task iii-problem in spatial data analysis

8/7/2019 Task III-Problem in Spatial Data Analysis

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PROBLEMS IN SPATIAL DATA ANALYSIS

(3 RD PRESENTATION)

Presented by:

TauFiQ(10-8705-601-8)

Master Degree of Civil and Environment EngineeringMaster Degree of Civil and Environment Engineering 20102010


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Objective:

To understand ways in which properties of spatialdata raise important issues for the statistical

analysis of such data.

3UREOHPV LQ 6SDWLDO 'DWD $QDO\VLV


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2.3.1 Conceptual Models & Inference Frameworks for Spatial Data

2.3.2 Modelling Spatial Variation (Next Meeting)

Discussion Materials :

6SDWLDO 'DWD $QDO\VLV3UREOHPV LQ 6SDWLDO 'DWD $QDO\VLV


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6SDWLDO 'DWD $QDO\VLV

2.3 Problems in Spatial Data Analysis2.3.1 Conceptual models and inference frameworks for

spatial data

The classical inference model assumes that data are the outcome of some well defined experiment. This experiment can

be replicated as many times as necessary.

In this classical context, Inference with spatial data, is concerned with making statements and assessing the evidence regarding

properties of the underlying process responsible for the data.



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The hypothetical universe of realisation or super-population is often viewed with considerable skepticism as a model for real spatial data analysis.

It is sometimes argued that the classical perspective is justifiable when the processes responsible for the observations appear to contain inherent random components and where other instances of the same process can be indicated.



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Another model for spatial data which has some features in

common with the classical inference model is where the datarepresent sample observations from a given surface. Henley (1981) describes that the spatial surface is continuously varyingbut fixed, all variation is associated with the actual form of the realsurface.

The model which Henley uses as the model for non parametricapproaches to geo-statistical site interpolation and mapping, reject assumptions of replication and stationarity. This is contrasts with

the earlier models for kriging where the realised surface is but one of many form a super-population of surfaces (Matheron, 1971).



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The difference between these two analogues of the classical

inference model lies in the existence of a universe of possible surfaces. Difficulties for classical inference arise if we adopt adeterministic perspective and the data represent an exhaustive survey.

The classical inference model still seems tenable if:a. there is random error associated with measurement of surface

properties

b. the surface is sampled c. the values at the sites are themselves the result of a sample



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Both ways of relating spatial data analysis to the framework provided by classical statistical inference assume that data arise as if from a

controlled experimental situation. This assumption does carry with it some implicit assumptions, in particular the axiom of correct specification. Leamer (1978) specifies the axiom as follows

a. The set of explanatory variables that are thought to determine the response variable must be: unique, complete, small in number,

observable b. Other determinations of the response variable must have a probability

distribution with at most a few unknown parameters c. All unknown parameters must be constant



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If there is no experiment defining or specifying the model that should be fit to the data, probabilities are not well defined. As a consequence, classicalinference procedures that depend on evaluating probabilities are not on firm

ground.

Leamer defines three groups of data analysts in terms of their response tothis situation: believers (those who report results as if they were the outcome of a controlled experiment), agnostics (those who do not deal with

standard errors and seek only descriptive summaries of data and discount all results until tried out on another set of data), and pragmatists (who thinkthat tehe agnostics go too far and that standard errors shoul be reported)

Leamer (1978) emphasis two other areas of difference with classicalinference procedures based on Fisher & Neyman-Pearson inference:

a. The purpose of statistical inference in the context of control experimentation is to estimate unknown parameters and test hypothesis

b. Classical judgments are made solely with respect to the current set of data



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The brackets after each description indicate the type of failure of The axiom of correct specification as follows (Leamer, 1978):a. Hypothesis testing

Several possible regression models justified by theoreticalconsiderations and the analyst test to see which one is best supported by the evidence

b. Interpretive searchingOne registration model is chosen to describe the data and the analyst tries to make the model fit the data better, perhaps by imposingconstraints on the parameters

b. Simplification searches

A regression model chosen under (a) or (b) may be very complicated and the analyst tries to reduce the complexity of the model whilst retaining adequacy of fit



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d. Proxy searches A regression model is chos en but it is known that variables canbe measur ed in many diff erent ways

e. Data selection sear chesFitting a model with diff erent subsets of data or diff erent

tr ansfor mations of the data and selecting the result thatappears bestf. Post-data model constr uction

Apurely inductive sear ch to tryand account as well as possiblefor obser ved var iation in a response var iable, of ten involves

sear ching for additional var iable s to impr ove the level of explanation


C ontinue


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Diaconis (1985) reviews alternatives to the usual classicaltheor ies of inf erence in the context of explanatory dataanalysis, where the pur pose of data analysis on non-exper imental data is to detect str ucture and pattern.

The choice of inf erence f r amewor k will ar ise again later and itis at least ar guable that the devising of appr opr iate inf erence

f r amewor ks is one of the most fundamental issues in spatialanalysis.



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THANK YOU

task iii-problem in spatial data analysis

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