Prediction and Simulation¶

After estimating a model, pysib provides two common ways to use it:

predict computes a one-step-ahead prediction using the measured output.
simulate computes the noise-free response to the input signal.

Both functions accept the model dictionary returned by any estimator.

One-step-ahead prediction¶

Use predict when you want to compare the measured output with the model's one-step-ahead prediction:

theta, model = pysib.arx(u, y, na=1, nb=1, nz=1)
yp = pysib.predict(u, y, model)

The prediction uses both the input signal u and the measured output signal y.

Conceptually, predict evaluates:

yp(t) = y(t) + H(z)^(-1) (G(z) u(t) - y(t))

where G(z) is the input/output model and H(z) is the noise model implied by the polynomial structure.

Use one-step-ahead prediction to inspect how well the model predicts the next output sample given the measured history.

Noise-free simulation¶

Use simulate when you want the deterministic response of the model to an input signal:

theta, model = pysib.oe(u, y, nb=1, nf=1, nz=1)
ys = pysib.simulate(u, model)

The simulation uses only the input signal u and the estimated model. It does not use the measured output y.

Conceptually, simulate evaluates:

ys(t) = G(z) u(t)

Use simulation to inspect the deterministic input/output dynamics estimated by the model.

Comparing prediction and simulation¶

Prediction and simulation answer different questions.

Function	Uses measured `y`?	Main purpose
`pysib.predict(u, y, model)`	yes	One-step-ahead prediction performance
`pysib.simulate(u, model)`	no	Noise-free input/output response

For noisy data, prediction can look better than simulation because it uses the measured output history. Simulation is often stricter when evaluating the deterministic model.

Plotting results¶

You can compare measured and modeled outputs with Matplotlib:

import matplotlib.pyplot as plt

plt.plot(y, label="measured")
plt.plot(yp, label="predicted")
plt.plot(ys, label="simulated")
plt.legend()
plt.show()

For Monte-Carlo parameter plots, see pysib.plota in the API Reference.

Model compatibility¶

Both predict and simulate depend on the shared model convention used by all estimators:

model["A"]
model["B"]
model["C"]
model["D"]
model["F"]

This means the same prediction and simulation functions can be used with ARX, OE, ARMAX, Box-Jenkins, and filtered models.