Module vickrey.likelihood.plot

Functions to make plots about the likelihood.

Functions

def plot_contour(tt, t_as, par, ax=None, x_bounds=None, y_bounds=None)

Expand source code

def plot_contour(
    tt,
    t_as,
    par,
    ax=None,
    x_bounds=None,
    y_bounds=None,
):
    """Plot a 2-dimensional slice of the likelihood function.

    Args:
        tt: Instance of the TravelTime class, containing the travel
            time function to plot the likelihood for.
        t_as: Vector of arrival time to plot the likelihood of.
        par: Parameters with which the likelihood will be plotted.
            Two entries must be None: the slice will be plotted
            using the other values, for the dimensions the None values
            are in.
        ax: matplotlib.pyplot.Axes instance, on which the contour will
            be plotted. If no axis is given, the current axis will be
            used.
        x_bounds, y_bounds: Bounds of the dimensions that will be
            plotted. If no value is given, the bounds will be
            automatically determined from a list of predefined bounds.

    Returns:
        contour: The contour, which has been plotted on axis ax.
    """
    indices = [i for i, v in enumerate(par) if not v]
    if len(indices) != 2:
        raise ValueError(
            f"The parameter list must have two None values.\n\
            {par} has instead {len(indices)}"
        )
    x_index, y_index = indices
    bounds = [(0.01, 0.6), (0.01, 0.6), (6.5, 11.0), (0.01, 0.6), (0.1, 2.0)]
    if not x_bounds:
        x_bounds = bounds[x_index]
    if not y_bounds:
        y_bounds = bounds[y_index]

    def log_lik(x, y):
        new_par = par.copy()
        new_par[x_index] = x
        new_par[y_index] = y
        return total_log_lik(tt, t_as)(*new_par)

    x_contour = jnp.linspace(*x_bounds, 51)
    y_contour = jnp.linspace(*y_bounds, 50)
    matrix_actual = vmap(vmap(log_lik, (0, None)), (None, 0))(
        x_contour, y_contour
    )
    if not ax:
        ax = plt.gca()
    contour = ax.contour(x_contour, y_contour, matrix_actual, levels=50)
    names = [r"\mu_\beta", r"\mu_\gamma", r"\mu_t", r"\sigma", r"\sigma_t"]
    ax.set_xlabel("$" + names[x_index] + "$")
    ax.set_ylabel("$" + names[y_index] + "$")
    return contour

Plot a 2-dimensional slice of the likelihood function.

Args

tt

Instance of the TravelTime class, containing the travel time function to plot the likelihood for.

t_as

Vector of arrival time to plot the likelihood of.

par

Parameters with which the likelihood will be plotted. Two entries must be None: the slice will be plotted using the other values, for the dimensions the None values are in.

ax

matplotlib.pyplot.Axes instance, on which the contour will be plotted. If no axis is given, the current axis will be used.

x_bounds, y_bounds: Bounds of the dimensions that will be plotted. If no value is given, the bounds will be automatically determined from a list of predefined bounds.

Returns

contour

The contour, which has been plotted on axis ax.

def plot_hist(tt, t_as, par, ax=None, par2=None, bins=80)

Expand source code

def plot_hist(tt, t_as, par, ax=None, par2=None, bins=80):
    """Plot an histogram of arrival times, with the likelihood of them.

    Args:
        tt: Instance of the TravelTime class, containing the travel
            time function to plot the likelihood for.
        t_as: Vector of arrival time to plot in the histogram.
        par: Parameters from which the likelihood function will be
            plotted.
        ax: matplotlib.pyplot.Axes instance, on which the histogram will
            be plotted. If no axis is given, the current axis will be
            used.
        par2: Second set of parameters, to compare the likelihoods
            coming from two different parameter values.
        bins: Number of bins to use when plotting the histogram.
    """
    if ax is None:
        ax = plt.gca()
    hist = ax.hist(t_as, bins, label="Arrival times")

    x = np.linspace(t_as.min(), t_as.max(), 200)
    liks = total_liks(tt, x)(*par)

    mult = hist[0].max() / liks.max()
    ax.fill_between(
        x,
        liks * mult,
        color="green",
        alpha=0.3,
        label="True likelihood value",
        edgecolor=None,
    )
    if par2 is not None:
        liks_wrong = total_liks(tt, x)(*par2)
        ax.fill_between(
            x,
            liks_wrong * mult,
            color="red",
            alpha=0.3,
            label="Wrong likelihood value",
            edgecolor=None,
        )

    ax.legend()

Plot an histogram of arrival times, with the likelihood of them.

Args

tt

Instance of the TravelTime class, containing the travel time function to plot the likelihood for.

t_as

Vector of arrival time to plot in the histogram.

par

Parameters from which the likelihood function will be plotted.

ax

matplotlib.pyplot.Axes instance, on which the histogram will be plotted. If no axis is given, the current axis will be used.

par2

Second set of parameters, to compare the likelihoods coming from two different parameter values.

bins

Number of bins to use when plotting the histogram.