def plot_gamma_exponential():
ge = GammaExponential(alpha=10, beta=5, n=100, x_mean=0.3)
ax = new_axes()
ge.prior().plot(x=rates, color='r', ax=ax)
ge.posterior().plot(x=rates, color='g', ax=ax)
ax.legend()
plt.show()
ax = new_axes()
ge.pdf().plot(x=durations, ax=ax)
ax.legend()
plt.show()
def plot(self, k: Iterable[int], color: str = 'C0', kind: str = 'bar', ax: Axes = None,
**kwargs) -> Axes:
"""
Plot the function.
:param k: Range of values of k to plot p(k) over.
:param color: Optional color for the series.
:param kind: Kind of plot e.g. 'bar', 'line'.
:param ax: Optional matplotlib axes to plot on.
:param kwargs: Additional arguments for the matplotlib plot function.
"""
data: Series = self.at(k)
ax = ax or new_axes()
# special kwargs
vlines = None
if 'vlines' in kwargs.keys():
vlines = kwargs.pop('vlines')
if self._name == 'PMF':
data.plot(kind=kind, label=self._parent.label, color=color,
ax=ax, **kwargs)
elif self._name == 'CDF':
data.plot(kind='line', label=self._parent.label, color=color,
drawstyle='steps-post', ax=ax,
**kwargs)
else:
raise ValueError('plot not implemented for {}'.format(self._name))
if vlines:
ax.vlines(x=k, ymin=0, ymax=data.values, color=color)
ax.set_xlabel(self._parent.x_label)
ax.set_ylabel(self._name)
return ax
def plot_wikipedia_pmfs():
"""
https://en.wikipedia.org/wiki/Binomial_distribution#/media/File:Binomial_distribution_pmf.svg
"""
ax = new_axes()
Binomial(n=20, p=0.5).plot(k=k_wiki,
kind='line',
color='blue',
ax=ax,
ls='',
marker='d')
Binomial(n=20, p=0.7).plot(k=k_wiki,
kind='line',
color='lightgreen',
ax=ax,
ls='',
marker='s')
Binomial(n=40, p=0.5).plot(k=k_wiki,
kind='line',
color='red',
ax=ax,
ls='',
marker='o')
ax.set_ylim(0, 0.25)
ax.set_title('Probability mass function')
ax.legend(loc='upper right')
plt.show()
def plot_parameters():
ax = new_axes()
dist.prior().plot(x=x, color='r', ax=ax)
dist.posterior().plot(x=x, color='g', ax=ax)
ax.legend()
plt.show()
def plot(self,
x: Iterable,
kind: str = 'line',
color: str = 'C0',
ax: Axes = None,
**kwargs) -> Axes:
"""
Plot the function.
:param x: Range of values of x to plot p(x) over.
:param kind: Kind of plot e.g. 'bar', 'line'.
:param color: Optional color for the series.
:param ax: Optional matplotlib axes to plot on.
:param kwargs: Additional arguments for the matplotlib plot function.
