Wolfram Data Repository

Immediate Computable Access to Curated Contributed Data

Sample Data: Myrtles

Source Notebook

Locations of myrtles (an evergreen shrub with glossy foliage, white flowers, purple-black berries), with healthy/diseased marks

Details

Locations of myrtles (an evergreen shrub with glossy aromatic foliage and white flowers followed by purple-black oval berries) in the observation region Rectangle[{0, 0}, {170.5, 213}] meters, annotated with healthy and diseased marks.

Examples

Basic Examples (1) 

In[1]:=
ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "Data"]
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Summary of the spatial point data:

In[2]:=
ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "Data"]["Summary"]
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Visualizations (3) 

Plot the spatial point data:

In[3]:=
ListPlot[ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "Data"], AspectRatio -> Full]
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Visualize the data with annotations:

In[4]:=
PointValuePlot[ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "Data"], PlotLegends -> Automatic]
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Plot the smooth point density:

In[5]:=
density = SmoothPointDensity[ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "Data"]]
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In[6]:=
Show[ContourPlot[density[{x, y}], {x, y} \[Element] ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "ObservationRegion"], ColorFunction -> "Rainbow"], ListPlot[ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "Data"], PlotStyle -> Black]]
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Analysis (5) 

Compute probability of finding a point within given radius of an existing point - NearestNeighborG is the CDF of the nearest neighbor distribution:

In[7]:=
nnG = NearestNeighborG[ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "Data"]]
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In[8]:=
maxR = nnG["MaxRadius"]
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In[9]:=
DiscretePlot[nnG[r], {r, maxR/100, maxR, maxR/100}, AxesLabel -> {"radius", "probability"}]
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NearestNeighborG as the CDF of nearest neighbor distribution can be used to compute the mean distance between a typical point and its nearest neighbor - the mean of a positive support distribution can be approximated via a Riemann sum of 1- CDF. To use Riemann approximation create the partition of the support interval from 0 to maxR into 100 parts and compute the value of the NearestNeighborG at the middle of each subinterval:

In[10]:=
step = maxR/100; middles = Subdivide[step/2, maxR - step/2, 99]; values = nnG[middles];

Now compute the Riemann sum to find the mean distance between a typical point and its nearest neighbor:

In[11]:=
Total[(1 - values)*step]
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Account for scale and units:

In[12]:=
%*ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "RegionScale"]
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Test for complete spacial randomness:

In[13]:=
SpatialRandomnessTest[ResourceData[\!\(\* TagBox["\"\<Sample Data: Myrtles\>\"", #& , BoxID -> "ResourceTag-Sample Data: Myrtles-Input", AutoDelete->True]\), "Data"], {"PValue", "TestConclusion"}] // Column
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Gosia Konwerska, "Sample Data: Myrtles" from the Wolfram Data Repository (2022)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation:
    • Diggle, P.J. (2013). Statistical Analysis of Spatial and Spatio-Temporal Point Patterns (third edition) Boca Raton: Chapman and Hall/CRC Press.

Publisher Information

  • Prepared for the Wolfram Data Repository By: Gosia Konwerska
    (Wolfram Research, Inc.)
  • Publisher of Record: Gosia Konwerska