Spatial Stochastic Model Research Articles

A spatial stochastic frontier model with fixed effects and endogenous environmental variables

ABSTRACT Stochastic frontier analysis (SFA) models often address fixed effects and endogeneity as separate issues. This study bridges this gap by proposing a unified approach within an ML (maximum likelihood) framework to manage both challenges simultaneously. The ML function is derived in a closed form, but its maximisation requires a numerical solution. To assess the properties of the ML estimator, a Monte Carlo simulation was performed. The simulation shows that the estimator performs reasonably well and gains efficiency asymptotically. The applicability of the estimator was further assessed through an empirical exercise that examined technical efficiency of the production function in a panel of European countries, managing spatiality, endogeneity, and fixed effects.

Influence of financial inclusion and industrial robots on the efficiency of China's OFDI: A heterogeneous spatial stochastic frontier analysis

Enhancing the efficacy of China's outward foreign direct investment (COFDI) constitutes a significant avenue for realizing the sustainable development of China's economy. This study analyzes panel data from 63 countries from 2010 to 2021 to create a heterogeneous spatial stochastic frontier model to examine how financial inclusion and industrial robotics in host nations affect COFDI efficiency. The findings are as follows. To begin with, COFDI manifests positive spatial spillover effects across countries. Moreover, from a spatial perspective, financial inclusion diminishes COFDI efficiency, whereas the interaction between financial inclusion and industrial robots increases its efficiency. Industrial robots, thus, counteract the diminishing impact of financial inclusion on COFDI efficiency. Additionally, concerning the heterogeneity of location choice and investment motivation in COFDI, the interaction between financial inclusion and industrial robots in developed economies augments COFDI efficiency as opposed to emerging market economies. Conversely, technology-seeking investment mitigates the adverse effects of financial inclusion on the efficacy of COFDI when juxtaposed with resource-seeking investment. This study provides theoretical insights and practical recommendations for improving the efficiency and guiding the destination selection of COFDI.

Fitting spatial stochastic frontier models in Stata

In this article, we introduce a new command, xtsfsp, for fitting spatial stochastic frontier models in Stata. Over the last decades, stochastic frontier models have seen important theoretical progress via the incorporation of various types of spatial components. Models that can account for spatial dependence and spillovers have been developed for efficiency and productivity analysis, drawing extensive attention from industry and academia. Because of the unavailability of the statistical packages, the empirical applications of the new stochastic frontier models appear to be lagging. The xtsfsp command provides a procedure for fitting spatial stochastic frontier models in the style of Orea and Álvarez (2019, Journal of Econometrics 213: 556-577) and Galli (2023, Spatial Economic Analysis 18: 239-258), enabling users to handle different sources of spatial dependence. In this article, we introduce spatial stochastic frontier models, describing the syntax and options of the new command and providing several examples to illustrate its usage.

A conjugate method for simulating the dynamics of stochastic urban spatial network models

Urban networks are integral components of urban systems, contributing to their functioning and shaping the overall dynamics of urban areas. They are characterized by their complexity, interdependence, and dynamic nature. The construction, analysis and understanding of urban network models is therefore essential to address complex urban challenges, fostering sustainable development, and improving the overall quality of life in systems like cities and regions. In this work, we present and analyze the properties of a stochastic spatial-interaction model of urban structures. In addition, we devise a suitable time-stepping integrator that allows analyzing the evolution of this stochastic system at large times intervals, providing information of the dynamical behavior of the system in its equilibrium state. Numerical simulation studies are carried out to illustrate the practical effectiveness of the proposed approach.

