Markov Transition Probability Check and Transform

In this example, use several markov transition matrixes where each row does not sum up to 1 due to simulation errors. Check if the gap between 1 and the row values are too big, and then normalize.

# Author: Fan Wang (fanwangecon.github.io)
import pyfan.stats.markov.transprobcheck as pyfan_stats_transprobcheck
import numpy as np
import matplotlib.pyplot as plt

Check Row Sum of a Five by Five Transition matrix

# construct data inputs
mt_ar1_trans = np.array([[0.4334, 0.5183, 0.0454, 0.0027, 0.0002],
                         [0.2624, 0.5967, 0.1245, 0.0145, 0.0016],
                         [0.1673, 0.5918, 0.2005, 0.0343, 0.0052],
                         [0., 0.0312, 0.6497, 0.2774, 0.0371],
                         [0., 0.0681, 0.6569, 0.2379, 0.0327],
                         [0., 0.2201, 0.581, 0.168, 0.0264]])
ar_row_sums_ar1 = np.sum(mt_ar1_trans, axis=1)
print(f'{ar_row_sums_ar1=}')

# Check with default conditions, does not pass
bl_ar1_sum_pass, bl_per_row_pass, bl_avg_row_pass = \
    pyfan_stats_transprobcheck.markov_trans_prob_check(mt_ar1_trans)
print(f'{bl_ar1_sum_pass=}')
print(f'{bl_per_row_pass=}')
print(f'{bl_avg_row_pass=}')

# Check with relaxed conditions, pass per row does not pass average
fl_atol_per_row = 1e-02
fl_atol_avg_row = 1e-03
bl_ar1_sum_pass, bl_per_row_pass, bl_avg_row_pass = \
    pyfan_stats_transprobcheck.markov_trans_prob_check(mt_ar1_trans, fl_atol_per_row, fl_atol_avg_row)
print(f'{bl_ar1_sum_pass=}')
print(f'{bl_per_row_pass=}')
print(f'{bl_avg_row_pass=}')

# Relax condition further, passes
fl_atol_per_row = 1e-02
fl_atol_avg_row = 5e-03
bl_ar1_sum_pass, bl_per_row_pass, bl_avg_row_pass = \
    pyfan_stats_transprobcheck.markov_trans_prob_check(mt_ar1_trans, fl_atol_per_row, fl_atol_avg_row)
print(f'{bl_ar1_sum_pass=}')
print(f'{bl_per_row_pass=}')
print(f'{bl_avg_row_pass=}')

# Start Plot
fig, ax = plt.subplots()

# Text Plot
ax.text(0.5, 0.5, f'{mt_ar1_trans} '
                  f'\n\n {fl_atol_per_row=} and {fl_atol_avg_row=} '
                  f'\n\n {bl_ar1_sum_pass=} \n {bl_per_row_pass=} \n {bl_avg_row_pass=}',
        horizontalalignment='center',
        verticalalignment='center',
        fontsize=10, color='black',
        transform=ax.transAxes)

# Labeling
ax.set_axis_off()
plt.show()

Out:

ar_row_sums_ar1=array([1.    , 0.9997, 0.9991, 0.9954, 0.9956, 0.9955])
bl_ar1_sum_pass=False
bl_per_row_pass=False
bl_avg_row_pass=False
bl_ar1_sum_pass=False
bl_per_row_pass=True
bl_avg_row_pass=False
bl_ar1_sum_pass=True
bl_per_row_pass=True
bl_avg_row_pass=True

Rescale a Three by Three Transition so Each Row Sums to One

mt_ar1_trans = np.array([[0.4334, 0.5183, 0.0454], [0.2624, 0.5967, 0.1245], [0.1673, 0.5918, 0.2005]])
bl_ar1_sum_pass, bl_per_row_pass, bl_avg_row_pass = pyfan_stats_transprobcheck.markov_trans_prob_check(mt_ar1_trans)
mt_ar1_trans_rescaled = pyfan_stats_transprobcheck.markov_condi_prob2one(mt_ar1_trans)
bl_ar1_sum_pass_rescaled, bl_per_row_pass_rescaled, bl_avg_row_pass_rescaled = \
    pyfan_stats_transprobcheck.markov_trans_prob_check(mt_ar1_trans_rescaled)

# Start Plot
fig, ax = plt.subplots()

# Text Plot
ax.text(0.5, 0.5, f'{mt_ar1_trans} '
                  f'\n\n {bl_ar1_sum_pass=}'
                  f'\n\n {mt_ar1_trans_rescaled}'
                  f'\n\n {bl_ar1_sum_pass_rescaled=}',
        horizontalalignment='center',
        verticalalignment='center',
        fontsize=10, color='black',
        transform=ax.transAxes)

# Labeling
ax.set_axis_off()
plt.show()