Local Parameter Estimates Research Articles

Coho salmon escapement and trends in migration timing to a data-poor river: estimates from a Bayesian hierarchical model

Data to inform fisheries management are often limited in remote or low economic value fisheries. Here, we use a Bayesian hierarchical modeling structure and two alternative migration timing models to estimate the annual escapement of coho salmon (Oncorhynchus kisutch) to the Chignik River (Alaska, USA) in years with little data, borrowing information from data-rich years to inform parameter estimates. Additionally, we examined trends in peak migration timing between 1922 and 2013 and relative to environmental conditions. Our analyses show that annual escapement estimates are prone to substantial errors unless daily escapement is enumerated for at least 7 days after peak migration date. Finally, peak migration date was negatively correlated with the strength of the Pacific Decadal Oscillation in May–August, and increased over time, though the significance of these associations was dependent on the specific form of the migration timing model used. The modeling approach we present here is easily adaptable to similar situations where data from alternative periods of time or spatial locations can be used to objectively inform local parameter estimates of population characteristics.

Estimating the Impact of Urbanization on Air Quality in China Using Spatial Regression Models

Urban air pollution is one of the most visible environmental problems to have accompanied China’s rapid urbanization. Based on emission inventory data from 2014, gathered from 289 cities, we used Global and Local Moran’s I to measure the spatial autorrelation of Air Quality Index (AQI) values at the city level, and employed Ordinary Least Squares (OLS), Spatial Lag Model (SAR), and Geographically Weighted Regression (GWR) to quantitatively estimate the comprehensive impact and spatial variations of China’s urbanization process on air quality. The results show that a significant spatial dependence and heterogeneity existed in AQI values. Regression models revealed urbanization has played an important negative role in determining air quality in Chinese cities. The population, urbanization rate, automobile density, and the proportion of secondary industry were all found to have had a significant influence over air quality. Per capita Gross Domestic Product (GDP) and the scale of urban land use, however, failed the significance test at 10% level. The GWR model performed better than global models and the results of GWR modeling show that the relationship between urbanization and air quality was not constant in space. Further, the local parameter estimates suggest significant spatial variation in the impacts of various urbanization factors on air quality.

Exploring, modelling and predicting spatiotemporal variations in house prices

Hedonic price modelling has long been a powerful tool to estimate house prices in the real estate market. Increasingly, traditional global hedonic price models that largely ignore spatial effects are being superseded by models that deal with spatial dependency and spatial heterogeneity. In addition, many novel methods integrating spatial economics, statistics and geographical information science (GIScience) have been developed recently to incorporate temporal effects into hedonic house price modelling. Here, a local spatial modelling technique, geographically weighted regression (GWR), which accounts for spatial heterogeneity in housing utility functions is applied to a 19-year set of house price data in London (1980–1998) in order to explore spatiotemporal variations in the determinants of house prices. Further, based on the local parameter estimates derived from GWR, a new method integrating GWR and time series (TS) forecasting techniques, GWR–TS, is proposed to predict future local parameters and thus future house prices. The results obtained from GWR demonstrate variations in local parameter estimates over both space and time. The forecasted future values of local estimates as well as house prices indicate that the proposed GWR–TS method is a useful addition to hedonic price modelling.

Marginal Likelihoods for Distributed Parameter Estimation of Gaussian Graphical Models

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance matrix, which can be computationally intensive in large dimensions. Approximate inference based on message-passing algorithms, on the other hand, can lead to unstable and biased estimation in loopy graphical models. In this paper, we propose a general framework for distributed estimation based on a maximum marginal likelihood (MML) approach. This approach computes local parameter estimates by maximizing marginal likelihoods defined with respect to data collected from local neighborhoods. Due to the non-convexity of the MML problem, we introduce and solve a convex relaxation. The local estimates are then combined into a global estimate without the need for iterative message-passing between neighborhoods. The proposed algorithm is naturally parallelizable and computationally efficient, thereby making it suitable for high-dimensional problems. In the classical regime where the number of variables $p$ is fixed and the number of samples $T$ increases to infinity, the proposed estimator is shown to be asymptotically consistent and to improve monotonically as the local neighborhood size increases. In the high-dimensional scaling regime where both $p$ and $T$ increase to infinity, the convergence rate to the true parameters is derived and is seen to be comparable to centralized maximum likelihood estimation. Extensive numerical experiments demonstrate the improved performance of the two-hop version of the proposed estimator, which suffices to almost close the gap to the centralized maximum likelihood estimator at a reduced computational cost.

