PointProcessFitTest

PointProcessFitTest[pdata]

tests whether the point collection pdata could be modeled by a Poisson point process.

PointProcessFitTest[pdata,pproc]

tests whether the point collection could be modeled by the point process pproc.

PointProcessFitTest[pdata,pproc,"property"]

returns the value of "property".

Details and Options

  • PointProcessFitTest performs a goodness-of-fit hypothesis test with null hypothesis that pdata was drawn from a point process pproc and alternative hypothesis that it was not.
  • By default, a probability value or -value is returned.
  • A small -value suggests that it is unlikely that pdata comes from a pproc.
  • The point data pdata can have the following forms:
  • {p1,p2,}points pi
    GeoPosition[],GeoPositionXYZ[],geographic points
    SpatialPointData[]spatial point collection
    {pts,reg}point collection pts and observation region reg
  • If the observation region reg is not given, a region is automatically computed using RipleyRassonRegion.
  • Under the null hypothesis , the points in pdata were drawn from pproc. In particular, this means they should have the same BesagL function.
  • The following tests can used:
  • "BesagL"computes BesagL on simulations of pproc and pdata
    "ChiSquare"based on binning, where standard bin count residuals are expected to be chi-square distributed, fast and approximate
    "ModifiedChiSquare"
  • based on binning, where counts are expected to be multinomially distributed, exact for small samples, using "ChiSquare" for large data
  • PointProcessFitTest[data,proc,"HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
  • PointProcessFitTest[data,pproc,"property"] can be used to directly give the value of "property".
  • Properties related to the reporting of test results include:
  • "AllTests"list of all applicable tests
    "AutomaticTest"test chosen if Automatic is used
    "PValue"list of -values
    "PValueTable"formatted table of -values
    "ShortTestConclusion"a short description of the conclusion of a test
    "TestConclusion"a description of the conclusion of a test
    "TestData"list of pairs of test statistics and -values
    "TestDataTable"formatted table of -values and test statistics
    "TestStatistic"list of test statistics
    "TestStatisticTable"formatted table of test statistics
  • The following options can be used:
  • SignificanceLevel0.05cutoff for diagnostics and reporting
    MethodAutomaticBesagL method takes suboptions

Examples

open allclose all

Basic Examples  (2)

Uniform point distribution on a disk:

The data came from a point process with homogeneous intensity:

Points distributed over a geographical region:

Estimated PoissonPointProcess:

Test the goodness of fit:

Scope  (10)

Testing  (7)

Testing:

The -values are typically large when points are uniformly distributed:

The -values are typically small when there is spatial heterogeneity:

Perform a particular test for spatial randomness:

Using Automatic applies the "BesagL" test:

The property "AutomaticTest" can be used to determine which test was chosen:

Perform all tests appropriate to the data simultaneously:

Use the property "AllTests" to see which tests are available:

Create a HypothesisTestData object for repeated property extraction:

The properties available for extraction:

Extract some properties from the HypothesisTestData object:

The -value and test statistic from the "BesagL" test:

Extract any number of properties simultaneously:

The -value and test statistic from a "BesagL" test:

Reporting  (3)

Tabulate the results from a selection of tests:

A full table of all appropriate test results:

A table of selected test results:

Retrieve the entries from a test table for customized reporting:

The -values are above 0.05, so there is not enough evidence to reject at that level:

Tabulate -values for a test or group of tests:

The -value from the table:

A table of -values from all appropriate tests:

Options  (2)

SignificanceLevel  (1)

The significance level is used for "TestConclusion" and "ShortTestConclusion":

The test conclusions may differ:

Full test conclusions:

MaxIterations  (1)

You can control the number of simulations with suboption MaxIterations:

Properties & Relations  (1)

PointProcessFitTest can be used to test equivalence of complete spatial randomness:

SpatialRandomnessTest has built-in, more specific tests:

Neat Examples  (1)

Distribution of the "ChiSquare" test statistic under a null hypothesis:

Wolfram Research (2020), PointProcessFitTest, Wolfram Language function, https://reference.wolfram.com/language/ref/PointProcessFitTest.html.

Text

Wolfram Research (2020), PointProcessFitTest, Wolfram Language function, https://reference.wolfram.com/language/ref/PointProcessFitTest.html.

BibTeX

@misc{reference.wolfram_2020_pointprocessfittest, author="Wolfram Research", title="{PointProcessFitTest}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/PointProcessFitTest.html}", note=[Accessed: 16-January-2021 ]}

BibLaTeX

@online{reference.wolfram_2020_pointprocessfittest, organization={Wolfram Research}, title={PointProcessFitTest}, year={2020}, url={https://reference.wolfram.com/language/ref/PointProcessFitTest.html}, note=[Accessed: 16-January-2021 ]}

CMS

Wolfram Language. 2020. "PointProcessFitTest." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PointProcessFitTest.html.

APA

Wolfram Language. (2020). PointProcessFitTest. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PointProcessFitTest.html