitly that the choice set is independent of the decisionmaker's preferences conditional on the explanatory variables of the models. This assumption is implausible in many choice situations where the decisionmaker selects his or her choice set. This paper estimates and tests a discrete choice model with endogenous choice sets based on Horowitz' theoretical work. To calibrate the model, a new probability simulator is introduced and a sequential estimation procedure is developed. The model and calibration methods are tested in an empirical application as well as Monte Carlo simulations. The empirical results are used to test the theory of endogenous choice sets and to examine the differences between the new model and a conventional choice model in parameter estimates and predicted choice probabilities. The empirical results strongly suggest that ignoring the endogeneity of choice sets in choice modeling can have serious consequences in applications.     

Probabilistic Seismic Design of Pile Foundations in Non Liquefiable Soil by Response Spectrum Approach

The behavior of pile foundations in non liquefiable soil under seismic loading is considerably influenced by the variability in the soil and seismic design parameters. Hence, probabilistic models for the assessment of seismic pile design are necessary. Deformation of pile foundation in non liquefiable soil is dominated by inertial force from superstructure. The present study considers a pseudo-static approach based on code specified design response spectra. The response of the pile is determined by equivalent cantilever approach. The soil medium is modeled as a one-dimensional random field along the depth. The variability associated with undrained shear strength, design response spectrum ordinate, and superstructure mass is taken into consideration. Monte Carlo simulation technique is adopted to determine the probability of failure and reliability indices based on pile failure modes, namely exceedance of lateral displacement limit and moment capacity. A reliability-based design approach for the free head pile under seismic force is suggested that enables a rational choice of pile design parameters.     

METROPOLITAN OUTMIGRATION PATTERN OF CANADIAN LABOUR FORCE ENTRANTS, 1971–76

This paper analyses the 1971 -76 metropolitan out-migration pattern of Canadian males in the labour force entrance age group. Migration is conceptualized within a three-level choice framework, and statistical inference is based on a multinomial logit model. It was found (1) that the propensity to outmigrate and the destination choice pattern vary substantially among the 23 metropolitan areas; (2) that 83 per cent of the variation in the destination choice probabilities of metropolitanward migrants can be explained by only five variables (log of distance, cultural dissimilarity, temperature, employment growth, and population size); and (3) that housing conditions are essentially the results (rather than the causes) of intermetropolitan migration .     

Establishing discovery probabilities of lithic artefacts in Palaeolithic and Mesolithic sites with core sampling

This paper reports the results of a study into the effectiveness of core sampling for discovering Palaeolithic and Mesolithic hunter-gatherer sites in the Netherlands and northwestern Belgium. Earlier work established optimal sampling strategies for use in archaeological heritage management survey in the Netherlands. However, the statistical model used for this was based on a limited amount of data on the distribution of lithic artefacts in Palaeolithic and Mesolithic sites. For the current study we have analyzed the distribution of artefacts in a selected number of excavated sites, and estimated discovery probabilities of these sites through simulation. The simulation results indicate that discovery probabilities are lower than expected due to the effect of clustering of finds. Furthermore, the density of flints in Palaeolithic and Mesolithic sites is generally lower than the estimates that were used for setting up the optimal sampling strategies, and a substantial number of sites is very small. This means that, in order to discover Palaeolithic and Mesolithic sites with sufficient reliability, we will have to apply more intensive survey strategies than have been recommended up to now.     

Measuring Impacts of Condition Variables in Rule‐Based Models of Space‐Time Choice Behavior: Method and Empirical Illustration

The use of rule‐based systems for modeling space‐time choice has gained increasing research interests over the last years. The potential advantage of the rule‐based approach is that it can handle interactions between a large set of predictors. Decision tree induction methods are available and have been explored for deriving rules from data. However, the complexity of the structures that are generated by such knowledge discovery methods hampers an interpretation of the rule‐set in behavioral terms with as a consequence that the models typically remain a black box. To solve this problem, this paper develops a method for measuring the size and direction of the impact of condition variables on the choice variable as predicted by the model. The paper illustrates the method based on location and transport‐mode choice models that are part of Albatross model—an activity‐based model of space‐time choice.     

