Stochastic Efficiency of Bayesian Markov Chain Monte Carlo in Spatial Econometric Models: An Empirical Comparison of Exact Sampling Methods

Spatial econometric specifications pose unique computational challenges to Bayesian analysis, making it difficult to estimate models efficiently. In the literature, the main focus has been on extending Bayesian analysis to increasingly complex spatial models. The stochastic efficiency of commonly used Markov Chain Monte Carlo (MCMC) samplers has received less attention by comparison. Specifically, Bayesian methods to analyze effective sample size and samplers that provide large effective size have not been thoroughly considered in the literature. Thus, we compare three MCMC techniques: the familiar Metropolis‐within‐Gibbs sampling, Slice‐within‐Gibbs sampling, and Hamiltonian Monte Carlo. The latter two methods, while common in other domains, are not as widely encountered in Bayesian spatial econometrics. We assess these methods across four different scenarios in which we estimate the spatial autoregressive parameter in a mixed regressive, spatial autoregressive specification (or, spatial lag model). We find that off‐the‐shelf implementations of the newer high‐yield simulation techniques require significant adaptation to be viable. We further find that the effective sizes are often significantly smaller than nominal sizes. In addition, we find that stopping simulation early may understate posterior credible interval widths when effective sample size is small. More broadly, we suggest that sample information and stopping rules deserve more attention in both applied and basic Bayesian spatial econometric research.     

THE GEOGRAPHICAL BASIS FOR DIFFERENTIATING THE SIZE OF FARMS

On the theory that optimization of farm size may enhance agricultural productivity, the author uses a game—theoretic model to find a solution for optimal farm size among the collective farms of Irkutsk Oblast. A game matrix, in which the players are the environment, using the strategies of a series of physical zones of agricultural production, and society, using the strategies of alternative farm sizes, yields a combination of farm sizes that would enhance total farm production in Irkutsk Oblast by 5 percent. The author notes that even greater improvements might be achieved in bringing types of farming more into line with physical and economic conditions of particular regions.     

Determining when rare (zoo-)archaeological phenomena are truly absent

Archaeologists are regularly faced with the dilemma of determining if the absence of a class of item is the result of that class never having been present in an area or if its absence is the result of sample deficiencies. This dilemma is especially apparent when a class of item is rare and has a patchy distribution. Comparison of samples that lack specimens of the class with samples that have specimens reveals criteria of an adequate sample. These criteria must be met by a sample in order to convincingly argue that the class of item was never present in the area from which the sample derives, and to provide guidelines for developing sampling designs aimed at discovering rare phenomena.     

Properties of Tests for Spatial Dependence in Linear Regression Models

Based on a large number of Monte Carlo simulation experiments on a regular lattice, we compare the properties of Moran's I and Lagrange multiplier tests for spatial dependence, that is, for both spatial error autocorrelation and for a spatially lagged dependent variable. We consider both bias and power of the tests for six sample sizes, ranging from twenty-five to 225 observations, for different structures of the spatial weights matrix, for several underlying error distributions, for misspecified weights matrices, and for the situation where boundary effects are present. The results provide an indication of the sample sizes for which the asymptotic properties of the tests can be considered to hold. They also illustrate the power of the Lagrange multiplier tests to distinguish between substantive spatial dependence (spatial lag) and spatial dependence as a nuisance (error autocorrelation).     

A study of dimensional differences of tooth marks (pits and scores) on bones modified by small and large carnivores

The use of tooth mark sizes to infer carnivore types when analyzing the modification of faunal assemblages has been criticized on the base of intense overlap in tooth mark size among differently sized carnivores. The present study analyzes this overlap and presents some critical explanations for it. This work is based on the largest collection of tooth pit dimensional data collected to date for some of the most relevant carnivore types. The study empirically shows that small and large carnivores can be clearly differentiated when using tooth pit size, with a higher discrimination when using tooth marks on dense shafts than on cancellous ends. It is argued that most previous studies of tooth mark sizes have reproduced a higher overlap probably because sample sizes were small, and experiments were carried out using small carcasses (which require a smaller bite force) or for a combination of factors.     

Spatial Search for the Lowest Price

Search for low prices often requires that individuals make decisions not only about the optimal amount of search, but also about the optimal route to be taken through a set of known locations. In this paper, the fixed sample size strategy used in economic models of search is extended to account for the travel costs that are incurred as alternatives are examined. Analytical results for the optimal amount of search are given, and alternative routing algorithms for a modified version of the traveling-salesman problem are evaluated.     

The Modified Triangular Graph: A Refined Method for Comparing Mortality Profiles in Archaeological Samples

Plotting the percentages of juvenile, prime, and old individuals on a triangular graph has become a popular method for analysing mortality profiles or age structures found in archaeological faunal samples. This method allows easy comparisons of multiple samples or multiple species and appears to work even with small sample sizes. However, the utility of triangular graphs is compromised for two reasons: (1) samples cannot be statistically compared and (2) the points on the graph are based on percentages, and, therefore, they do not provide information about sample size. The modified triangular graph described here offers a method for approximating 95% confidence intervals around the data points by using bootstrapping. Samples with non-overlapping contours are likely to have had different pre- or post-depositional histories. The 95% density contours reflect sample size since they shrink as samples get larger. Thus, the modified triangular graph allows more confident comparisons of three age class data.     