Asymptotically Efficient Distributed Estimation With Exponential Family Statistics

This paper studies the problem of distributed parameter estimation in multiagent networks with exponential family observation statistics. A certainty-equivalence type distributed estimator of the consensus-plus-innovations form is proposed in which, at each observation sampling epoch, agents update their local parameter estimates by appropriately combining the data received from their neighbors and the locally sensed new information (innovation). Under global observability of the networked sensing model, i.e., the ability to distinguish between different instances of the parameter value based on the joint observation statistics, and mean connectivity of the inter-agent communication network, the proposed estimator is shown to yield consistent parameter estimates at each network agent. Further, it is shown that the distributed estimator is asymptotically efficient, in that, the asymptotic covariances of the agent estimates coincide with that of the optimal centralized estimator, i.e., the inverse of the centralized Fisher information rate. From a technical viewpoint, the proposed distributed estimator leads to non-Markovian mixed time-scale stochastic recursions and the analytical methods developed in this paper contribute to the general theory of distributed stochastic approximation.

Gaussian Markov random field based improved texture descriptor for image segmentation

This paper proposes a novel robust texture descriptor based on Gaussian Markov random fields (GMRFs). A spatially localized parameter estimation technique using local linear regression is performed and the distributions of local parameter estimates are constructed to formulate the texture features. The inconsistencies arising in localized parameter estimation are addressed by applying generalized inverse, regularization and an estimation window size selection criterion. The texture descriptors are named as local parameter histograms (LPHs) and are used in texture segmentation with the k-means clustering algorithm. The segmentation results on general texture datasets demonstrate that LPH descriptors significantly improve the performance of classical GMRF features and achieve better results compared to the state-of-the-art texture descriptors based on local feature distributions. Impressive natural image segmentation results are also achieved and comparisons to the other standard natural image segmentation algorithms are also presented. LPH descriptors produce promising texture features that integrate both statistical and structural information about a texture. The region boundary localization can be further improved by integrating colour information and using advanced segmentation algorithms.

Modelling the Spatial Nature of Household Residential Mobility within Municipalities in Colombia

In this paper, we examine household residential mobility within Colombian municipalities and determine whether the factors that trigger residential movement vary across the country. Using Geographically Weighted Regression (GWR) and detailed data from the 2005 Census for all municipalities in Colombia, our analysis takes into account the spatial variation in the relationship between household residential mobility and the associated housing, socioeconomic and environmental factors derived from theory and previous empirical research. Our findings demonstrate that household residential mobility is strongly and positively associated with living conditions, age and income, and negatively associated with homeownership and household composition within municipalities. The comparison of global (Ordinary Least Squares regression) and local (GWR) parameter estimates reveals the presence of a non-stationary effect on household residential mobility for the predictor variables considered, and highlights the importance of local variation of the relationships. In addition to contributing to the debate on the dynamics of residential mobility in Colombia, the study results have implications for effective policy-making with regard to urban expansion and settlement of various groups.

Scrub Typhus and Comparisons of Four Main Ethnic Communities in Taiwan in 2004 versus 2008 Using Geographically Weighted Regression

Purpose:On the main island of Taiwan, a higher risk of scrub typhus infection has been reported in endemic clusters in Southeastern Taiwan and in mountainous township areas. However, research on health care problems associated with scrub typhus in Taiwanese ethnic peoples is limited. This study employs spatial analysis of areal data to determine spatial features related to scrub typhus and the four main Taiwanese ethnicities: Hoklo, Hakka, Mainlander, and aboriginal communities, respectively.Methods:We used a GWR spatial method to analyze the local regressed relationships between scrub typhus incidence and ethnic community percentage in 349 townships in Taiwan, and the subsequent spatial regressed resultants and local parameter estimates were compared between two periods of 2004 and 2008 by kappa statistics.Results:In the GWR models, the spatial regressed relationships of scrub typhus incidences and the Hoklo communities showed significant and negative parameter estimates in numerous locations, showing clusters in Southeastern and Southwestern Taiwan, and areas of the central and southern mountainous townships. Both Hakka and Mainlander communities in the mountainous townships showed less-regressed clusters with scrub typhus prevalence. However, clusters of Aboriginal populations were positively correlated with scrub typhus in highly infected mountainous areas and in Southeastern Taiwan. The kappa value results and the comparisons of local parameter estimates in the 349 townships in Taiwan between 2004 and 2008 indicated that the incidence of scrub typhus in the Hoklo communities was substantial, in the Hakka communities was fair, in the Mainlander communities was slight, and in the aboriginal communities was moderate, respectively.Conclusion:The aboriginal communities have been closely associated with higher risks of scrub typhus in the mountainous townships and in the southeastern portion of Taiwan.