"""
data: Series = self.at(x)
ax = ax or new_axes()
if self._name in ('PDF', 'CDF', 'log(PDF)'):
data.plot(kind=kind,
label=self._parent.label,
color=color,
ax=ax,
**kwargs)
else:
raise ValueError('plot not implemented for {}'.format(self._name))
ax.set_xlabel(self._parent.x_label)
ax.set_ylabel(self._name)
return ax
def plot_wikipedia_cdfs():
ax = new_axes()
InvGamma(alpha=1, beta=1).cdf().plot(x=x, color='red', ax=ax)
InvGamma(alpha=2, beta=1).cdf().plot(x=x, color='green', ax=ax)
InvGamma(alpha=3, beta=1).cdf().plot(x=x, color='blue', ax=ax)
InvGamma(alpha=3, beta=0.5).cdf().plot(x=x, color='cyan', ax=ax)
ax.legend()
plt.show()
def plot_wikipedia_pdfs():
"""
https://en.wikipedia.org/wiki/Exponential_distribution#/media/File:Exponential_probability_density.svg
"""
ax = new_axes()
Exponential(lambda_=0.5).plot(x=x, color='orange', ax=ax)
Exponential(lambda_=1).plot(x=x, color='purple', ax=ax)
Exponential(lambda_=1.5).plot(x=x, color='lightblue', ax=ax)
ax.set_ylim(0, 1.5)
plt.show()
def plot_predictions():
ax = new_axes()
predicted = dist.rvs(100000)
ax.hist(predicted, bins=100, density=True, label='PPD samples')
x_actual = arange(predicted.min(), predicted.max(), 0.01)
actual = norm(loc=mu, scale=sigma).pdf(x_actual)
ax.plot(x_actual, actual, label='True Distribution')
ax.legend()
plt.show()
def plot_wikipedia_cdfs():
"""
https://en.wikipedia.org/wiki/Lomax_distribution#/media/File:LomaxCDF.png
"""
ax = new_axes()
Lomax(lambda_=1, alpha=2).cdf().plot(x=x, color='blue', ax=ax)
Lomax(lambda_=2, alpha=2).cdf().plot(x=x, color='green', ax=ax)
Lomax(lambda_=4, alpha=1).cdf().plot(x=x, color='red', ax=ax)
Lomax(lambda_=6, alpha=1).cdf().plot(x=x, color='orange', ax=ax)
plt.show()
def plot_wikipedia_pdfs():
"""
https://en.wikipedia.org/wiki/Laplace_distribution#/media/File:Laplace_pdf_mod.svg
"""
ax = new_axes()
Laplace(mu=0, b=1).plot(x=x, color='red', ax=ax)
Laplace(mu=0, b=2).plot(x=x, color='black', ax=ax)
Laplace(mu=0, b=4).plot(x=x, color='blue', ax=ax)
Laplace(mu=-5, b=4).plot(x=x, color='green', ax=ax)
ax.legend(loc='upper right')
plt.show()
def plot_wikipedia_pdfs():
"""
https://en.wikipedia.org/wiki/Normal_distribution#/media/File:Normal_Distribution_PDF.svg
"""
ax = new_axes()
Normal(mu=0, sigma_sq=0.2).plot(x=x, color='blue', ax=ax)
Normal(mu=0, sigma_sq=1.0).plot(x=x, color='red', ax=ax)
Normal(mu=0, sigma_sq=5.0).plot(x=x, color='orange', ax=ax)
Normal(mu=-2, sigma_sq=0.5).plot(x=x, color='green', ax=ax)
ax.legend(loc='upper right')
plt.show()
def plot_wikipedia_cdfs():
"""
https://en.wikipedia.org/wiki/Beta-binomial_distribution#/media/File:Beta-binomial_cdf.png
"""
ax = new_axes(width=10, height=10)
BetaBinomial(alpha=0.2, beta=0.25, n=10).cdf().plot(k=k, color='black', ax=ax)
BetaBinomial(alpha=0.7, beta=2, n=10).cdf().plot(k=k, color='red', ax=ax)
BetaBinomial(alpha=2, beta=2, n=10).cdf().plot(k=k, color='green', ax=ax)
BetaBinomial(alpha=600, beta=400, n=10).cdf().plot(k=k, color='blue', ax=ax)
ax.legend()
plt.show()
def plot_wikipedia_cdfs():
"""
https://en.wikipedia.org/wiki/Poisson_distribution#/media/File:Poisson_pmf.svg
"""
ax = new_axes(width=10, height=10)
Poisson(lambda_=1).cdf().plot(k=k_wikipedia, color='gray', mfc='orange', marker='o', ax=ax)
Poisson(lambda_=4).cdf().plot(k=k_wikipedia, color='gray', mfc='purple', marker='o', ax=ax)