On the use of species-area curves to detect the effects of sample size

Archaeologists have long been concerned about sample size. To monitor the relationship between sample size and the magnitude of a variable of interest, archaeologists have constructed three distinct kinds of what in ecology are known as species area curves (SACs). Sampling to redundancy SACs involve adding successive samples cumulatively to determine if the information provided by new samples is unique or redundant with information provided by earlier (smaller) samples. Rarefaction SACs involve pooling multiple samples and then rarifying the pooled sample—making it smaller probabilistically—so that the originally large but rarified sample may be compared with originally small samples. Regression SACs determine if there is a significant statistical relationship between samples of different sizes and the magnitude of the variable of interest per sample. Each of the three SACs used by archaeologists has a distinct analytical purpose.     

基于卡马格尼模型的有效城市规模研究——以中国81个城市为样本的实证分析

近年,最优城市规模的问题走到了研究的十字路口,美国学者理查德森指出实际上并不存在最优的城市规模,而只存在依赖各种因素的有效城市规模。基于此观点及城市规模膨胀所引发的新一轮学术讨论,通过梳理城市规模研究领域内的已有文献成果,对新古典主义城市规模、最优城市规模、有效城市规模等主要研究范式的优缺点进行对比分析,发现有效城市规模研究范式相比其他城市规模研究范式确实更具现实合理性,但其同时也存在一些自身的缺陷。进而,基于中国2012年81个样本城市的横截面数据,探讨了中国的有效城市规模情况,发现现阶段中国城市规模的有效性尚处于合理范围内,且同城市规模存在反向变化关系,表现出了大规模城市效率低于小规模城市的特征。     

Size does matter: methodological comments on sieve size and species richness in fishbone assemblages

Vale and Gargett (J. Archaeol. Sci. 29 (2002) 57) discuss the finds from sieving experiments through 6 mm, 3 mm, and 1 mm mesh sizes from Arrawarra-I, a coastal midden site in Australia. They claimed that the relationship between sieve mesh size and both taxonomic richness and abundance is not straightforward. We reanalyzed Vale and Gargett's data to estimate species richness in larger sample sizes. By fitting logarithmic series to the data, we calculated the alpha diversity, and used that statistics to predict number of species expected at a given sample size. This statistical method is called “the equivalent alpha diversity method for abundifaction”. We demonstrate that taxonomic diversity would have been higher (14 species rather then 10) for an NISP of 2000 bones, sieved through a 1 mm mesh. We also demonstrate that Vale and Gargett's conclusion is flawed due to their small sample size (432 identified bones out of 60,000), inadequate sampling methods and poor analytical methodology. By using Vale and Gargett's data, we reach the opposite conclusion, and show that the use of 3 and 1 mm mesh sieves is indeed important in measuring diversity of archaeological assemblages in general, and of fish assemblages in particular.     

The Effect on Attribute Prediction of Location Uncertainty in Spatial Data

A datum is considered spatial if it contains location information. Typically, there is also attribute information, whose distribution depends on its location. Thus, error in location information can lead to error in attribute information, which is reflected ultimately in the inference drawn from the data. We propose a statistical model for incorporating location error into spatial data analysis. We investigate the effect of location error on the spatial lag, the covariance function, and optimal spatial linear prediction (that is, kriging). We show that the form of kriging after adjusting for location error is the same as that of kriging without adjusting for location error. However, location error changes entries in the matrix of explanatory variables, the matrix of co‐variances between the sample sites, and the vector of covariances between the sample sites and the prediction location. We investigate, through simulation, the effect that varying trend, measurement error, location error, range of spatial dependence, sample size, and prediction location have on kriging after and without adjusting for location error. When the location error is large, kriging after adjusting for location error performs markedly better than kriging without adjusting for location error, in terms of both the prediction bias and the mean squared prediction error.     

The Mormon Historical Demography Project

Abstract

This article describes the background and reconstruction of the Belgian 1961 census sample file. Recently, a complete codebook for the sample file has been drawn up, and the representativeness of the sample has been evaluated as accurate, except for the loss of cases that occurred for three Belgian subregions. With the addition of the 1961 census sample, cross-sectional microdata from the five successive population censuses since that year, covering a broad range of topics, are now available to the research community. The reconstruction of the 1961 census sample was part of the activities of the HISSTAT project, which is currently being run by a consortium of research institutions in Belgium to bring together cross-sectional aggregated data since 1800, aggregated longitudinal data since 1880, and cross-sectional microdata since 1961, all covering the entire country.     