Modelling long-term fire occurrence factors in Spain by accounting for local variations with geographically weighted regression

Abstract. Humans are responsible for most forest fires in Europe, but anthropogenic factors behind these events are still poorly understood. We tried to identify the driving factors of human-caused fire occurrence in Spain by applying two different statistical approaches. Firstly, assuming stationary processes for the whole country, we created models based on multiple linear regression and binary logistic regression to find factors associated with fire density and fire presence, respectively. Secondly, we used geographically weighted regression (GWR) to better understand and explore the local and regional variations of those factors behind human-caused fire occurrence. The number of human-caused fires occurring within a 25-yr period (1983–2007) was computed for each of the 7638 Spanish mainland municipalities, creating a binary variable (fire/no fire) to develop logistic models, and a continuous variable (fire density) to build standard linear regression models. A total of 383 657 fires were registered in the study dataset. The binary logistic model, which estimates the probability of having/not having a fire, successfully classified 76.4% of the total observations, while the ordinary least squares (OLS) regression model explained 53% of the variation of the fire density patterns (adjusted R2 = 0.53). Both approaches confirmed, in addition to forest and climatic variables, the importance of variables related with agrarian activities, land abandonment, rural population exodus and developmental processes as underlying factors of fire occurrence. For the GWR approach, the explanatory power of the GW linear model for fire density using an adaptive bandwidth increased from 53% to 67%, while for the GW logistic model the correctly classified observations improved only slightly, from 76.4% to 78.4%, but significantly according to the corrected Akaike Information Criterion (AICc), from 3451.19 to 3321.19. The results from GWR indicated a significant spatial variation in the local parameter estimates for all the variables and an important reduction of the autocorrelation in the residuals of the GW linear model. Despite the fitting improvement of local models, GW regression, more than an alternative to "global" or traditional regression modelling, seems to be a valuable complement to explore the non-stationary relationships between the response variable and the explanatory variables. The synergy of global and local modelling provides insights into fire management and policy and helps further our understanding of the fire problem over large areas while at the same time recognizing its local character.

Local Hedonic House-Price Modelling for Urban Planners: Advantages of Using Local Regression Techniques

Hedonic house-price models have long been used in urban studies to investigate important factors characterizing cities (eg, the demand for amenities or housing submarkets). Traditionally, the formulation of hedonic models has been solved using global spatial econometric techniques. The development of local regression methods brought new insights into urban planning as the relationships between house prices and their determinants can be estimated locally and therefore mapped across space. Such maps provide planners and policy makers with valuable location-specific information to support their decision-making processes. A feature that is frequently overlooked when performing spatial local analysis is testing the statistical significance of local parameter estimates over space. This can be done by mapping the t-value of parameter estimates ( t-surfaces). In this study we propose the use of a mixed geographically weighted regression (mixed-GWR) technique to estimate a hedonic house-price model in Zurich. Mixed-GWR is an extended version of GWR by which some parameters are allowed to vary over space, while others remained fixed. To obtain spatially explicit results in a more meaningful way, we propose the use of t-surfaces to explore the statistical significance of selected local parameter estimates over space. We also follow the Bonferroni correction to overcome the problem of multiple hypothesis testing in local regression modelling. Results reveal interesting patterns in the spatial variability of local estimates for planners. For instance, areas are identified over which public policies such as house taxing have little or no effect on house pricing. Similarly, economic distortions in the housing market can be examined through the variability of residents' willingness to pay for larger dwellings. Also, urban development processes such as densification of cities can be supported by spatially exploring relevant socioeconomic variables.

Neighborhood characteristics and depressive symptoms of older people: Local spatial analyses

Depressive symptoms in community-dwelling older people significantly increase the risk of developing clinically diagnosable depressive disorders. Knowledge of the spatial distribution of depressive symptoms in the older population can add important information to studies of neighborhood contextual factors and mental health outcomes, but analysis of spatial patterns is rarely undertaken. This study uses spatial statistics to explore patterns of clustering in depressive symptoms using data from a statewide survey of community-dwelling older people in New Jersey from 2006 to 2008. A significant overall pattern of clustering in depressive symptoms was observed at the state level. In a subsequent local clustering analysis, places with high levels of depressive symptoms near to other places with high levels of depressive symptoms were identified. The relationships between the level of depressive symptoms in a place and poverty, residential stability and crime were analyzed using geographically weighted regression. Significant local parameter estimates for the three independent variables were observed. Local parameters for the poverty variable were positive and significant almost everywhere in the state. The significant local parameters for residential stability and crime varied in their association with depressive symptoms in different regions of the state. This study is among the first to examine spatial patterns in depressive symptoms among community-dwelling older people, and it demonstrates the importance of exploring spatial variations in the relationships between neighborhood contextual factors and health outcomes.

