tests

conjugate/distributions.py

@@ -42,7 +42,7 @@
 import numpy as np
 
 from scipy import stats, __version__ as scipy_version
-from scipy.special import gammaln
+from scipy.special import gammaln, i0
 
 from conjugate._typing import NUMERIC
 from conjugate.plot import (
@@ -691,7 +691,7 @@ class GammaKnownRateProportional:
 
     def approx_log_likelihood(
         self, alpha: NUMERIC, beta: NUMERIC, ln=np.log, gammaln=gammaln
-    ):
+    ) -> NUMERIC:
         """Approximate log likelihood.
 
         Args:
@@ -730,7 +730,7 @@ class GammaProportional:
 
     def approx_log_likelihood(
         self, alpha: NUMERIC, beta: NUMERIC, ln=np.log, gammaln=gammaln
-    ):
+    ) -> NUMERIC:
         """Approximate log likelihood.
 
         Args:
@@ -768,7 +768,7 @@ class BetaProportional:
 
     def approx_log_likelihood(
         self, alpha: NUMERIC, beta: NUMERIC, ln=np.log, gammaln=gammaln
-    ):
+    ) -> NUMERIC:
         """Approximate log likelihood.
 
         Args:
@@ -788,3 +788,76 @@ def approx_log_likelihood(
             - self.k * gammaln(alpha)
             - self.k * gammaln(beta)
         )
+
+
+@dataclass
+class VonMises(ContinuousPlotDistMixin, SliceMixin):
+    """Von Mises distribution.
+
+    Args:
+        mu: mean
+        kappa: concentration
+
+    """
+
+    mu: NUMERIC
+    kappa: NUMERIC
+
+    def __post_init__(self) -> None:
+        self.min_value = -np.pi
+        self.max_value = np.pi
+
+    @property
+    def dist(self):
+        return stats.vonmises(loc=self.mu, kappa=self.kappa)
+
+
+@dataclass
+class VonMisesKnownConcentration:
+    """Von Mises known concentration distribution.
+
+    Taken from <a href=https://web.archive.org/web/20090529203101/http://www.people.cornell.edu/pages/df36/CONJINTRnew%20TEX.pdf>Section 2.13.1</a>.
+
+    Args:
+        a: positive value
+        b: value between 0 and 2 pi
+
+    """
+
+    a: NUMERIC
+    b: NUMERIC
+
+    def log_likelihood(self, mu: NUMERIC, cos=np.cos, ln=np.log, i0=i0) -> NUMERIC:
+        """Approximate log likelihood.
+
+        Args:
+            mu: mean
+            cos: cosine function
+            ln: log function
+            i0: modified bessel function of order 0
+
+        Returns:
+            log likelihood
+
+        """
+        return self.a + cos(mu - self.b) - ln(i0(self.a))
+
+
+@dataclass
+class VonMisesKnownDirectionProportional:
+    c: NUMERIC
+    r: NUMERIC
+
+    def approx_log_likelihood(self, kappa: NUMERIC, ln=np.log, i0=i0) -> NUMERIC:
+        """Approximate log likelihood.
+
+        Args:
+            kappa: concentration
+            ln: log function
+            i0: modified bessel function of order 0
+
+        Returns:
+            log likelihood up to a constant
+
+        """
+        return kappa * self.r - self.c * ln(i0(kappa))

conjugate/models.py

@@ -26,6 +26,8 @@
     StudentT,
     MultivariateStudentT,
     Lomax,
+    VonMisesKnownConcentration,
+    VonMisesKnownDirectionProportional,
 )
 from conjugate._typing import NUMERIC
 
@@ -1248,3 +1250,60 @@ def beta(
     k_post = proportional_prior.k + n
 
     return BetaProportional(p=p_post, q=q_post, k=k_post)
+
+
+def von_mises_known_concentration(
+    cos_total: NUMERIC,
+    sin_total: NUMERIC,
+    n: NUMERIC,
+    kappa: NUMERIC,
+    von_mises_prior: VonMisesKnownConcentration,
+    sin=np.sin,
+    cos=np.cos,
+    arctan2=np.arctan2,
+) -> VonMisesKnownConcentration:
+    """VonMises likelihood with known concentration parameter.
+
+    Taken from <a href=https://web.archive.org/web/20090529203101/http://www.people.cornell.edu/pages/df36/CONJINTRnew%20TEX.pdf>Section 2.13.1</a>.
+
+    Args:
+        cos_total: sum of all cosines
+        sin_total: sum of all sines
+        n: total number of samples in cos_total and sin_total
+        kappa: known concentration parameter
+        von_mises_prior: VonMisesKnownConcentration prior
+
+    Returns:
+        VonMisesKnownConcentration posterior distribution
+
+    """
+    sin_total_post = von_mises_prior.a * sin(von_mises_prior.b) + sin_total
+    a_post = kappa * sin_total_post
+
+    b_post = arctan2(
+        sin_total_post, von_mises_prior.a * cos(von_mises_prior.b) + cos_total
+    )
+
+    return VonMisesKnownConcentration(a=a_post, b=b_post)
+
+
+def von_mises_known_direction(
+    centered_cos_total: NUMERIC,
+    n: NUMERIC,
+    proportional_prior: VonMisesKnownDirectionProportional,
+) -> VonMisesKnownDirectionProportional:
+    """VonMises likelihood with known direction parameter.
+
+    Taken from <a href=https://web.archive.org/web/20090529203101/http://www.people.cornell.edu/pages/df36/CONJINTRnew%20TEX.pdf>Section 2.13.2</a>
+
+    Args:
+        centered_cos_total: sum of all centered cosines. sum cos(x - known direction))
+        n: total number of samples in centered_cos_total
+        proportional_prior: VonMisesKnownDirectionProportional prior
+
+    """
+
+    return VonMisesKnownDirectionProportional(
+        c=proportional_prior.c + n,
+        r=proportional_prior.r + centered_cos_total,
+    )

conjugate/plot.py

@@ -134,6 +134,9 @@ def _create_x_values(self) -> np.ndarray:
         return np.linspace(self.min_value, self.max_value, 100)
 
     def _setup_labels(self, ax) -> None:
+        if isinstance(ax, plt.PolarAxes):
+            return
+
         ax.set_xlabel("Domain")
         ax.set_ylabel("Density $f(x)$")
 

tests/test_example_plots.py

@@ -4,7 +4,14 @@
 
 import matplotlib.pyplot as plt
 
-from conjugate.distributions import Beta, Dirichlet, Gamma, Normal, NormalInverseGamma
+from conjugate.distributions import (
+    Beta,
+    Dirichlet,
+    Gamma,
+    Normal,
+    NormalInverseGamma,
+    VonMises,
+)
 from conjugate.models import (
     binomial_beta,
     binomial_beta_posterior_predictive,
@@ -186,3 +193,17 @@ def sample(n: int):
     ax.legend()
 
     return fig
+
+
+@pytest.mark.mpl_image_compare
+def test_polar_plot() -> None:
+    kappas = np.array([0.5, 1, 5, 10])
+    dist = VonMises(0, kappa=kappas)
+
+    fig = plt.figure(figsize=(12, 6))
+    ax = fig.add_subplot(121, projection="polar")
+    dist.plot_pdf(ax=ax)
+
+    ax = fig.add_subplot(122)
+    dist.plot_pdf(ax=ax)
+    return fig