From e8963a86ead0f5516948b3ad55b410b7fc5fb194 Mon Sep 17 00:00:00 2001 From: "Miss Islington (bot)" <31488909+miss-islington@users.noreply.github.com> Date: Mon, 14 Aug 2023 07:58:54 -0700 Subject: [PATCH] [3.12] Add another example to the statistics docs (GH-107904) (#107941) Add another example to the statistics docs (GH-107904) (cherry picked from commit 2b6dc2accc315ce279d259ed39e058a225068531) Co-authored-by: Raymond Hettinger --- Doc/library/kde_example.png | Bin 0 -> 332212 bytes Doc/library/statistics.rst | 57 ++++++++++++++++++++++++++++++++++++ 2 files changed, 57 insertions(+) create mode 100644 Doc/library/kde_example.png diff --git a/Doc/library/kde_example.png b/Doc/library/kde_example.png new file mode 100644 index 0000000000000000000000000000000000000000..f45048956999741a6889bdfe85c40e1f25e8863b GIT binary patch literal 332212 zc-ri|XH-*L*EUR*AOcZ(2MegwfDn)lDk>m01nH1N5P?u4y@V1(rRhN+ND~Vv9YK0W z5;dU+NPqwVVrZdv5&~a1-}AihxIOoH#(2)J_s2~J**n=gJ1c9>dCluuYp(tD<_#0> 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approximate `Binomial distributions `_ when the sample size is large and when the probability of a successful @@ -1000,6 +1011,10 @@ probability that the Python room will stay within its capacity limits? >>> mean(trial() <= k for i in range(10_000)) 0.8398 + +Naive bayesian classifier +************************* + Normal distributions commonly arise in machine learning problems. Wikipedia has a `nice example of a Naive Bayesian Classifier @@ -1054,6 +1069,48 @@ The final prediction goes to the largest posterior. This is known as the 'female' +Kernel density estimation +************************* + +It is possible to estimate a continuous probability density function +from a fixed number of discrete samples. + +The basic idea is to smooth the data using `a kernel function such as a +normal distribution, triangular distribution, or uniform distribution +`_. +The degree of smoothing is controlled by a single +parameter, ``h``, representing the variance of the kernel function. + +.. testcode:: + + import math + + def kde_normal(sample, h): + "Create a continous probability density function from a sample." + # Smooth the sample with a normal distribution of variance h. + kernel_h = NormalDist(0.0, math.sqrt(h)).pdf + n = len(sample) + def pdf(x): + return sum(kernel_h(x - x_i) for x_i in sample) / n + return pdf + +`Wikipedia has an example +`_ +where we can use the ``kde_normal()`` recipe to generate and plot +a probability density function estimated from a small sample: + +.. doctest:: + + >>> sample = [-2.1, -1.3, -0.4, 1.9, 5.1, 6.2] + >>> f_hat = kde_normal(sample, h=2.25) + >>> xarr = [i/100 for i in range(-750, 1100)] + >>> yarr = [f_hat(x) for x in xarr] + +The points in ``xarr`` and ``yarr`` can be used to make a PDF plot: + +.. image:: kde_example.png + :alt: Scatter plot of the estimated probability density function. + .. # This modelines must appear within the last ten lines of the file. kate: indent-width 3; remove-trailing-space on; replace-tabs on; encoding utf-8; -- 2.47.3