Poisson(lambda_=10).cdf().plot(k=k_wikipedia, color='gray', mfc='lightblue', marker='o', ax=ax)
ax.set_title('Cumulative distribution function')
ax.legend(loc='lower right')
plt.show()
def plot_wikipedia_cdfs():
"""
https://en.wikipedia.org/wiki/Student%27s_t-distribution#/media/File:Student_t_cdf.svg
"""
ax = new_axes()
StudentsT(nu=1).cdf().plot(x=x_wikipedia_1, color='orange', ax=ax)
StudentsT(nu=2).cdf().plot(x=x_wikipedia_1, color='purple', ax=ax)
StudentsT(nu=5).cdf().plot(x=x_wikipedia_1, color='lightblue', ax=ax)
StudentsT(nu=1e9).cdf().plot(x=x_wikipedia_1, color='black', ax=ax)
ax.legend(loc='lower right')
plt.show()
def plot_wikipedia_pmfs():
"""
https://en.wikipedia.org/wiki/Poisson_distribution#/media/File:Poisson_pmf.svg
"""
ax = new_axes(width=10, height=10)
Poisson(lambda_=1).plot(k=k_wikipedia, kind='line', color='gray', mfc='orange', marker='o', ax=ax)
Poisson(lambda_=4).plot(k=k_wikipedia, kind='line', color='gray', mfc='purple', marker='o', ax=ax)
Poisson(lambda_=10).plot(k=k_wikipedia, kind='line', color='gray', mfc='lightblue', marker='o', ax=ax)
ax.set_ylim(0, 0.4)
ax.set_title('Probability mass function')
ax.legend(loc='upper right')
plt.show()
def plot_wikipedia_cdfs():
"""
https://en.wikipedia.org/wiki/Beta_distribution#/media/File:Beta_distribution_cdf.svg
"""
ax = new_axes(width=10, height=10)
Beta(0.5, 0.5).cdf().plot(x=x, color='red', ax=ax)
Beta(5, 1).cdf().plot(x=x, color='blue', ax=ax)
Beta(1, 3).cdf().plot(x=x, color='green', ax=ax)
Beta(2, 2).cdf().plot(x=x, color='purple', ax=ax)
Beta(2, 5).cdf().plot(x=x, color='orange', ax=ax)
ax.set_title('Cumulative distribution function')
ax.legend(loc='upper left')
plt.show()
def plot_wikipedia_pdfs():
"""
https://en.wikipedia.org/wiki/Beta_distribution#/media/File:Beta_distribution_pdf.svg
"""
ax = new_axes(width=10, height=10)
Beta(0.5, 0.5).pdf().plot(x=x, color='red', ax=ax)
Beta(5, 1).pdf().plot(x=x, color='blue', ax=ax)
Beta(1, 3).pdf().plot(x=x, color='green', ax=ax)
Beta(2, 2).pdf().plot(x=x, color='purple', ax=ax)
Beta(2, 5).pdf().plot(x=x, color='orange', ax=ax)
ax.set_ylim(0, 2.5)
ax.set_title('Probability density function')
ax.legend(loc='upper center')
plt.show()
def plot_wikipedia_cdfs():
"""
https://en.wikipedia.org/wiki/Gamma_distribution#/media/File:Gamma_distribution_cdf.svg
"""
ax = new_axes()
Gamma.from_k_theta(k=1, theta=2).cdf().plot(x=x, color='red', ax=ax)
Gamma.from_k_theta(k=2, theta=2).cdf().plot(x=x, color='orange', ax=ax)
Gamma.from_k_theta(k=3, theta=2).cdf().plot(x=x, color='yellow', ax=ax)
Gamma.from_k_theta(k=5, theta=1).cdf().plot(x=x, color='green', ax=ax)
Gamma.from_k_theta(k=9, theta=0.5).cdf().plot(x=x, color='black', ax=ax)
Gamma.from_k_theta(k=7.5, theta=1).cdf().plot(x=x, color='blue', ax=ax)
Gamma.from_k_theta(k=0.5, theta=1).cdf().plot(x=x, color='purple', ax=ax)
ax.set_ylim(0, 1)
ax.legend(loc='lower right')
plt.show()
def plot_2d(self, x1: Union[Iterable, ndarray], x2: Union[Iterable, ndarray],
color_map: str = 'viridis', ax: Axes = None) -> Axes:
"""
Plot a 2-dimensional function as a grid heat-map.
:param x1: Range of values of x1 to plot p(x1, x2) over.
:param x2: Range of values of x2 to plot p(x1, x2) over.
:param color_map: Optional colormap for the heat-map.
:param ax: Optional matplotlib axes to plot on.