DISCRETE SPATIAL CHOICE MODELS FOR AGGREGATE DESTINATIONS*

ABSTRACT. In problems of spatial choice, the choice set is typically more aggregated than the one considered by decision-makers, often because choice data are available only at the aggregate level. These aggregate choice units will exhibit heterogeneity in utility and in size. To be consistent with utility maximization, a choice model must estimate choice probabilities on the basis of the maximum utility within heterogeneous aggregates. The ordinary multinomial logit model applied to aggregate choice units fails this criterion as it is estimated on the basis of average utility. In this paper, we derive and discuss a model which utilizes the theory underlying the nested logit model to estimate the appropriate maximum utilities of aggregates. We also demonstrate that the aggregate alternative error terms are asymptotically Gumbel, thereby relaxing the assumption of extreme value distributed error terms. This is accomplished with help from the asymptotic theory of extremes.     

Modeling post-depositional mixing of archaeological deposits

We develop a series of simple mathematical models that describe vertical mixing of archaeological deposits. The models are based on assigning probabilities that single artifact specimens are moved between discrete stratigraphic layers. A recursion relation is then introduced to describe the time evolution of mixing. Simulations are used to show that there may be important regularities that characterize the mixing of archaeological deposits including stages of dissipation, accumulation and equilibration. We discuss the impact of post-depositional mixing on the apparent occupation intensities at modeled stratified archaeological sites. The models may also help clarify some of the problems inherent in making general inferences about the nature culture change based on mixed archaeological deposits. We demonstrate the modeling approach by developing a post-depositional mixing model for the Barger Gulch Folsom site.     

REAL-TIME RISK ANALYSIS FOR HYBRID EARTHQUAKE EARLY WARNING SYSTEMS

Earthquake Early Warning Systems (EEWS), based on real-time prediction of ground motion or structural response measures, may play a role in reducing vulnerability and/or exposition of buildings and lifelines. In fact, recently seismologists developed efficient methods for rapid estimation of event features by means of limited information of the P-waves. Then, when an event is occurring, probabilistic distributions of magnitude and source-to-site distance are available and the prediction of the ground motion at the site, conditioned to the seismic network measures, may be performed in analogy with the Probabilistic Seismic Hazard Analysis (PSHA). Consequently the structural performance may be obtained by the Probabilistic Seismic Demand Analysis (PSDA), and used for real-time risk management purposes. However, such prediction is performed in very uncertain conditions which have to be taken into proper account to limit false and missed alarms. In the present study, real-time risk analysis for early warning purposes is discussed. The magnitude estimation is performed via the Bayesian approach, while the earthquake localization is based on the Voronoi cells. To test the procedure it was applied, by simulation, to the EEWS under development in the Campanian region (southern Italy). The results lead to the conclusion that the PSHA, conditioned to the EEWS, correctly predicts the hazard at the site and that the false/missed alarm probabilities may be controlled by set up of an appropriate decisional rule and alarm threshold.     

Housing Choice in a Regulated Market: A Nested Multinomial Logit Analysis

The paper integrates several important elements of the institutionalized and regulated nature of the housing market and analyzes the relationship between household type and housing choice in Vienna within a nested multinomial logit framework. In particular, the concept of household specific choice sets is used to account for institutional, informational and income-based constraints of the choice process. Government subsidies (such as housing and rent allowances, non-interest-bearing state loans) are explicitly taken into account in the definition of variables. Housing choice is considered in three stages: the choice of a dwelling unit given dwelling type and residential zone, the choice of a dwelling type given residential zone, and the marginal choice of a residential zone. The coefficients are derived by means of a sequential ML-procedure. The empirical results clearly indicate that demographic variables have significant impacts on housing choice behavior. Income as a single explanatory variable as well as its interacting with size measures and the quality of the house are found to be important criteria for dwelling unit choice, as housing cost variables for dwelling type choice behavior. The dwelling unit and dwelling type choice submodels fit reasonably well, whereas the residential zone model is less successful.     