Optimal Facility Location in a One-Dimensional Spatial Market

This paper analyzes properties of the optimal spatial arrangement of what may be interpreted as a class of public facilities. Optimality is defined as cost minimization. Three different optimality criteria are considered, and for each, the necessary and, sufficient conditions, market area size, and production levels, are derived. The relationship between optimal production levels and number of facilities needed is also considered. Next the results of implementing various pricing strategies are analyzed with emphasis given to marginal and uniform pricing. It is shown that, given certain conditions, all facilities incur operating deficits, given marginal pricing. Estimates on the level of the deficits are derived in terms of location rents. Finally, in the appendix, several important results from other studies are derived as special cases of the basic model.     

Sample preparation for accelerator-based radiocarbon dating

Although several efficient sample preparation methods have been devised for conventional radiocarbon dating, the advent of the accelerator mass spectrometer (AMS) dating technique with its much smaller sample requirement and different counting method has meant that new preparation routes have had to be developed. Techniques used for the Oxford AMS system are described in this paper.     

EMERGENCE OF LEAPFROGGING FROM RESIDENTIAL CHOICE WITH ENDOGENOUS GREEN SPACE: ANALYTICAL RESULTS

Leapfrog development is a typical form of sprawl. This paper aims at analyzing the existence, size, and persistence of leapfrogging in a dynamic urban economic model with endogenous green amenities. We analyze whether incoming households choose to settle at the fringe of the city or to jump further away depending on their preferences and the structure of the city. We first provide an analytical treatment of the conditions and characteristics under which a first leapfrog occurs and show how the optimal choice is affected by the size of the city, income, commuting costs, as well as the size of the area where green amenities are considered. We then study how further leapfrogging and multiple urban rings may appear and be maintained in the long‐run equilibrium, and how infill processes take place through time.     

Urban evolution in the USA

On a sustained basis, cities are of non-uniform relative sizes.This paper addresses three basic issues which arise from thissimple observation by examining the size distribution of UScities over the period 1900–1990. First, we explore thereasons why there is a wide distribution of city sizes. Second,we characterize the evolution of the size distribution of cities,documenting growth in sizes and numbers of cities. We ask whetherthe relative size distribution of cities has remained stableover time, or if it has displayed, instead, a tendency to collapse,flatten, or otherwise change its shape. We also examine evidenceon whether the size distribution obeys Zipf's Law. Third, weexamine the degree and determinants of mobility of individualcities within this distribution, asking to what extent citiesare moving up and down in the distribution and how this movementis influenced by cities' geographic characteristics. We usea newly constructed data with consistent metropolitan area definitionsover this century, discussing the issues and linking our resultsto the relevant literature.     

MULTIPLIER ESTIMATES: TO BIAS OR NOT TO BIAS?*

ABSTRACT It is well known that multiplier estimates within an interindustry context may be biased when the input coefficients are stochastic. Several conditions have been derived under which the estimates were shown to be biased, all with the same sign. In contrast to these analytical results, however, simulations using a stochastic transactions table unexpectedly reported the unbiasedness of multiplier estimates. This note argues that the sample sizes were too small. It is shown that for increased sample sizes the multiplier estimates are all positively and significantly biased, in line with the analytical results, but the biases are very small.     

制备方法对土遗址重塑样稳定性的影响研究

土建筑遗址本体的保护受遗址土的物理、水理、力学及所处环境差异的影响，重塑样是替代土遗址测试其各种性质的重要手段，重塑样拌制土性质的稳定性是科学评价、对比分析试验研究的基础和前提。本研究基于不同拌制土的方法，通过观察、拍照、量取土团粒大小以及同条件制备样品的无侧限抗压强度等，综合评价不同拌制土方法的影响条件。研究发现，采用人工拌土、闷土时间在24 h的土所制的试样最具稳定性，随着闷土时间再增加，土样强度在逐渐降低。本研究为土建筑遗址室内试验研究和工程现场拌制土料提供理论参考和技术支撑。     

Relics of 16th-century gutted herring from a Dutch vessel

Abstract

During the excavation of a 16th-century vessel at Biddinghuizen in the Netherlands, barrels containing the remains of thousands of herring were found. The skeletal element distribution made it clear that these fish had been preserved by means of gutting. The large amount of material, combined with the differences in the size and composition of the samples taken allowed the complex to serve as a good reference framework for the variability in the occurrence of preserved herring of this type. The method, described by Seeman (1986), of identifying gutted herring on the basis of archaeological material has been extended to include more diagnostic skeletal elements, criteria for sample sizes and requirements concerning the elements that must be present in a sample to obtain reliable conclusions.     

Statistical Characterization of Structural Demand under Earthquake Loading. Part 1: Robust Estimation of the Central Value of the Data

This article is the first of two companion articles addressing the statistical characterization of seismic demand. Performance-based earthquake engineering methodologies often require the characterization of central value estimates of structural demand. Since outliers can occur in the data, central value estimates should be determined by robust estimation methods. The performance of 50 robust central value estimators is evaluated, for different sample sizes, using the chord rotation, curvature, shear force, and inter-story drift demands obtained after analyzing five reinforced concrete structures under real earthquake records scaled to several intensities. Based on the results, seven estimators are proposed for different sample sizes.