Prior Information in Spatial Analysis

1978 ◽  
Vol 10 (1) ◽  
pp. 51-70 ◽  
Author(s):  
J Odland
Keyword(s):  
Spatial Data ◽  
Statistical Models ◽  
Prior Information ◽  
Population Distribution ◽  
Analytical Models ◽  
Distribution Model ◽  
Density Functions ◽  
Growth Processes ◽  
Statistical Procedures ◽  
General Statistical

Formal statistical procedures which incorporate prior, or nonsample, information can be used to enlarge the theoretical and empirical content of analytical models, and can be widely applied to adapt general statistical procedures for special investigative situations which arise in the analysis of spatial data. A class of methods which operate by modifying the parameter space of general statistical models in accordance with prior information is presented in this paper. The prior information can be obtained from theoretical or empirical sources, and the models can be given Bayesian as well as non-Bayesian interpretations. The utility of the methods is demonstrated by applying them to estimate parameters for urban-population-density functions. The resulting estimates incorporate nonsample information on total populations as well as sample information on subarea densities. The logic of the population-distribution model is also extended to take account of possible growth processes by incorporating prior information derived from earlier distributions and by incorporating the characteristics of possible growth processes.

Log-Linear Models with Dependent Spatial Data

1983 ◽  
Vol 15 (6) ◽  
pp. 801-813 ◽  
Author(s):  
B Fingleton
Keyword(s):  
Spatial Data ◽  
Statistical Models ◽  
Linear Models ◽  
Square Lattice ◽  
Categorical Variables ◽  
Systematic Sampling ◽  
Pairwise Correlations ◽  
Independent Observations ◽  
Intersection Points ◽  
Log Linear

Log-linear models are an appropriate means of determining the magnitude and direction of interactions between categorical variables that in common with other statistical models assume independent observations. Spatial data are often dependent rather than independent and thus the analysis of spatial data by log-linear models may erroneously detect interactions between variables that are spurious and are the consequence of pairwise correlations between observations. A procedure is described in this paper to accommodate these effects that requires only very minimal assumptions about the nature of the autocorrelation process given systematic sampling at intersection points on a square lattice.

Numerical Simulation of Inversion Population Distribution in Diode-End-Pumped Quasi-Three-Level Laser

2011 ◽  
Vol 345 ◽  
pp. 338-342
Author(s):  
Zhi Zhang Song ◽  
Qin An Li ◽  
Tao Zhang
Keyword(s):  
Numerical Simulation ◽  
Solid State ◽  
Continuous Wave ◽  
Population Distribution ◽  
Gain Medium ◽  
Solid State Laser ◽  
Distribution Model ◽  
State Laser ◽  
Level Laser

In this paper, the inversion population distribution model in the gain medium are given and simulated numerically corresponding to different cavity conditions for the continuous wave diode-end-pumped quasi-three-level solid-state laser.

scholarly journals An Integrative Dynamic Model of Colombian Population Distribution, Based on the Maximum Entropy Principle and Matter, Energy, and Information Flow

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1172
Author(s):  
César Cardona-Almeida ◽  
Nelson Obregón ◽  
Fausto A. Canales
Keyword(s):  
Maximum Entropy ◽  
Information Exchange ◽  
New Technologies ◽  
Population Distribution ◽  
Knowledge Society ◽  
Maximum Entropy Principle ◽  
Distribution Model ◽  
Human Society ◽  
Natural Systems ◽  
Entropy Principle

Human society has increased its capacity to exploit natural resources thanks to new technologies, which are one of the results of information exchange in the knowledge society. Many approaches to understanding the interactions between human society and natural systems have been developed in the last decades, and some have included considerations about information. However, none of them has considered information as an active variable or flowing entity in the human–natural/social-ecological system, or, moreover, even as a driving force of their interactions. This paper explores these interactions in socio-ecological systems by briefly introducing a conceptual frame focused on the exchange of information, matter, and energy. The human population is presented as a convergence variable of these three physical entities, and a population distribution model for Colombia is developed based on the maximum entropy principle to integrate the balances of related variables as macro-state restrictions. The selected variables were electrical consumption, water demand, and higher education rates (energy, matter, and information). The final model includes statistical moments for previous population distributions. It is shown how population distribution can be predicted yearly by combining these variables, allowing future dynamics exploration. The implications of this model can contribute to bridging information sciences and sustainability studies.

