def sample_path(P, init=0, sample_size=1000):
"""
Generates one sample path from a finite Markov chain with (n x n) Markov
matrix P on state space S = {0,...,n-1}.
Parameters:
* P is a nonnegative 2D NumPy array with rows that sum to 1
* init is either an integer in S or a nonnegative array of length n
with elements that sum to 1
* sample_size is an integer
If init is an integer, the integer is treated as the determinstic initial
condition. If init is a distribution on S, then X_0 is drawn from this
distribution.
Returns: A NumPy array containing the sample path
"""
# === set up array to store output === #
X = np.empty(sample_size, dtype=int)
if isinstance(init, int):
X[0] = init
else:
X[0] = discreteRV(init).draw()
# === turn each row into a distribution === #
# In particular, let P_dist[i] be the distribution corresponding to the
# i-th row P[i,:]
n = len(P)
P_dist = [discreteRV(P[i, :]) for i in range(n)]
# === generate the sample path === #
for t in range(sample_size - 1):
X[t + 1] = P_dist[X[t]].draw()
return X
def sample_path(P, init=0, sample_size=1000):
"""
Generates one sample path from a finite Markov chain with (n x n) Markov
matrix P on state space S = {0,...,n-1}.
Parameters:
* P is a nonnegative 2D NumPy array with rows that sum to 1
* init is either an integer in S or a nonnegative array of length n
with elements that sum to 1
* sample_size is an integer
If init is an integer, the integer is treated as the determinstic initial
condition. If init is a distribution on S, then X_0 is drawn from this
distribution.
Returns: A NumPy array containing the sample path
"""
# === set up array to store output === #
X = np.empty(sample_size, dtype=int)
if isinstance(init, int):
X[0] = init
else:
X[0] = discreteRV(init).draw()
# === turn each row into a distribution === #
# In particular, let P_dist[i] be the distribution corresponding to the
# i-th row P[i,:]
n = len(P)
P_dist = [discreteRV(P[i,:]) for i in range(n)]
# === generate the sample path === #
for t in range(sample_size - 1):
X[t+1] = P_dist[X[t]].draw()
return X
import matplotlib.pyplot as plt
import numpy as np
from discrete_rv import discreteRV
from career import *
from compute_fp import compute_fixed_point
wp = workerProblem()
v_init = np.ones((wp.N, wp.N))*100
v = compute_fixed_point(bellman, wp, v_init)
optimal_policy = get_greedy(wp, v)
F = discreteRV(wp.F_probs)
G = discreteRV(wp.G_probs)
def gen_first_passage_time():
t = 0
i = j = 0
theta_index = []
epsilon_index = []
while 1:
if optimal_policy[i, j] == 1: # Stay put
return t
elif optimal_policy[i, j] == 2: # New job
j = int(G.draw())
else: # New life
i, j = int(F.draw()), int(G.draw())
t += 1
M = 25000 # Number of samples
samples = np.empty(M)
for i in range(M):
samples[i] = gen_first_passage_time()
Simulate job / career paths and compute the waiting time to permanent job /
career. In reading the code, recall that optimal_policy[i, j] = policy at
(theta_i, epsilon_j) = either 1, 2 or 3; meaning 'stay put', 'new job' and
'new life'.
"""
import matplotlib.pyplot as plt
import numpy as np
from discrete_rv import discreteRV
from career import *
from compute_fp import compute_fixed_point
wp = workerProblem()
v_init = np.ones((wp.N, wp.N)) * 100
v = compute_fixed_point(bellman, wp, v_init)
optimal_policy = get_greedy(wp, v)
F = discreteRV(wp.F_probs)
G = discreteRV(wp.G_probs)
def gen_path(T=20):
i = j = 0
theta_index = []
epsilon_index = []
for t in range(T):
if optimal_policy[i, j] == 1: # Stay put
pass
elif optimal_policy[i, j] == 2: # New job
j = int(G.draw())
else: # New life
i, j = int(F.draw()), int(G.draw())
theta_index.append(i)
