Source code for quantecon.lae

r"""
Computes a sequence of marginal densities for a continuous state space
Markov chain :math:`X_t` where the transition probabilities can be represented
as densities. The estimate of the marginal density of :math:`X_t` is

.. math::

    \frac{1}{n} \sum_{i=0}^n p(X_{t-1}^i, y)

This is a density in :math:`y`.

References
----------

https://lectures.quantecon.org/py/stationary_densities.html

"""
from textwrap import dedent
import numpy as np


[docs]class LAE: """ An instance is a representation of a look ahead estimator associated with a given stochastic kernel p and a vector of observations X. Parameters ---------- p : function The stochastic kernel. A function p(x, y) that is vectorized in both x and y X : array_like(float) A vector containing observations Attributes ---------- p, X : see Parameters Examples -------- >>> psi = LAE(p, X) >>> y = np.linspace(0, 1, 100) >>> psi(y) # Evaluate look ahead estimate at grid of points y """ def __init__(self, p, X): X = X.flatten() # So we know what we're dealing with n = len(X) self.p, self.X = p, X.reshape((n, 1)) def __repr__(self): return self.__str__() def __str__(self): m = """\ Look ahead estimator - number of observations : {n} """ return dedent(m.format(n=self.X.size)) def __call__(self, y): """ A vectorized function that returns the value of the look ahead estimate at the values in the array y. Parameters ---------- y : array_like(float) A vector of points at which we wish to evaluate the look- ahead estimator Returns ------- psi_vals : array_like(float) The values of the density estimate at the points in y """ k = len(y) v = self.p(self.X, y.reshape((1, k))) psi_vals = np.mean(v, axis=0) # Take mean along each row return psi_vals.flatten()