Transportation infrastructure and carbon emissions: New evidence with spatial spillover and endogeneity

Over the past two decades, China’s transportation infrastructure has expanded and emerged as a vital pillar of the national economy. In the context of commitments to carbon neutrality, it is imperative to assess how developing transportation infrastructure affects overall environmental goals. However, to the best of our knowledge, existing literature offers conflicting evidence about the overall impact of transportation infrastructure on carbon emissions. Using a novel spatial stochastic frontier model that accounts for spatial spillover and endogeneity, we find that previous research paradigms underestimated the contribution of transportation infrastructure to decarbonization: Instead of being a hindrance, the corrected effect substantially enhances decarbonization. These results remain robust in different weight matrices, instrumental variables, and distance function specifications. Furthermore, this study identifies economic agglomeration and technological innovation as key mechanisms of the decarbonization effect. From a regional perspective, we observe that western China shows the most pronounced emission reduction effect, followed by central China. In contrast, in eastern China, the transportation infrastructure does not support carbon emission reduction effectively. Therefore, policymakers should carefully consider the regional disparities in decarbonization and formulate distinct investment plans on transportation tailored to each region.

Using convolutional neural networks for stereological characterization of 3D hetero-aggregates based on synthetic STEM data

The 3D nano/microstructure of materials can significantly influence their macroscopic properties. In order to enable a better understanding of such structure-property relationships, 3D microscopy techniques can be deployed, which are however often expensive in both time and costs. Often 2D imaging techniques are more accessible, yet they have the disadvantage that the 3D nano/microstructure of materials cannot be directly retrieved from such measurements. The motivation of this work is to overcome the issues of characterizing 3D structures from 2D measurements for hetero-aggregate materials. For this purpose, a method is presented that relies on machine learning combined with methods of spatial stochastic modeling for characterizing the 3D nano/microstructure of materials from 2D data. More precisely, a stochastic model is utilized for the generation of synthetic training data. This kind of training data has the advantage that time-consuming experiments for the synthesis of differently structured materials followed by their 3D imaging can be avoided. More precisely, a parametric stochastic 3D model is presented, from which a wide spectrum of virtual hetero-aggregates can be generated. Additionally, the virtual structures are passed to a physics-based simulation tool in order to generate virtual scanning transmission electron microscopy (STEM) images. The preset parameters of the 3D model together with the simulated STEM images serve as a database for the training of convolutional neural networks, which can be used to determine the parameters of the underlying 3D model and, consequently, to predict 3D structures of hetero-aggregates from 2D STEM images. Furthermore, an error analysis is performed with respect to structural descriptors, e.g. the hetero-coordination number. The proposed method is applied to image data of TiO2-WO3 hetero-aggregates, which are highly relevant in photocatalysis processes. However, the proposed method can be transferred to other types of aggregates and to different 2D microscopy techniques. Consequently, the method is relevant for industrial or laboratory setups in which product quality is to be quantified by means of inexpensive 2D image acquisition.

Simulated Future Shifts in Wildfire Regimes in Moist Forests of Pacific Northwest, USA

AbstractFire is an integral natural disturbance in the moist temperate forests of the Pacific Northwest of the United States, but future changes remain uncertain. Fire regimes in this climatically and biophysically diverse region are complex, but typically climate limited. One challenge for interpreting potential changes is conveying projection uncertainty. Using projections of Energy Release Component (ERC) derived from 12 global climate models (GCM) that vary in performance relative to the region's contemporary climate, we simulated thousands of plausible fire seasons with the stochastic spatial fire spread model FSim for mid‐21st century (2035–2064) under RCP8.5 emissions scenario for five northwestern pyromes. The magnitude of projected changes to burn probability, fire size, and number of fires varied among pyromes and GCMs. We projected the largest increases in burn probability and fire size in the cooler and wetter northern parts of the region (North Cascades, Olympics & Puget Lowlands) and Oregon West Cascades, with more moderate changes projected for the Washington West Cascades and Oregon Coast Range. We provide new insights into changing fire regimes characterized by the possibility of shifts toward more frequent and large fires (especially >40,000 ha), as well as shifts in seasonality, including more fires burning at the beginning of fall when extreme synoptic weather events have the potential to increase fire spread. Our work highlights the potential geographic variability in climate change effects in some of the most productive moist temperate forests of the world and points to a rapid acceleration of fire in the coming decades.

