Add Fisher paper quotes and references

Notebooks/Introductory/Likelihood-Function.ipynb

@@ -116,11 +116,17 @@
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    "metadata": {},
    "source": [
-    "As the likelihood is a function of the parameters only, then it is seen that it is **a function of probability density functions given observed data**. \n",
+    "The likelihood function has proven to be a difficult object to define clearly, as even Fisher only defined it as\n",
+    "\n",
+    "> \"the term \\[...\\] to designate the state of our information with respect to the parameters of hypothetical populations, and it is shown that the quantitative measure of likelihood does not obey the mathematical laws of probability.\" \\[1\\]\n",
+    "\n",
+    "As the likelihood is a function of the parameters only, then it is seen that it is **a function of probability density functions given observed data**.\n",
     "\n",
     "Its values represent the relative compatability (in some sense) of parameter values with the considered model given the observed data. The greater the value of the likelihood for a parameter value the more compatable the model (with that parameter value) is with the data. There is no sense of an absolute scale of a likelihood (given its formation from an arbitrary number of products of p.d.f.s), but rather its scale is the relative scale of its minimum value and maximum value.\n",
     "\n",
-    "The likelihood is **not** a probability density. This can most easily be realized by noting that as the likelihood is a function of the parameters only it has no contstraint that it is normalized to unity. Indeed, it is not even required to be normalizable. \\[1\\]"
+    ">\"There is therefore an absolute measure of probability in that the unit is chosen so as to make all the elementary probabilities add up to unity. There is no such absolute measure of likelihood.\" \\[1\\]\n",
+    "\n",
+    "The likelihood is **not** a probability density. This can most easily be realized by noting that as the likelihood is a function of the parameters only it has no contstraint that it is normalized to unity. Indeed, it is not even required to be normalizable. \\[1,2\\]"
    ]
   },
   {
@@ -136,7 +142,7 @@
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    "metadata": {},
    "source": [
-    "### Example: A single sample from the Bernoulli distribution \\[2\\]"
+    "### Example: A single sample from the Bernoulli distribution \\[3\\]"
    ]
   },
   {
@@ -237,7 +243,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Example: The likelihood function for the mean of a Guassian"
+    "### Example: The likelihood function for the mean of a Gaussian"
    ]
   },
   {
@@ -396,8 +402,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "- \\[1\\] K. Cranmer, \"[Practical Statistics for the LHC](https://inspirehep.net/record/1356277),\" arXiv:1503.07622 \\[hep-ex\\].\n",
-    "- \\[2\\] [Cross Validated: What is the reason that a likelihood function is not a pdf?](https://stats.stackexchange.com/questions/31238/what-is-the-reason-that-a-likelihood-function-is-not-a-pdf)"
+    "- \\[1\\] R. Fisher, \"[On the Mathematical Foundations of Theoretical Statistics](http://www.jstor.org/stable/91208)\", _Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character_, Vol. 222, (1922), pp. 309-368\n",
+    "   - This is the paper in which Fisher first introduces the idea of the \"method of maximum likelihood\".\n",
+    "- \\[2\\] K. Cranmer, \"[Practical Statistics for the LHC](https://inspirehep.net/record/1356277),\" arXiv:1503.07622 \\[hep-ex\\].\n",
+    "- \\[3\\] [Cross Validated: What is the reason that a likelihood function is not a pdf?](https://stats.stackexchange.com/questions/31238/what-is-the-reason-that-a-likelihood-function-is-not-a-pdf)"
    ]
   }
  ],