Wolfram Data Repository

Immediate Computable Access to Curated Contributed Data

British Coal Mining Disaster Data

Source Notebook

British coal mine disaster data by year for the years 1851-1962

Details

Data are in the format (year, number of disasters).

Examples

Basic Examples (1) 

In[1]:=
ts = ResourceData[\!\(\* TagBox["\"\<British Coal Mining Disaster Data\>\"", #& , BoxID -> "ResourceTag-British Coal Mining Disaster Data-Input", AutoDelete->True]\)]
Out[1]=

Isolate the number of disasters by year:

In[2]:=
count = ts["Values"]
Out[2]=

Visualizations

In[3]:=
ts = ResourceData[\!\(\* TagBox["\"\<British Coal Mining Disaster Data\>\"", #& , BoxID -> "ResourceTag-British Coal Mining Disaster Data-Input", AutoDelete->True]\)]; count = ts["Values"]; DiscretePlot[count[[k]], {k, 1, Length[count]}, Sequence[ Axes -> False, Frame -> True, FrameLabel -> {"1850+year", "number of disasters"}, BaseStyle -> {FontFamily -> "Arial", FontSize -> 14}, AspectRatio -> 1]]
Out[4]=

Analysis (2) 

The year of the most prominent change can be found by the following procedure. Let k denote this year and assume that the data on either side of k are Poisson distributed with respective means θ and λ. Then the likelihood of k on a log scale is given by the following function:

In[5]:=
logLikelihood[k_, count_] := Module[{count1, count2, \[Theta], \[Lambda]}, {count1, count2} = N[{Take[count, {1, k}], Take[count, {k + 1, Length[count]}]}]; \[Theta] = Mean[count1]; \[Lambda] = Mean[count2]; Total[count1] Log[\[Theta]] - Length[count1] \[Theta] + Total[count2] Log[\[Lambda]] - Length[count2] \[Lambda]]

An estimate for the posterior probability mass of the unknown value of k under the assumption of a flat prior probability mass function for k is:

In[6]:=
ts = ResourceData[\!\(\* TagBox["\"\<British Coal Mining Disaster Data\>\"", #& , BoxID -> "ResourceTag-British Coal Mining Disaster Data-Input", AutoDelete->True]\)]; count = ts["Values"]; posterior = Table[logLikelihood[k, count], {k, 1, Length[count]}]; posterior = Exp[posterior - Max[posterior]]; posterior = posterior/Total[posterior]; ListLinePlot[posterior, Sequence[ PlotRange -> All, Axes -> False, Frame -> True, FrameLabel -> {"1850+year", "probability mass"}, BaseStyle -> {FontFamily -> "Arial", FontSize -> 14}, AspectRatio -> 1, Filling -> Axis]]
Out[11]=

Marshall Bradley, "British Coal Mining Disaster Data" from the Wolfram Data Repository (2022)  

Data Resource History

  • Date Created:

Source Metadata

  • Citation:
    • Lesaffre, Emmanuel and Lawson, Andrew (2012), Bayesian Biostatistics, Wiley.

Publisher Information

  • Prepared for the Wolfram Data Repository By: Marshall Bradley
  • Publisher of Record: Marshall Bradley