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[likelihood_var.md] Update np.random → Generator API #995

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[likelihood_var.md] Update np.random → Generator API #995

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26 changes: 14 additions & 12 deletions lectures/likelihood_var.md
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Original file line number Diff line number Diff line change
Expand Up @@ -62,6 +62,8 @@ import quantecon as qe
from numba import jit
from typing import NamedTuple, Optional, Tuple
from collections import namedtuple

rng = np.random.default_rng()
```

## VAR model setup
Expand Down Expand Up @@ -217,7 +219,7 @@ def log_likelihood_path(X, model):

return log_L

def simulate_var(model, T, N_paths=1):
def simulate_var(model, T, rng, N_paths=1):
"""
Simulate paths from the VAR model
"""
Expand All @@ -227,13 +229,13 @@ def simulate_var(model, T, N_paths=1):

for i in range(N_paths):
# Draw initial state
x = mvn.rvs(mean=model.μ_0, cov=model.Σ_0)
x = mvn.rvs(mean=model.μ_0, cov=model.Σ_0, random_state=rng)
x = np.atleast_1d(x)
paths[i, 0] = x

# Simulate forward
for t in range(T):
w = np.random.randn(m)
w = rng.standard_normal(m)
x = model.A @ x + model.C @ w
paths[i, t+1] = x

Expand Down Expand Up @@ -322,7 +324,7 @@ Let's generate 100 paths of length 200 from model $f$ and compute the likelihood
# Simulate from model f
T = 200
N_paths = 100
paths_from_f = simulate_var(model_f, T, N_paths)
paths_from_f = simulate_var(model_f, T, rng, N_paths)

L_ratios_f = compute_likelihood_ratio_var(paths_from_f, model_f, model_g)

Expand Down Expand Up @@ -384,8 +386,8 @@ Let's generate 50 paths of length 50 from both models and compute the likelihood
T = 50
N_paths = 50

paths_from_f = simulate_var(model2_f, T, N_paths)
paths_from_g = simulate_var(model2_g, T, N_paths)
paths_from_f = simulate_var(model2_f, T, rng, N_paths)
paths_from_g = simulate_var(model2_g, T, rng, N_paths)

# Compute likelihood ratios
L_ratios_ff = compute_likelihood_ratio_var(paths_from_f, model2_f, model2_g)
Expand Down Expand Up @@ -453,11 +455,11 @@ def model_selection_analysis(T_values, model_f, model_g, N_sim=500):

for T in T_values:
# Simulate from model f
paths_f = simulate_var(model_f, T, N_sim//2)
paths_f = simulate_var(model_f, T, rng, N_sim//2)
L_ratios_f = compute_likelihood_ratio_var(paths_f, model_f, model_g)

# Simulate from model g
paths_g = simulate_var(model_g, T, N_sim//2)
paths_g = simulate_var(model_g, T, rng, N_sim//2)
L_ratios_g = compute_likelihood_ratio_var(paths_g, model_f, model_g)

# Decision rule: choose f if log L_T >= 0
Expand Down Expand Up @@ -683,12 +685,12 @@ def create_samuelson_var_model(a, b, γ, G, σ, stationary_init=False,

return model, G_obs, info

def simulate_samuelson(model, G_obs, T, N_paths=1):
def simulate_samuelson(model, G_obs, T, rng, N_paths=1):
"""
Simulate Samuelson model
"""
# Simulate state paths
states = simulate_var(model, T, N_paths)
states = simulate_var(model, T, rng, N_paths)

# Extract observables using G matrix
if N_paths == 1:
Expand Down Expand Up @@ -731,8 +733,8 @@ T = 50
N_paths = 50

# Get both states and observables
states_f, obs_f = simulate_samuelson(model_sam_f, G_obs_f, T, N_paths)
states_g, obs_g = simulate_samuelson(model_sam_g, G_obs_g, T, N_paths)
states_f, obs_f = simulate_samuelson(model_sam_f, G_obs_f, T, rng, N_paths)
states_g, obs_g = simulate_samuelson(model_sam_g, G_obs_g, T, rng, N_paths)

output_paths_f = obs_f[:, :, 0]
output_paths_g = obs_g[:, :, 0]
Expand Down
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