"""
x1_grid, x2_grid = meshgrid(x1, x2)
x1_x2 = dstack((x1_grid, x2_grid))
f = self._method(x1_x2)
ax = ax or new_axes()
ax.contourf(x1_grid, x2_grid, f, cmap=color_map)
ax.set_xlabel('x1')
ax.set_ylabel('x2')
return ax
def plot_wikipedia_cdfs():
"""
https://en.wikipedia.org/wiki/Binomial_distribution#/media/File:Binomial_distribution_cdf.svg
"""
ax = new_axes()
Binomial(n=20, p=0.5).cdf().plot(k=k_wiki,
kind='line',
color='blue',
ax=ax)
Binomial(n=20, p=0.7).cdf().plot(k=k_wiki,
kind='line',
color='lightgreen',
ax=ax)
Binomial(n=40, p=0.5).cdf().plot(k=k_wiki, kind='line', color='red', ax=ax)
ax.set_ylim(0, 1.0)
ax.set_title('Cumulative distribution function')
ax.legend(loc='upper right')
plt.show()
def plot_simplex(self, num_contours: int = 100, num_sub_div: int = 8,
color_map: str = 'viridis', border: bool = True, ax: Axes = None) -> Axes:
"""
Plot a 3-dimensional functions as a simplex heat-map.
:param num_contours: The number of levels of contours to plot.
:param num_sub_div: Number of recursive subdivisions to create.
:param color_map: Optional colormap for the plot.
:param border: Whether to plot a border around the simplex heatmap.
:param ax: Optional matplotlib axes to plot on.
"""
corners = array([[0, 0], [1, 0], [0.5, 0.75 ** 0.5]])
triangle = Triangulation(corners[:, 0], corners[:, 1])
mid_points = [
(corners[(i + 1) % 3] + corners[(i + 2) % 3]) / 2
for i in range(3)
]
def to_barycentric(cartesian):
"""
Converts 2D Cartesian to barycentric coordinates.
:param cartesian: A length-2 sequence containing the x and y value.
"""
s = [(corners[i] - mid_points[i]).dot(cartesian - mid_points[i]) / 0.75
for i in range(3)]
s_clipped = clip(a=s, a_min=0, a_max=1)
return s_clipped / norm(s_clipped, ord=1)
refiner = UniformTriRefiner(triangle)
tri_mesh = refiner.refine_triangulation(subdiv=num_sub_div)
f = [self._method(to_barycentric(xy))
for xy in zip(tri_mesh.x, tri_mesh.y)]
ax = ax or new_axes()
ax.tricontourf(tri_mesh, f, num_contours, cmap=color_map)
ax.set_aspect('equal')
ax.set_xlim(0, 1)
ax.set_ylim(0, 0.75 ** 0.5)
ax.set_axis_off()
if border:
ax.triplot(triangle, linewidth=1)
return ax
def plot(self,
x: ndarray,
color: str = 'C1',
ax: Optional[Axes] = None) -> Axes:
"""
Plot the prior probability of the parameter θ given the priors α, β
`p(x|α,β)`
:param x: vector of possible `x`s
:param color: Optional color for the series.
:param ax: Optional matplotlib axes
:rtype: Axes
"""
ax = ax or new_axes()
self._distribution.pdf().at(x).plot(kind='line',
label=self._label,
color=color or 'C0',
ax=ax)
ax.set_xlabel(self._x_label)
ax.set_ylabel(self._y_label)
ax.legend()
return ax
def plot(self,
x: Union[Iterable[Iterable], ndarray],
color: str = 'C0',
ax: Axes = None) -> Axes:
"""
Plot the function.
:param x: Range of values of x to plot p(x) over.
:param color: Optional color for the series.
:param ax: Optional matplotlib axes to plot on.
"""
x = array(x)
data = self.at(x)
if x.ndim != 2:
raise ValueError('x must have 2 dimensions: [num_points, K]')
ax = ax or new_axes()
if self._num_dims > 2:
data = data.sort_values(ascending=False)
data.plot.bar(color=color, label=str(self._parent), ax=ax)
ax.set_xlabel('x')
ax.set_ylabel(self._name)
ax.legend(loc='upper right')
return ax