An Area‐Based Approach for Estimating Extreme Precipitation Probability

Accurate estimates of heavy rainfall probabilities reduce loss of life, property, and infrastructure failure resulting from flooding. NOAA's Atlas‐14 provides point‐based precipitation exceedance probability estimates for a range of durations and recurrence intervals. While it has been used as an engineering reference, Atlas‐14 does not provide direct estimates of areal rainfall totals which provide a better predictor of flooding that leads to infrastructure failure, and more relevant input for storm water or hydrologic modeling. This study produces heavy precipitation exceedance probability estimates based on basin‐level precipitation totals. We adapted a Generalized Extreme Value distribution to estimate Intensity‐Duration‐Frequency curves from annual maximum totals. The method exploits a high‐resolution precipitation data set and uses a bootstrapping approach to borrow spatially across homogeneous regions, substituting space in lieu of long‐time series. We compared area‐based estimates of 1‐, 2‐, and 4‐day annual maximum total probabilities against point‐based estimates at rain gauges within watersheds impacted by five recent extraordinary precipitation and flooding events. We found considerable differences between point‐based and area‐based estimates. It suggests that caveats are needed when using pointed‐based estimates to represent areal estimates as model inputs for the purpose of storm water management and flood risk assessment.     

Allowing Traffic Over Mainshock-Damaged Bridges

A criterion is proposed for deciding whether, after a damaging mainshock, a bridge can still be open for either emergency or ordinary traffic. The criterion is based on the comparison between the collapse risk of the mainshock-damaged structure and the pre-mainshock risk of the intact structure. The approach requires fragilities for multiple damage states for the intact structure, and transition probabilities from these states to collapse for the damaged structure. The aftershock risk decreases with time, hence a decision for reopening might have to wait until the risk level goes down to an acceptable value. A realistic application demonstrates the approach.     

Teaching mathematics in geography degrees: Motivation,necessities and approach

Abstract

Within the constraints of viewing geography as an applied discipline with a large number of arts‐based students, the primary problem of teaching mathematics in a geography degree is argued to be one of contending the motivation for a symbolic and analytical approach. This paper explores ways in which motivation for mathematics can be impressed on students and then discusses those areas of mathematics necessary in geography. The final section explores an applied approach to mathematics teaching based on the concept of systems.     

MIRACLES, HISTORICAL TESTIMONIES, AND PROBABILITIES

The topic and methods of David Hume's “Of Miracles” resemble his historiographical more than his philosophical works. Unfortunately, Hume and his critics and apologists have shared the pre‐scientific, indeed a historical, limitations of Hume's original historical investigations. I demonstrate the advantages of the critical methodological approach to testimonies, developed initially by German biblical critics in the late eighteenth century, to a priori discussions of miracles. Any future discussion of miracles and Hume must use the critical method to improve the quality and relevance of the debate. Hume's definition of miracles as breaking the laws of nature is anachronistic. The concept of immutable laws of nature was introduced only in the seventeenth century, thousands of years after the Hebrews had introduced the concept of miracles. Holder and Earman distinguish the posterior probability of the occurrence of a particular miracle from that of the occurrence of some miracle. I argue that though this distinction is significant, their formulae for evaluating the respective probabilities are not useful. Even if miracle hypotheses have low probabilities, it may still be rational to accept and use them if there is no better explanation for the evidence of miracles. Biblical critics and historians do not examine the probabilities of miracle hypotheses, or any other hypotheses about the past, in isolation, but in comparison with competing hypotheses that attempt to better explain, increase the likelihood of a broader scope of evidence, as well as be more fruitful. The fruitful and simple theories of Hume's later and better contemporaries, the founders of biblical criticism, offer the best explanation of the broadest scope of evidence of miracles. Moreover, they do so by being linguistically sensitive to the ways “miracle” was actually used by those who claimed to have observed them. The lessons of this analysis for historians and philosophers of history—that the acceptance of historical hypotheses is a comparative endeavor, and that the claims of those in the past must be assessed in their own terms—ought to be clear.     

A Statistical Method for the Detection of Geographic Clustering

Kernel‐based, smoothed estimates of spatial variables are useful in exploratory analyses because they yield a clear visual image of geographic variability in the underlying variable. In this paper I suggest an approach for assessing the significance of peaks in the surface that result from the application of the smoothing kernel. The approach may also be thought of as a method for assessing the maximum among a set of suitably defined local statistics. Local statistics for data on a regular grid of cells are first defined by using a Gaussian kernel. Results from integral geometry are then used to find the probability that the maximum local statistic (M) exceeds a given critical value (M). Approximations are provided that make implementation of the approach straightforward. Future work will address several other issues associated with local statistics that have been defined in this way, including edge effects, and the effects of global spatial autocorrelation on the choice of critical value.     