Nonstationary modeling for multivariate spatial processes

We derive a class of matrix valued covariance functions where the direct and cross-covariance functions are Matérn. The parameters of the Matérn class are allowed to vary with location, yielding local variances, local ranges, local geometric anisotropies and local smoothnesses. We discuss inclusion of a nonconstant cross-correlation coefficient and a valid approximation. Estimation utilizes kernel smoothed empirical covariance matrices and a locally weighted minimum Frobenius distance that yields local parameter estimates at any location. We derive the asymptotic mean squared error of our kernel smoother and discuss the case when multiple field realizations are available. Finally, the model is illustrated on two datasets, one a synthetic bivariate one-dimensional spatial process, and the second a set of temperature and precipitation model output from a regional climate model.

Mapping the results of local statistics: Using geographically weighted regression.

The application of geographically weighted regression (GWR) - a local spatial statistical technique used to test for spatial nonstationarity - has grown rapidly in the social, health and demographic sciences. GWR is a useful exploratory analytical tool that generates a set of location-specific parameter estimates which can be mapped and analysed to provide information on spatial nonstationarity in relationships between predictors and the outcome variable. A major challenge to GWR users, however, is how best to map these parameter estimates. This paper introduces a simple mapping technique that combines local parameter estimates and local t-values on one map. The resultant map can facilitate the exploration and interpretation of nonstationarity.

A hyperparameter consensus method for agreement under uncertainty

This paper addresses the problem of information consensus in a team of networked agents by presenting a generic consensus method that permits agreement to a Bayesian fusion of uncertain local parameter estimates. In particular, the method utilizes the concept of conjugacy of probability distributions to achieve a steady-state estimate consistent with a Bayesian combination of each agent’s local knowledge, without requiring complex channel filters or being limited to normally distributed uncertainties. It is shown that this algorithm, termed hyperparameter consensus, is adaptable to many local uncertainty distributions within the exponential family, and will converge to a Bayesian fusion of local estimates with some standard assumptions on the network topology.

Viscoelastic properties of soft gels: comparison of magnetic resonance elastography and dynamic shear testing in the shear wave regime

Magnetic resonance elastography (MRE) is used to quantify the viscoelastic shear modulus, G*, of human and animal tissues. Previously, values of G* determined by MRE have been compared to values from mechanical tests performed at lower frequencies. In this study, a novel dynamic shear test (DST) was used to measure G* of a tissue-mimicking material at higher frequencies for direct comparison to MRE. A closed-form solution, including inertial effects, was used to extract G* values from DST data obtained between 20 and 200 Hz. MRE was performed using cylindrical ‘phantoms’ of the same material in an overlapping frequency range of 100–400 Hz. Axial vibrations of a central rod caused radially propagating shear waves in the phantom. Displacement fields were fit to a viscoelastic form of Navier's equation using a total least-squares approach to obtain local estimates of G*. DST estimates of the storage G′ (Re[G*]) and loss modulus G″ (Im[G*]) for the tissue-mimicking material increased with frequency from 0.86 to 0.97 kPa (20–200 Hz, n = 16), while MRE estimates of G′ increased from 1.06 to 1.15 kPa (100–400 Hz, n = 6). The loss factor (Im[G*]/Re[G*]) also increased with frequency for both test methods: 0.06–0.14 (20–200 Hz, DST) and 0.11–0.23 (100–400 Hz, MRE). Close agreement between MRE and DST results at overlapping frequencies indicates that G* can be locally estimated with MRE over a wide frequency range. Low signal-to-noise ratio, long shear wavelengths and boundary effects were found to increase residual fitting error, reinforcing the use of an error metric to assess confidence in local parameter estimates obtained by MRE.

