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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Bayesian Correlated t-test
Module correlated_ttest in bayesiantests can be used to perform the correlated t-test on the performance of two classifiers that have been assessed by $m$-runs of $k$-fold cross-validation  on the same dataset
This notebook demonstrates the use of the module.
We will load the classification accuracies of the naive Bayesian classifier (NBC) and AODE on the dataset Anneal from the file Data/nbc_anneal.csv and Data/aode_anneal.csv.  The classifiers have been evaluated by 10-runs of 10-fold cross-validation.
Step1:  Functions in the module accept the following arguments.
x
Step2:  We can also plot the posterior distribution.
Step3:  We will load the classification accuracies of NBC and AODE on the dataset Audiology from the file.  The classifiers have been evaluated by 10-runs of 10-fold cross-validation.
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Python Code:
import numpy as np
Acc_nbc =  np.loadtxt('Data/nbc_anneal.csv',  delimiter=',', skiprows=1)
Acc_aode = np.loadtxt('Data/aode_anneal.csv', delimiter=',', skiprows=1)
names = ("AODE", "NBC")
x=np.zeros((len(Acc_nbc),2),'float')
x[:,0]=Acc_aode/100
x[:,1]=Acc_nbc/100
#we consider the difference of accuracy scaled in (0,1)
Explanation: Bayesian Correlated t-test
Module correlated_ttest in bayesiantests can be used to perform the correlated t-test on the performance of two classifiers that have been assessed by $m$-runs of $k$-fold cross-validation  on the same dataset
This notebook demonstrates the use of the module.
We will load the classification accuracies of the naive Bayesian classifier (NBC) and AODE on the dataset Anneal from the file Data/nbc_anneal.csv and Data/aode_anneal.csv.  The classifiers have been evaluated by 10-runs of 10-fold cross-validation.
End of explanation
import bayesiantests as bt
rope=0.01
left, within, right = bt.correlated_ttest(x, rope=rope,runs=10,verbose=True,names=names)
Explanation: Functions in the module accept the following arguments.
x: a 2-d array with scores of two models (each row corresponding to a data set) or a vector of differences.
rope: the region of practical equivalence. We consider two classifiers equivalent if the difference in their performance is smaller than rope. 
runs:  number of repetitions of cross validation 
names: the names of the two classifiers; if x is a vector of differences, positive values mean that the second (right) model had a higher score.
verbose: when True the functions also prints out the probabilities
End of explanation
import warnings
warnings.filterwarnings('ignore')
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as snb
#generate samples from posterior (it is not necesssary because the posterior is a Student)
samples=bt.correlated_ttest_MC(x, rope=rope,runs=10,nsamples=50000)
#plot posterior
snb.kdeplot(samples, shade=True) 
#plot rope region
plt.axvline(x=-rope,color='orange')
plt.axvline(x=rope,color='orange')
#add label
plt.xlabel('Nbc-Aode on Anneal dataset');
Explanation: We can also plot the posterior distribution.
End of explanation
import numpy as np
Acc_nbc =  np.loadtxt('Data/nbc_audiology.csv',  delimiter=',', skiprows=1)
Acc_aode = np.loadtxt('Data/aode_audiology.csv', delimiter=',', skiprows=1)
names = ("AODE", "NBC")
diff=(Acc_nbc-Acc_aode)/100.0 #we consider the difference of accuracy scaled in (0,1)
import bayesiantests as bt
rope=0.01
left, within, right = bt.correlated_ttest(diff, rope=rope,runs=10,verbose=True,names=names)
import warnings
warnings.filterwarnings('ignore')
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as snb
#generate samples from posterior (it is not necesssary because the posterior is a Student)
samples=bt.correlated_ttest_MC(diff, rope=rope,runs=10,nsamples=50000)
#plot posterior
snb.kdeplot(samples, shade=True) 
#plot rope region
plt.axvline(x=-rope,color='orange')
plt.axvline(x=rope,color='orange')
#add label
plt.xlabel('Nbc-Aode on Audiology dataset');
Explanation: We will load the classification accuracies of NBC and AODE on the dataset Audiology from the file.  The classifiers have been evaluated by 10-runs of 10-fold cross-validation.
End of explanation
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