A Micro-Econometric Store Choice Model Incorporating Multi- and Omni-Channel Shopping: The Case of Furniture Retailing in Germany

Online retailing and multi-/omni-channel shopping are gaining in importance. However, there is a significant lack of research focused on incorporating online shopping into models of spatial shopping behavior. The present study aims (1) to construct a store choice model which includes both physical and online stores as well as the opportunity for omni-channel shopping, and (2) to identify the main drivers of spatial shopping behavior given the availability of both channels. Based on a representative survey, this study employs a revealed-preference approach toward store choice and expenditures in furniture retailing. The statistical analysis is performed using a hurdle model approach, with the expenditures of individual consumers at (online or physical) furniture stores serving as the dependent variable. Results show that channel choice (online vs. offline) is mainly influenced by psychographic characteristics, place of residence, and age of the consumers. Store choice and expenditures are primarily explained by store features such as assortment size, omni-channel integration, and accessibility. This study demonstrates that e-shopping can be integrated into a store choice model and that both the modeling approach and the subsequent findings are of significance for retail companies and spatial planning.     

The prey as patch model: optimal handling of resources with diminishing returns

Foraging theory provides archaeology with a valuable set of tools for investigating the constraints that influenced procurement decisions of the past. The prey-choice model has been used extensively by archaeologists, but has significant limitations given the nature of archaeological data. This paper suggests that the seldom-used Marginal Value Theorem (MVT) is a valuable tool for examining the ecological constraints on foraging decisions and merits further archaeological application. Ethnoarchaeological and experimental cases are presented demonstrating how patch–gains curves can be generated from quantitative data on butchering return rates and handling times. Results indicate that such curves are diminishing return functions. This provides a basis for examining the linkage between processing intensity and resource fluctuation. This model allows archaeologists to address the relationship between attribute-states of faunal remains and predicted optimal post-acquisition decisions. The MVT is valuable to ethnoarchaeology because it identifies how mean foraging return rate influences the handling of acquired prey and makes quantified predictions of return rate based on processing intensity. The MVT can also be applied to archaeological studies of foraging behavior and processing intensity as it can be used to estimate the set of environmental constraints in which a given kill was made (e.g., “good” vs. “bad” times). This approach may also identify the degree to which certain currencies, such as fat, are optimized at the expense of others, such as total caloric intake.     

Ageing well: the time–spaces of possibility for older female Latvian migrants in the UK

In this article, we explore the relationships between ageing, place and migration based on life history interviews with 37 female Latvian migrants in the UK. Reflecting an approach that sees migration as both embodied and emplaced, we conceptualise ageing and migration as entwined becomings that reconfigure the possibilities of a ‘better life’ in different time–spaces. Our approach combines time-geography with a well-being-based approach to migration constraints and outcomes. Our stress is on vitality – the ways in which migrants are able to mobilise resources and enact agency even in an environment where some aspects of life and working conditions are restrictive and exploitative. Hence, older Latvian women are able to transgress negative perceptions of ageing in their home country and achieve a measure of empowerment, both economic and psychosocial by moving to the UK.     

Contiguity Constraints for Single‐Region Site Search Problems

This paper proposes an explicit set of constraints as a general approach to the contiguity problem in site search modeling. Site search models address the challenging problem of identifying the best area in a study region for a particular land use, given that there are no candidate sites. Criteria that commonly arise in a search include a site's area, suitability, cost, shape, and proximity to surrounding geographic features. An unsolved problem in this modeling arena is the identification of a general set of mathematical programming constraints that can guarantee a contiguous solution (site) for any 0–1 integer‐programming site search formulation. The constraints proposed herein address this problem, and we evaluate their efficacy and efficiency in the context of a regular and irregular tessellation of geographic space. An especially efficient constraint form is derived from a more general form and similarly evaluated. The results demonstrate that the proposed constraints represent a viable, general approach to the contiguity problem.