Regional effects of terrorism on economic growth in Turkey: A geographically weighted regression approach

The economic growth effects of terrorism have generally been examined in a cross-country framework where socio-economic differences among the countries are ignored. This highly restrictive assumption may result in heterogeneity bias, which could be overcome by resorting to country studies rather than cross-country analysis. Moreover, the relationship between the terrorist incidents and various factors may not be stationary in space. The majority of terrorist incidents in Turkey are concentrated mainly in Eastern, and South Eastern Turkey and big cities. Thus, the geographical dispersion of terrorist incidents in Turkey may result in uneven regional impact, necessitating local parameter estimates. This study analyses the effects of terrorism on economic growth across provinces of Turkey for the time period 1987—2001. Following a traditional global regression analysis, spatial variations in the relationships are examined with geographically weighted regression (GWR) to obtain locally different parameter estimates. A GWR approach allows the modeling of relationships that vary over space by introducing distance-based weights to provide parameter estimates for each variable and each geographical location. Empirical evidence indicates that a GWR model significantly improves the model fitting over the traditional global model. Even though the traditional convergence analysis reveals that terrorism hinders economic growth, GWR results indicate that its provincial effects are more pronounced for the Eastern and South Eastern provinces compared to the Western provinces. Moreover, empirical findings suggest that there is a considerable variation in speeds of convergence of provinces, which cannot be captured by the traditional beta convergence analysis.

Multiple local whittle estimation in stationary systems

Moving from univariate to bivariate jointly dependent long-memory time series introduces a phase parameter $(\gamma)$, at the frequency of principal interest, zero; for short-memory series $\gamma=0$ automatically. The latter case has also been stressed under long memory, along with the ``fractional differencing'' case $\gamma=(\delta_2-\delta_1)\pi /2$, where $\delta_1$, $\delta_2$ are the memory parameters of the two series. We develop time domain conditions under which these are and are not relevant, and relate the consequent properties of cross-autocovariances to ones of the (possibly bilateral) moving average representation which, with martingale difference innovations of arbitrary dimension, is used in asymptotic theory for local Whittle parameter estimates depending on a single smoothing number. Incorporating also a regression parameter $(\beta)$ which, when nonzero, indicates cointegration, the consistency proof of these implicitly defined estimates is nonstandard due to the $\beta$ estimate converging faster than the others. We also establish joint asymptotic normality of the estimates, and indicate how this outcome can apply in statistical inference on several questions of interest. Issues of implemention are discussed, along with implications of knowing $\beta$ and of correct or incorrect specification of $\gamma$, and possible extensions to higher-dimensional systems and nonstationary series.

Exploring the spatio-temporal dynamics of geographical processes with geographically weighted regression and geovisual analytics

The paper examines the potential for combining a spatial statistical methodology – Geographically Weighted Regression (GWR) – with geovisual analytical exploration to help understand complex spatio-temporal processes. This is done by applying the combined statistical – exploratory methodology to a simulated data set in which the behaviour of regression parameters was controlled across space and time. A variety of complex spatio-temporal processes was captured through space-time (i.e. as spatio-temporal) varying parameters whose values were known. The task was to see if the proposed methodology could uncover these complex processes from the data alone. The results of the experiment confirm that the combined methodology can successfully identify spatio-temporal patterns in the local GWR parameter estimates that correspond to the controlled behaviour of the original parameters.

Contagion and Crises Clusters: Toward a Regional Warning System?

This paper studies the spatial heterogeneity of the relationship between contagious currency crises and their determinants using a Geographically Weighted Regression (GWR) framework. This novel method enables a vector of local parameter estimates to be estimated for each country of the data set, according to its nearest neighbours. The approach makes it possible to derive locally-specific models, thereby improving standard prevention schemes and assessments for international financial assistance. Our findings suggest that economic attributes and imbalances of neighbouring countries can be introduced into country-specific warning systems.

Spatial patterns of rural poverty and their relationship with welfare-influencing factors in Bangladesh

This study determines the spatial variation of rural poverty in Bangladesh and its relation to people’s livelihood assets affecting their ability to procure food. We estimated household income for over 1 million census households using a predictor model based on a nationally representative sample survey data set. We computed and mapped poverty indices for 415 rural subdistricts revealing distinct areas with high poverty incidence that correspond with ecologically depressed areas. However, other livelihood-influencing factors such as education, accessibility and services are significantly correlated with poverty. This indicates the need for continued focus on providing education and access to income-generating opportunities so that the poor can better meet their food needs. Geographically weighted regression analysis indicated spatial differences in the relative importance of various poverty-influencing factors. Multivariate clustering of the local parameter (β) estimates of the determinant factors revealed distinct spatial relationships, which have implications on poverty alleviation interventions specific to the different regions.