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Sample Data: London Cholera

Source Notebook

Locations of the 1854 London cholera outbreak near Golden Square annotated with marks including the number of cases, distance (in meters) to the contaminated Broad Street water pump, distance (in meters) to a non-Broad Street pump, and whether or not the Broad Street pump was the closest pump

Details

Locations of the 1854 London cholera outbreak near Golden Square in the observation region GeoBoundsRegion[{{51.51065909836119`, 51.51581097178905`}, {-0.14008439736259973`, -0.13222907147321172`}}], annotated with marks including the number of cases, distance (in meters) to the contaminated Broad Street water pump, distance (in meters) to a non-Broad Street pump, and whether or not the Broad Street pump was the closest pump.

Examples

Basic Examples (2) 

Retrieve the data:

In[1]:=
ResourceData[\!\(\*
TagBox["\"\<Sample Data: London Cholera\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: London Cholera-Input",
AutoDelete->True]\), "Data"]
Out[1]=

Summary of the spatial point data:

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

Visualizations (2) 

Plot the locations:

In[3]:=
GeoListPlot[ResourceData[\!\(\*
TagBox["\"\<Sample Data: London Cholera\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: London Cholera-Input",
AutoDelete->True]\), "Data"], GeoBackground -> "VectorMonochrome"]
Out[3]=

Visualize the number of cases per location with information whether the contaminated pump was the closest:

In[4]:=
legend = With[{cases = Union[ResourceData[\!\(\*
TagBox["\"\<Sample Data: London Cholera\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: London Cholera-Input",
AutoDelete->True]\), "Data"][{"Annotations", "Cases"}][[1]]]}, PointLegend[ColorData[97, "ColorList"][[1 ;; Length[cases]]], cases, LegendLabel -> "number of cases \n per location", LegendMarkerSize -> 20, LegendFunction -> Frame]];
In[5]:=
Legended[PointValuePlot[ResourceData[\!\(\*
TagBox["\"\<Sample Data: London Cholera\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: London Cholera-Input",
AutoDelete->True]\), "Data"], {1 -> Automatic, 2 -> None, 3 -> None, 4 -> None}, GeoBackground -> "VectorMonochrome"], legend]
Out[5]=

Analysis (3) 

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

In[6]:=
nnG = NearestNeighborG[ResourceData[\!\(\*
TagBox["\"\<Sample Data: London Cholera\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: London Cholera-Input",
AutoDelete->True]\), "Data"]]
Out[6]=
In[7]:=
maxRadius = nnG["MaxRadius"]
Out[7]=
In[8]:=
maxR = QuantityMagnitude[maxRadius, "km"]
Out[8]=
In[9]:=
DiscretePlot[
 nnG[Quantity[r, "Kilometers"]], {r, maxR/100, maxR, maxR/100}, AxesLabel -> {"radius", "probability"}]
Out[9]=

Mean distance between a typical point and its nearest neighbor (for positive support distribution can be approximated via a Riemann sum of 1-CDF):

In[10]:=
step = Quantity[maxR/100, "km"];
partition = Table[{k, k + step}, {k, Quantity[0, "km"], Quantity[maxR, "km"], step}];
values = nnG[Mean /@ partition];
In[11]:=
Total[(1 - values)*step]
Out[11]=

Test for complete spacial randomness:

In[12]:=
SpatialRandomnessTest[ResourceData[\!\(\*
TagBox["\"\<Sample Data: London Cholera\>\"",
#& ,
BoxID -> "ResourceTag-Sample Data: London Cholera-Input",
AutoDelete->True]\), "Data"], {"PValue", "TestConclusion"}]
Out[12]=

Gosia Konwerska, "Sample Data: London Cholera" from the Wolfram Data Repository (2021) 

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