giddy.markov.Markov

class giddy.markov.Markov(class_ids, classes=None)

Classic Markov transition matrices.

Parameters

class_idsarray

(n, t), one row per observation, one column recording the state of each observation, with as many columns as time periods.

classesarray

(k, 1), all different classes (bins) of the matrix.

Examples

>>> import numpy as np
>>> from giddy.markov import Markov
>>> c = [['b','a','c'],['c','c','a'],['c','b','c']]
>>> c.extend([['a','a','b'], ['a','b','c']])
>>> c = np.array(c)
>>> m = Markov(c)
>>> m.classes.tolist()
['a', 'b', 'c']
>>> m.p
array([[0.25      , 0.5       , 0.25      ],
       [0.33333333, 0.        , 0.66666667],
       [0.33333333, 0.33333333, 0.33333333]])
>>> m.steady_state
array([0.30769231, 0.28846154, 0.40384615])

US nominal per capita income 48 states 81 years 1929-2009

>>> import libpysal
>>> import mapclassify as mc
>>> f = libpysal.io.open(libpysal.examples.get_path("usjoin.csv"))
>>> pci = np.array([f.by_col[str(y)] for y in range(1929,2010)])

set classes to quintiles for each year

>>> q5 = np.array([mc.Quantiles(y).yb for y in pci]).transpose()
>>> m = Markov(q5)
>>> m.transitions
array([[729.,  71.,   1.,   0.,   0.],
       [ 72., 567.,  80.,   3.,   0.],
       [  0.,  81., 631.,  86.,   2.],
       [  0.,   3.,  86., 573.,  56.],
       [  0.,   0.,   1.,  57., 741.]])
>>> m.p
array([[0.91011236, 0.0886392 , 0.00124844, 0.        , 0.        ],
       [0.09972299, 0.78531856, 0.11080332, 0.00415512, 0.        ],
       [0.        , 0.10125   , 0.78875   , 0.1075    , 0.0025    ],
       [0.        , 0.00417827, 0.11977716, 0.79805014, 0.07799443],
       [0.        , 0.        , 0.00125156, 0.07133917, 0.92740926]])
>>> m.steady_state
array([0.20774716, 0.18725774, 0.20740537, 0.18821787, 0.20937187])

Relative incomes

>>> pci = pci.transpose()
>>> rpci = pci/(pci.mean(axis=0))
>>> rq = mc.Quantiles(rpci.flatten()).yb.reshape(pci.shape)
>>> mq = Markov(rq)
>>> mq.transitions
array([[707.,  58.,   7.,   1.,   0.],
       [ 50., 629.,  80.,   1.,   1.],
       [  4.,  79., 610.,  73.,   2.],
       [  0.,   7.,  72., 650.,  37.],
       [  0.,   0.,   0.,  48., 724.]])
>>> mq.steady_state
array([0.17957376, 0.21631443, 0.21499942, 0.21134662, 0.17776576])

Attributes

parray

(k, k), transition probability matrix.

steady_statearray

(k, ), ergodic distribution.

transitionsarray

(k, k), count of transitions between each state i and j.

__init__(self, class_ids, classes=None)

Initialize self. See help(type(self)) for accurate signature.