Merge pull request #9 from wd60622/add-normal-known-mean

Add normal known mean

.github/release.yml

@@ -0,0 +1,18 @@
+# This file has been mostly taken verbatim from https://github.com/pymc-devs/pymc/blob/main/.github/release.yml
+changelog:
+  exclude:
+    labels:
+      - no releasenotes
+  categories:
+    - title: New Features 🎉
+      labels:
+        - enhancement
+    - title: Bugfixes 🐛
+      labels:
+        - bug
+    - title: Documentation 📖
+      labels:
+        - docs
+    - title: Maintenance 🔧
+      labels:
+        - "*"

.github/workflows/publish.yml

@@ -0,0 +1,14 @@
+name: Python package
+on:
+  push:
+    tags:
+      - "v*.*.*"
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v3
+      - name: Build and publish to pypi
+        uses: JRubics/poetry-publish@v1.17
+        with:
+          pypi_token: ${{ secrets.PYPI_TOKEN }}

conjugate/distributions.py

@@ -279,7 +279,6 @@ class BetaNegativeBinomial(SliceMixin):
         n: number of successes
         alpha: shape parameter
 
-
     """
 
     n: NUMERIC
@@ -369,7 +368,15 @@ def dist(self):
 
 @dataclass
 class NormalInverseGamma:
-    """Normal inverse gamma distribution."""
+    """Normal inverse gamma distribution.
+
+    Args:
+        mu: mean
+        delta_inverse: covariance matrix
+        alpha: shape
+        beta: scale
+
+    """
 
     mu: NUMERIC
     delta_inverse: NUMERIC
@@ -433,3 +440,23 @@ def sample_beta(
             return beta, variance
 
         return beta
+
+
+@dataclass
+class StudentT(ContinuousPlotDistMixin, SliceMixin):
+    """StudentT distribution.
+
+    Args:
+        mu: mean
+        sigma: standard deviation
+        nu: degrees of freedom
+
+    """
+
+    mu: NUMERIC
+    sigma: NUMERIC
+    nu: NUMERIC
+
+    @property
+    def dist(self):
+        return stats.t(self.nu, self.mu, self.sigma)

conjugate/models.py

@@ -14,7 +14,9 @@
     NegativeBinomial,
     BetaNegativeBinomial,
     BetaBinomial,
+    InverseGamma,
     NormalInverseGamma,
+    StudentT,
 )
 from conjugate._typing import NUMERIC
 
@@ -193,6 +195,54 @@ def exponetial_gamma(x_total: NUMERIC, n: NUMERIC, gamma_prior: Gamma) -> Gamma:
     return Gamma(alpha=alpha_post, beta=beta_post)
 
 
+def normal_known_mean(
+    x_total: NUMERIC,
+    x2_total: NUMERIC,
+    n: NUMERIC,
+    mu: NUMERIC,
+    inverse_gamma_prior: InverseGamma,
+) -> InverseGamma:
+    """Posterior distribution for a normal likelihood with a known mean and a variance prior.
+
+    Args:
+        x_total: sum of all outcomes
+        x2_total: sum of all outcomes squared
+        n: total number of samples in x_total
+        mu: known mean
+        inverse_gamma_prior: InverseGamma prior for variance
+
+    Returns:
+        InverseGamma posterior distribution for the variance
+
+    """
+    alpha_post = inverse_gamma_prior.alpha + (n / 2)
+    beta_post = inverse_gamma_prior.beta + (
+        0.5 * (x2_total - (2 * mu * x_total) + (n * (mu**2)))
+    )
+
+    return InverseGamma(alpha=alpha_post, beta=beta_post)
+
+
+def normal_known_mean_posterior_predictive(
+    mu: NUMERIC, inverse_gamma: InverseGamma
+) -> StudentT:
+    """Posterior predictive distribution for a normal likelihood with a known mean and a variance prior.
+
+    Args:
+        mu: known mean
+        inverse_gamma: InverseGamma prior
+
+    Returns:
+        StudentT posterior predictive distribution
+
+    """
+    return StudentT(
+        n=2 * inverse_gamma.alpha,
+        mu=mu,
+        sigma=(inverse_gamma.beta / inverse_gamma.alpha) ** 0.5,
+    )
+
+
 def linear_regression(
     X: NUMERIC,
     y: NUMERIC,

pyproject.toml

@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "conjugate-models"
-version = "0.1.5"
+version = "0.1.6"
 description = "Bayesian Conjugate Models in Python"
 authors = ["Will Dean <wd60622@gmail.com>"]
 license = "MIT"