Assessing Quality of Spatial Models Using the Structural Similarity Index and Posterior Predictive Checks

Model assessment is one of the most important aspects of statistical analysis. In geographical analysis, models represent spatial processes, where variability in mapped output results from uncertainty in parameter estimates. Slight spatial misalignments can cause inflated error scores when comparing maps of observed and predicted variables using traditional error metrics at the level of individual spatial units. We conceptualize spatial model assessment as a continuous value map comparison problem and employ methods from image analysis to score model outputs. The structural similarity index, a measure that attempts to replicate the human visual system using a local region approach, is used as an exploratory map comparison statistic. The measure is implemented within a Bayesian spatial modeling framework as a discrepancy measure in a posterior predictive check of model fit. Results are reported for simulation studies representing a variety of spatial processes in a spatial and space–time context. A case study of rainfall mapping in Sri Lanka demonstrates the proposed methodology applied to assessment of Bayesian kriging interpolations. Both simulation studies as well as the case study demonstrate that the approach reveals hidden spatial structure not uncovered by traditional methods. The spatially sensitive assessment methodology provides a diagnostic tool to support spatial modeling and analysis. La evaluación de modelos es uno de los aspectos más importantes de análisis estadístico. En el análisis geográfico, los modelos representan procesos espaciales en los que la variabilidad en los outputs es el resultado de la incertidumbre en los parámetros estimados. Leves desajustes espaciales pueden inflar los valores de error en la comparación entre los mapas de las observaciones y los mapas de las predicciones de las variables si es que se usan medidas tradicionales de medición de error al nivel de unidades espaciales individuales. Los autores conceptualizan la evaluación de modelos espaciales como un problema de comparación mapas de valor continuo y emplea métodos de análisis de imágenes para cuantificar los resultados del modelo. Se utiliza el índice de similitud estructural (SSIM), una medida que intenta replicar el sistema visual humano utilizando un enfoque de región local, como técnica de exploratoria comparación estadística de mapas. El índice es implementado dentro de un marco de modelización espacial bayesiano como medida de discrepancia en la comprobación posterior de predicción del desempeño del modelo. Los resultados se presentan para varios casos de simulación que representan una serie de procesos espaciales en un contexto espacio‐temporal y espacial. Un estudio de caso de mapeo de lluvias en Sri Lanka sirve como demostración de la metodología propuesta y su aplicación a la evaluación de las interpolaciones tipo krigeage (kriging) bayesianas. Tanto los estudios de simulación, así como el estudio de caso demuestran que el enfoque propuesto revela la estructura espacial oculta no evidenciada por métodos tradicionales. La metodología de evaluación espacialmente sensible que se presenta en este artículo proporciona una herramienta de diagnóstico para apoyar la elaboración de modelos y análisis espacial. 模型评估是统计分析中最为重要的内容之一。在地理分析中用模型表达空间过程,参数估计的不确定性会导致地图输出结果的可变性。当采用传统误差指标度量,在个体空间单位水平上进行观测和预测变量的地图比较时,微小的空间错位就可能导致误差的倍增。为此,本文通过将空间模型评估指标概念化为一个连续值图比较问题,并利用图像分析方法来评定模型输出。一种尝试以局域方法仿制人类视觉系统的度量指标——结构相似指数(SSIM),被用作为探索性地图的比较统计量。在贝叶斯空间模型框架下实现其量算,并将其作为一个偏差度量应用于模型拟合的后预测校验。仿真研究的结果显示出空间及时空环境下多类空间过程。以斯里兰卡降雨过程图为案例,展示了上述方法对贝叶斯克里格插值的准确性评估。仿真研究与实证结果均证明本文提出的方法可揭示以往传统方法掩盖的空间结构特征,空间敏感性评价为本研究的空间建模和分析提供了一个诊断工具。     

Consumer city

Urban economics has traditionally viewed cities as having advantagesin production and disadvantages in consumption. We argue thatthe role of urban density in facilitating consumption is extremelyimportant and understudied. As firms become more mobile, thesuccess of cities hinges more and more on cities' role as centresof consumption. Empirically, we find that high amenity citieshave grown faster than low amenity cities. Urban rents havegone up faster than urban wages, suggesting that the demandfor living in cities has risen for reasons beyond rising wages.The rise of reverse commuting suggests the same consumer cityphenomena.l     

WHAT DO BUSINESS CLIMATE INDEXES TEACH US ABOUT STATE POLICY AND ECONOMIC GROWTH?*

ABSTRACT State business climate indexes capture state policies that might affect economic growth. State rankings in these indexes vary wildly, raising questions about what the indexes measure and which policies are important for growth. Indexes focused on productivity do not predict economic growth, while indexes emphasizing taxes and costs predict growth of employment, wages, and output. Analysis of sub‐indexes of the tax‐and‐cost‐related indexes points to two policy factors associated with faster growth: less spending on welfare and transfer payments; and more uniform and simpler corporate tax structures. But factors beyond the control of policy have a stronger relationship with economic growth.     

