Python Sample Programs
Programs at these websites can be freely downloaded
and used.
The constructer of these websites disclaims all
responsibility.
The user takes responsibility for his/her usage.
Yasuharu Okamoto
Another Website-1, Website-2, Website-3
It is easy to install Python in Windows.
When you want to use a version other than the latest one of Python, you can choose the version.
Two ways of choice of Python are explained.
For some modules, a version of the module must be selected for the version of the Python.
These selection are automatically done by Anaconda.
Easy Ways to PyStan and PyMC3
in Windows
PyStan (the Python interface for Stan) and PyMC3 can be used easily in Windows,
when they are installed in Anaconda, which can be installed easily.
On PyStan 2.18 /Windows Errors (2018.10.28)
An easy way to install Python3 on CenOS 7
A simple Python script of painting figures is presented as an example.
Calling Python Script from C/C++
Program
Python script is called from C/C++ program and
Python script calls a command.
A Simple Python Script of a
Digital Clock
A simple Python script of a digital clock is presented.
Common
Quantification of Categorical Data
This quantification gives numerical values to categorical items, which can be used with other numerical items in various analysis.
That is, this quantification can be used as data preprocessing in machine learning.
One Hot Encoding and Common
Quantification
One Hot Encoding and common quantification are methods to preprocess categorical attributes (variables).
One Hot Encoding treats values of categorical attributes individually and is used in machine learning.
On the other hand, common quantification treats values of categorical attribute from the point of view of maximization of the variance of the attribute.
Comparison of the two methods is presented with the programs.
Principal Components
Analysis with Rotation
Principal components analysis is interpreted from the point of view of
orthogonal projection of the data space onto its subspace.
Demonstration of The Curse of
Dimensionality
Python scripts, which show the curse of dimensionality, were presented.
3D-Drawing of a
Bivariate Normal Distribution
A simple script for drawing a bivariate normal distribution was prepared.
3D-Drawing of a Binomial
Distribution in Bayesian Statistics
A joint distribution of probability parameter and frequency data
was displayed as a 3-D graphic image.
Drawing a Graph of Fisher
Information Functions in IRT
A graph of item information functions and the test information function was drawn by a simple program in Python.
LfEcuyer, et al.fs (2002) algorithm of random number generation has long period, about 2**191,
and is easily partitioned into subsequences, each of which has practically sufficient long period.
Their algorithm can be easily implemented purely in Python.
MCMC with
Multiprocessing in Python
Multiple Markov chains are run concurrently using multiprocessing in Python
We can save much time by storing a Stan model and sampling results by a Stan model
using the package pickle of Python.
Sampling data by PyMC3 can be saved in a file using the pickle library.
You can read out this file to use in the following analysis.
Variation of Posterior
Distribution: Simulation with PyStan using pickle
Posterior distribution in Bayesian analysis depends on the data, which is sampled randomly from a population.
So, posterior distribution varies from a sample to another one. This random variation of posterior distribution was investigated by simulation.
Bayesian Point Estimates and
Highest Density Intervals
Relations of highest density intervals (HDIs) and the three estimates, mean, median, and MAP estimate, were investigated by simulation.
Stan Scripts for Estimation of JND
and PSE
Stan scripts for analyses of data from 2AFC experiments
which use more than two response categories were developed.
A Stan script for a usual method using binary judgment was also developed.
Bayesian Estimation of
JND and PSE
Psychometric functions are estimated by Bayesian analysis of discrimination data from
two-alternative procedure (the standard method in psychophysics),
three-alternative procedure, which is proposed by some authors and allows
gdonft knowh judgment, or four-alternative procedure, in which gprobableh judgments
are allowed. Just noticeable difference (JND) and the point of subjective equality (SPE)
are estimated based on the psychometric functions.
Bayesian Analysis in Signal Detection
Theory (SDT)
Python scripts using Stan (PyStan) were developed for analyses of
Data in Signal Detection Theory. The programs analyze data from a Yes/No experiment or
data from that using a rating method.
A Stan Script for IRT of Binary Items
A logistic model for binary items in Item Response Theory was employed
to develop a Stan script, which was used by a Python script.
A Stan Script for IRT of Polytomous
Items
The graded response model for polytomous items was employed
to develop a Stan script, which was used by a Python script.
Posterior Probability of gEffectiveh as a Function of the Power of the Test
How the probability of gEffectiveh changes
after the results of the statistical test shows that geffectiveh is significant
is dependent on the power of the statistical test.
Variables in Python are references to objects, so they can be used like pointers in C/C++.
A sample program, in which objects are linked using pointer-like variables, is written in Pyhton.
Sample Programs using Stan in Python
Simple programs in Python for Bayesian analysis of univariate and multivariate data were written
using PyStan, the Python interface to Stan.
Simple Stan scripts for a normal distribution and a bivariate normal distribution are presented.
Scripts are written in PyStan 3.