A spatial measure-valued model for radiation-induced DNA damage kinetics and repair under protracted irradiation condition

In the present work, we develop a general spatial stochastic model to describe the formation and repair of radiation-induced DNA damage. The model is described mathematically as a measure-valued particle-based stochastic system and extends in several directions the model developed in Cordoni et al. (Phys Rev E 103:012412, 2021; Int J Radiat Biol 1–16, 2022a; Radiat Res 197:218–232, 2022b). In this new spatial formulation, radiation-induced DNA damage in the cell nucleus can undergo different pathways to either repair or lead to cell inactivation. The main novelty of the work is to rigorously define a spatial model that considers the pairwise interaction of lesions and continuous protracted irradiation. The former is relevant from a biological point of view as clustered lesions are less likely to be repaired, leading to cell inactivation. The latter instead describes the effects of a continuous radiation field on biological tissue. We prove the existence and uniqueness of a solution to the above stochastic systems, characterizing its probabilistic properties. We further couple the model describing the biological system to a set of reaction–diffusion equations with random discontinuity that model the chemical environment. At last, we study the large system limit of the process. The developed model can be applied to different contexts, with radiotherapy and space radioprotection being the most relevant. Further, the biochemical system derived can play a crucial role in understanding an extremely promising novel radiotherapy treatment modality, named in the community FLASH radiotherapy, whose mechanism is today largely unknown.

Economic and Environmental Efficiency, Subsidies and Spatio-Temporal Effects in Agriculture

In this paper, we investigate how farms' environmental and economic efficiency is shaped by Pillar I CAP subsidies over time and by spatial effects originating from subsidies received by neighbours. To reach this goal, we estimate a spatial stochastic frontier model including intra and inter province spatial effects and differentiate among environmental and economic outcomes to evaluate the direct and indirect effects of subsidies on both aspects. The results of the analysis indicate that on one hand, subsidies are helping farmers to achieve environmental sustainability especially after the 2013 reform, on the other, they are leading to increased economic inefficiency levels. Considering spatial effects originating from subsidies, we find positive and significant spillovers occurring among closest neighbours both from the economic and the environmental perspective.

Modeling the freezing process of aqueous solutions considering thermal gradients and stochastic ice nucleation

Despite its importance to multiple scientific fields and industries, the freezing process of aqueous solutions is not yet completely understood. In particular, the relationship between temperature gradients within a solution and the occurrence of stochastic ice nucleation remains elusive. To address this knowledge gap, we have derived a novel stochastic spatial freezing model from first principles. The model predicts with quantitative accuracy how temperature gradients affect the stochastic ice nucleation of sucrose solutions in vials. This motivated a detailed study of the freezing-stage in freeze-drying, revealing that a broad range of temperatures are present at the time of nucleation at different positions within the vial. This must be considered when interpreting experimental studies that measure the temperature only at a single point with a thermocouple. To ensure that both researchers and practitioners benefit from this modeling work, we provide open source access to it within our python package ethz-snow.

Free energy calculations for membrane morphological transformations and insights to physical biology and oncology.

In this chapter, we aim to bridge basic molecular and cellular principles surrounding membrane curvature generation with rewiring of cellular signals in cancer through multiscale models. We describe a general framework that integrates signaling with other cellular functions like trafficking, cell-cell and cell-matrix adhesion, and motility. The guiding question in our approach is: how does a physical change in cell membrane configuration caused by external stimuli (including those by the extracellular microenvironment) alter trafficking, signaling and subsequent cell fate? We answer this question by constructing a modeling framework based on stochastic spatial continuum models of cell membrane deformations. We apply this framework to explore the link between trafficking, signaling in the tumor microenvironment, and cell fate. At each stage, we aim to connect the results of our predictions with cellular experiments.

