Initial commit, setting up the laplace approximation for a student t

python/likelihoods/likelihood_function.py

@@ -0,0 +1,51 @@
+import GPy
+from scipy.special import gamma, gammaln
+
+class student_t(GPy.likelihoods.likelihood_function):
+    """Student t likelihood distribution
+    For nomanclature see Bayesian Data Analysis 2003 p576
+
+    Laplace:
+    Needs functions to calculate
+    ln p(yi|fi)
+    dln p(yi|fi)_dfi
+    d2ln p(yi|fi)_d2fi
+    """
+    def __init__(self, deg_free, sigma=1):
+        self.v = deg_free
+        self.sigma = 1
+
+    def link_function(self, y_i, f_i):
+        """link_function $\ln p(y_i|f_i)$
+
+        :y_i: datum number i
+        :f_i: latent variable f_i
+        :returns: float(likelihood evaluated for this point)
+
+        """
+        e = y_i - f_i
+        return gammaln((v+1)*0.5) - gammaln(v*0.5) - np.ln(v*np.pi*sigma)*0.5 - (v+1)*0.5*np.ln(1 + ((e/sigma)**2)/v)
+
+    def link_grad(self, y_i, f_i):
+        """gradient of the link function at y_i, given f_i w.r.t f_i
+
+        :y_i: datum number i
+        :f_i: latent variable f_i
+        :returns: float(gradient of likelihood evaluated at this point)
+
+        """
+        pass
+
+    def link_hess(self, y_i, f_i, f_j):
+        """hessian at this point (the hessian will be 0 unless i == j)
+        i.e. second derivative w.r.t f_i and f_j
+
+        :y_i: @todo
+        :f_i: @todo
+        :f_j: @todo
+        :returns: @todo
+
+        """
+        if f_i =
+        pass
+