Biomolecular archaeology of ancient tuberculosis: response to “Deficiencies and challenges in the study of ancient tuberculosis DNA” by Wilbur et al. (2009)

It is sixteen years since the first detection of Mycobacterium tuberculosis DNA in archaeological specimens, yet the validity of findings continues to be questioned. Rigorous scientific scrutiny and debate is valuable and has led to a coalescence of procedures and precautions amongst those actively engaged in this work. It is disappointing that these good practices are not recognised by certain scientists whose primary expertise is in the related fields of archaeology, palaeopathology, and eukaryote ancient DNA. There is a danger that by constant repetition, disputable and inadequately justified concerns will assume the status of self-perpetuating myths and misunderstandings. We discuss these issues with reference to a recent article in this journal, in which clear peer-reviewed scientific data were specifically targeted as part of a general critique of the field of the palaeomicrobiology of tuberculosis. We believe we have given sufficient evidence and cogent argument to persuade the unbiased reader that the views in the critique by Wilbur et al. are unjustified.     

Paleopathological and Molecular Study on Two Cases of Ancient Childhood Leprosy from the Roman and Byzantine Empires

This study is based on the paleaopathology of leprosy on human skeletal remains and the detection of ancient Mycobacterium leprae DNA. Two cases of childhood leprosy were recognized. The first case was in a Roman necropolis at Martellona (Rome, Central Italy), dated to the 2nd to 3rd centuries ce . The skeleton of a child aged 4–5 years, from tomb 162, is the youngest individual in Italy from this time period, with the clear rhino‐maxillary syndrome and other bony changes indicative of leprosy. The second case from a burial at Kovuklukaya, in the Sinop region of Northern Turkey, was from the 8th to the 10th centuries, during the Byzantine era. The endocranium of a 4–5‐month‐old infant with new bone formation—an indication of chronic inflammation—was positive for M. leprae DNA. Infant and childhood leprosy is uncommon today, and there is a scarcity of information in the osteoarchaeological literature of leprosy in the past, especially in children. The significance of these cases is that it adds to an understanding of the history of the disease in the former Roman Empire. It is hoped that over time sufficient data can be obtained to understand the epidemiological dynamics and clinical evolution of leprosy from the ancient period until today. Copyright © 2012 John Wiley & Sons, Ltd.     

Contextualizing Early Urbanization: Settlement Cores,Early States and Agro-pastoral Strategies in the Fertile Crescent During the Fourth and Third Millennia BC

This paper employs data from selected sample survey areas in the northern Fertile Crescent to demonstrate how initial urbanization developed along several pathways. The first, during the Late Chalcolithic period, was within a dense pattern of rural settlement. There followed a profound shift in settlement pattern that resulted in the formation of large walled or ramparted sites (‘citadel cities’) associated with a more dynamic phase of urbanization exemplified by short cycles of growth and collapse. By the later third millennium BC, the distribution of larger centres had expanded to include the drier agro-pastoral zone of northern and central Syria, termed here the ‘zone of uncertainty’. This configuration, in turn, formed the context for Middle Bronze Age settlement, and the pattern of political rivalries and alliances that typified the second millennium BC. Evidence is marshalled from archaeological surveys and landscape analyses to examine these multiple paths to urbanization from the perspectives of (a) staple production within major agricultural lowlands; (b) the shift towards higher risk animal husbandry within climatically marginal regions; (c) changes in local and inter-regional networks (connectivity); and (d) ties and rights to the land. Textile production forms the core of the proposed model, which emphasizes how the demand for wool and associated pasture lands opened up new landscapes for agro-pastoral production and settlement. The resultant landscapes of settlement are then compared with the picture in the southern Levant where a more restricted zone of uncertainty may have limited the opportunities for agro-pastoral production.     

CHANGES IN THE LOCATION OF EMPLOYMENT AND OWNERSHIP: EVIDENCE FROM CALIFORNIA*

ABSTRACT We use the National Establishment Time‐Series database to describe shifts in the geographic dispersion of employment and ownership of firms. Focusing on data on business establishments in California, and establishments anywhere in the United States that are owned by firms headquartered in California, we find shifts in the operations of businesses headquartered in California to other states. However, this shift has been offset by increased employment in the state by firms headquartered elsewhere, resulting in California's share of national employment holding quite constant. The evidence points to increasing geographic dispersion of firms' operations, especially in industries with lower communication costs.