A Spatial Stochastic Frontier Model with Endogenous Variables Including Frontier and Error

A Spatial Stochastic Frontier Model with Endogenous Variables Including Frontier and Error

Efficient Water-Saving Irrigation, Space Efficiency and Agricultural Development — Study Based on Spatial Stochastic Frontier Model

Efficient Water-Saving Irrigation, Space Efficiency and Agricultural Development — Study Based on Spatial Stochastic Frontier Model

Lotka-Volterra predator-prey model with periodically varying carrying capacity.

We study the stochastic spatial Lotka-Volterra model for predator-prey interaction subject to a periodically varying carrying capacity. The Lotka-Volterra model with on-site lattice occupation restrictions (i.e., finite local carrying capacity) that represent finite food resources for the prey population exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by the existence of spatiotemporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis in order to specifically delineate the impact of stochastic fluctuations and spatial correlations. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The (quasi-)stationary regime of our periodically varying Lotka-Volterra predator-prey system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity-switching environments, the mean-field rate equationspredict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast and slow periodic switching. The analysis of the mean-field equationsin the fast-switching regime enables a semiquantitative description of the (quasi-)stationary state.

Periodicity and Variability in Daily Activity Satisfaction: Toward a Space-Time Modeling of Subjective Well-Being

Understanding how geographical environments influence peoples’ subjective experiences of daily activities is of great potential for improving subjective well-being (SWB), a subject that is presently limited by a lack of available data and proper statistical methods. Focusing on Beijing and using a unique data set that linked residents’ seven-day mobility trajectories at a fine spatiotemporal resolution to their complete activity participation and momentary well-being, this article investigates the temporal dynamics of and geographical contextual effects on SWB of daily activities. We developed a unified spatial multilevel stochastic process model to simultaneously capture periodicity, stochastic dynamics, and individual heterogeneity effects. Results show that momentary SWB has a twenty-four-hour periodicity and evolves stochastically around individual equilibrium states depending on key life-circumstance variables. Migrants and low-income residents tend to have lower equilibrium states than their counterparts. Real-time air pollution exposure significantly lowers daily activity satisfaction levels, and an inverted-U-shaped relationship exists between city vibrancy and satisfaction.

Quantifying impacts of competition and demand on the risk for fertilizer plant locations

Fertilizer is an essential commodity traded in international and domestic markets and spatial competition is important feature impacting interfirm rivalry. In the case of North American fertilizer, numerous plants have been announced to either expand or open new plants (nitrogen-based fertilizer plants), exerting competitive pressures on an industry with surplus capacity but highly competitive in terms of production costs and technology. Proposed new plants and expansions are being induced by changes in the composition of crops, changes in the price of natural gas which affects the cost of producing domestic anhydrous ammonia. Developments in the fertilizer industry have become more volatile in the post-COVID period, and concurrent with the escalation in fuel prices, the Ukraine invasion, related embargoes on Russian trade, the world's largest exporter, and operations of the Grain Corridor. The purpose of this study is to quantify risks for plant expansion (brownfield and greenfield) of nitrogen fertilizer plants in North America, given the spatial competition and the corresponding dynamic market boundaries. Specifically, we quantify risks associated with fertilizer plant expansions, identify the optimal locations of new plants, and characterize spatial competition as a result of new entrants. A model is specified that integrates Geographical Information Systems (GIS) data into a stochastic mixed-integer network spatial optimization model using Monte Carlo simulations to account for risk in the random variables. The results are reprocessed into GIS for interpretation. The impact of risk in these variables results in market boundaries that are random. Specifically, competition for these new plants has embedded risks for new entrants on the probability of production and market penetration.

A spatial stochastic frontier model introducing inefficiency spillovers

Abstract This paper develops a spatial Durbin stochastic frontier model for panel data introducing spillover effects in the determinants of technical efficiency (SDF-STE). The model nests several existing spatial and non-spatial stochastic frontier specifications and is estimated using maximum-likelihood techniques. Estimates are shown to be unbiased even for small sample sizes and for alternative specifications of the spatial weight matrix implementing different Monte Carlo simulations. Finally, an application to the Italian accommodation sector is provided. Empirical findings suggest the relevance of the SDF-STE model in capturing labour productivity and knowledge spillover effects.