ArcEGMO-URBAN — Hydrological model for point sources in river basins

2005 ◽  
Vol 52 (5) ◽  
pp. 249-256 ◽  
Author(s):  
M. Biegel ◽  
J. Schanze ◽  
P. Krebs
Keyword(s):  
Spatial Data ◽  
Population Distribution ◽  
Wastewater Treatment Plants ◽  
Remote Sensing Data ◽  
River Basins ◽  
Point Sources ◽  
Urban Land Use ◽  
Nitrogen And Phosphorus ◽  
Sewer Systems ◽  
Pumping Stations

The new model ArcEGMO-URBAN aims at deterministic and spatiotemporal modelling of water, nitrogen and phosphorus fluxes from all urbanised areas of a river basin considering all potential sources. Pollution loads are calculated for discrete urban patches and balanced on the level of hydrological sub-basins. Modelling results can be defined by the user of any level of spatial and/or temporal aggregation, e.g. matter balances for river basins or river sections and years or months, respectively. To process spatial data, a Geographic Information System is linked to the model. Information on urban land use and general characteristics of river basins is based on digital coverages, partly generated from remote-sensing data. Moreover, statistical data, e.g. on population, sewer systems, wastewater treatment plants etc. are included. Stormwater runoff from impervious surfaces is calculated as one input to the sewer network. Wastewater is considered with its main sewer system, pumping stations and treatment plants. Finally, the discharge is balanced for discrete river sections. Modelling results attest ArcEGMO-URBAN its ability to realistically quantify matter fluxes and major pollution sources as well as their seasonal variation. This makes the model an applicable tool for the analysis of scenarios with e.g. varying population distribution or climatic and technological conditions.

scholarly journals Challenges of ecological monitoring: estimating population abundance from sparse trap counts

2011 ◽  
Vol 9 (68) ◽  
pp. 420-435 ◽  
Author(s):  
Natalia Petrovskaya ◽  
Sergei Petrovskii ◽  
Archie K. Murchie
Keyword(s):  
Population Size ◽  
Numerical Integration ◽  
Spatial Data ◽  
Population Distribution ◽  
Species Abundance ◽  
Ecological Monitoring ◽  
Field Studies ◽  
Pest Species ◽  
Population Size Estimates ◽  
Size Estimates

Ecological monitoring aims to provide estimates of pest species abundance—this information being then used for making decisions about means of control. For invertebrate species, population size estimates are often based on trap counts which provide the value of the population density at the traps' location. However, the use of traps in large numbers is problematic as it is costly and may also be disruptive to agricultural procedures. Therefore, the challenge is to obtain a reliable population size estimate from sparse spatial data. The approach we develop in this paper is based on the ideas of numerical integration on a coarse grid. We investigate several methods of numerical integration in order to understand how badly the lack of spatial data can affect the accuracy of results. We first test our approach on simulation data mimicking spatial population distributions of different complexity. We show that, rather counterintuitively, a robust estimate of the population size can be obtained from just a few traps, even when the population distribution has a highly complicated spatial structure. We obtain an estimate of the minimum number of traps required to calculate the population size with good accuracy. We then apply our approach to field data to confirm that the number of trap/sampling locations can be much fewer than has been used in many monitoring programmes. We also show that the accuracy of our approach is greater that that of the statistical method commonly used in field studies. Finally, we discuss the implications of our findings for ecological monitoring practice and show that the use of trap numbers ‘smaller than minimum’ may still be possible but it would result in a paradigm shift: the population size estimates should be treated probabilistically and the arising uncertainty may introduce additional risk in decision-making.

A Comparison of Some Multivariate Weibull Distributions

2010 ◽  
Author(s):  
Bernt J. Leira
Keyword(s):  
Probability Density ◽  
Density Function ◽  
Statistical Models ◽  
Mechanical Design ◽  
Bending Moment ◽  
Probability Density Functions ◽  
Density Functions ◽  
Weibull Distributions ◽  
Linear Combinations ◽  
Simplified Procedure

Three different possible choices of statistical models for multivariate Weibull distributions are considered and compared. The concept of “a correlation field” is introduced and is subsequently applied for the purpose of comparing the different models. Linear combinations of Weibull distributed random variables are considered, and expressions for the corresponding probability density functions are established. Furthermore, a simplified procedure for approximating the resulting density function is described. Comparison is made between the statistical moments of increasing order for the specific case of two Weibull components. This example of application arises e.g. in connection with mechanical design of a column which is subjected to a bi-axial bending moment.

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