Do regional integration and trade linkages promote productivity spillovers? Evidence from the European Union

ABSTRACT This study examines the productivity and efficiency spillovers in the presence of trade linkages in 27 European Union countries from 1990 to 2019. The European Union is one of the largest trading blocs in the world and has implemented costly policies and reforms to improve productivity growth. Meanwhile, trade-induced productivity and efficiency spillovers have often been overlooked in the literature, and examining them could provide further clarity to the productivity puzzle. Using a spatial Durbin model and a bilateral trade matrix, this study estimates a spatial stochastic production frontier model using data from the Penn World Table and the World Integrated Trade Solution. We decompose production frontier estimates to obtain the spillover effects of total factor productivity growth and technical efficiency from a network of bilateral trading partners. Our results provide evidence of productivity and efficiency spillovers; however, the gains are uneven. Policy implications are discussed.

Spatial Stochastic Model of the Pre-B Cell Receptor.

Survival and proliferation of immature B lymphocytes requires expression and tonic signaling of the pre-B cell receptor (pre-BCR). This low level, ligand-independent signaling is likely achieved through frequent, but short-lived, homo interactions. Tonic signaling is also central in the pathology of precursor B acute lymphoblastic leukemia (B-ALL). In order to understand how repeated, transient events can lead to sustained signaling and to assess the impact of receptor accumulation induced by the membrane landscape, we developed a spatial stochastic model of receptor aggregation and downstream signaling events. Our rule- and agent-based model builds on previous mature BCR signaling models and incorporates novel parameters derived from single particle tracking of pre-BCR on surfaces of two different B-ALL cell lines, 697 and Nalm6. Live cell tracking of receptors on the two cell lines revealed characteristic differences in their dimer dissociation rates and diffusion coefficients. We report here that these differences affect pre-BCR aggregation and consequent signal initiation events. Receptors on Nalm6 cells, which have a lower off-rate and lower diffusion coefficient, more frequently form higher order oligomers than pre-BCR on 697 cells, resulting in higher levels of downstream phosphorylation in the Nalm6 cell line.

Systematic comparison of modeling fidelity levels and parameter inference settings applied to negative feedback gene regulation

Quantitative stochastic models of gene regulatory networks are important tools for studying cellular regulation. Such models can be formulated at many different levels of fidelity. A practical challenge is to determine what model fidelity to use in order to get accurate and representative results. The choice is important, because models of successively higher fidelity come at a rapidly increasing computational cost. In some situations, the level of detail is clearly motivated by the question under study. In many situations however, many model options could qualitatively agree with available data, depending on the amount of data and the nature of the observations. Here, an important distinction is whether we are interested in inferring the true (but unknown) physical parameters of the model or if it is sufficient to be able to capture and explain available data. The situation becomes complicated from a computational perspective because inference needs to be approximate. Most often it is based on likelihood-free Approximate Bayesian Computation (ABC) and here determining which summary statistics to use, as well as how much data is needed to reach the desired level of accuracy, are difficult tasks. Ultimately, all of these aspects-the model fidelity, the available data, and the numerical choices for inference-interplay in a complex manner. In this paper we develop a computational pipeline designed to systematically evaluate inference accuracy for a wide range of true known parameters. We then use it to explore inference settings for negative feedback gene regulation. In particular, we compare a detailed spatial stochastic model, a coarse-grained compartment-based multiscale model, and the standard well-mixed model, across several data-scenarios and for multiple numerical options for parameter inference. Practically speaking, this pipeline can be used as a preliminary step to guide modelers prior to gathering experimental data. By training Gaussian processes to approximate the distance function values, we are able to substantially reduce the computational cost of running the pipeline.