diff --git a/GPy/core/parameterization/priors.py b/GPy/core/parameterization/priors.py
index c21f6bc5..71b9833e 100644
--- a/GPy/core/parameterization/priors.py
+++ b/GPy/core/parameterization/priors.py
@@ -1309,3 +1309,52 @@ class Exponential(Prior):
 
     def rvs(self, n):
         return np.random.exponential(scale=self.l, size=n)
+
+class StudentT(Prior):
+    """
+    Implementation of the student t probability function, coupled with random variables.
+
+    :param mu: mean
+    :param sigma: standard deviation
+    :param nu: degrees of freedom
+
+    .. Note:: Bishop 2006 notation is used throughout the code
+
+    """
+    domain = _REAL
+    _instances = []
+
+    def __new__(cls, mu=0, sigma=1, nu=4):  # Singleton:
+        if cls._instances:
+            cls._instances[:] = [instance for instance in cls._instances if instance()]
+            for instance in cls._instances:
+                if instance().mu == mu and instance().sigma == sigma and instance().nu == nu:
+                    return instance()
+        newfunc = super(Prior, cls).__new__
+        if newfunc is object.__new__:
+            o = newfunc(cls)
+        else:
+            o = newfunc(cls, mu, sigma, nu)
+        cls._instances.append(weakref.ref(o))
+        return cls._instances[-1]()
+
+    def __init__(self, mu, sigma, nu):
+        self.mu = float(mu)
+        self.sigma = float(sigma)
+        self.sigma2 = np.square(self.sigma)
+        self.nu = float(nu)
+
+    def __str__(self):
+        return "St({:.2g}, {:.2g}, {:.2g})".format(self.mu, self.sigma, self.nu)
+
+    def lnpdf(self, x):
+        from scipy.stats import t
+        return t.logpdf(x,self.nu,self.mu,self.sigma)
+
+    def lnpdf_grad(self, x):
+        return -(self.nu + 1.)*(x - self.mu)/( self.nu*self.sigma2 + np.square(x - self.mu) )
+
+    def rvs(self, n):
+        from scipy.stats import t
+        ret = t.rvs(self.nu, loc=self.mu, scale=self.sigma, size=n)
+        return ret    
diff --git a/GPy/kern/src/basis_funcs.py b/GPy/kern/src/basis_funcs.py
index 7a5f84dd..81b308b0 100644
--- a/GPy/kern/src/basis_funcs.py
+++ b/GPy/kern/src/basis_funcs.py
@@ -142,9 +142,9 @@ class LogisticBasisFuncKernel(BasisFuncKernel):
         self.centers = np.atleast_2d(centers)
         self.ARD_slope = ARD_slope
         if self.ARD_slope:
-            self.slope = Param('slope', slope * np.ones(self.centers.size), Logexp())
+            self.slope = Param('slope', slope * np.ones(self.centers.size))
         else:
-            self.slope = Param('slope', slope, Logexp())
+            self.slope = Param('slope', slope)
         super(LogisticBasisFuncKernel, self).__init__(input_dim, variance, active_dims, ARD, name)
         self.link_parameter(self.slope)
 
diff --git a/GPy/testing/prior_tests.py b/GPy/testing/prior_tests.py
index ca03ad93..23822a5a 100644
--- a/GPy/testing/prior_tests.py
+++ b/GPy/testing/prior_tests.py
@@ -6,6 +6,29 @@ import numpy as np
 import GPy
 
 class PriorTests(unittest.TestCase):
+    def test_studentT(self):
+        xmin, xmax = 1, 2.5*np.pi
+        b, C, SNR = 1, 0, 0.1
+        X = np.linspace(xmin, xmax, 500)
+        y  = b*X + C + 1*np.sin(X)
+        y += 0.05*np.random.randn(len(X))
+        X, y = X[:, None], y[:, None]
+        studentT = GPy.priors.StudentT(1, 2, 4)
+        
+        m = GPy.models.SparseGPRegression(X, y)
+        m.Z.set_prior(studentT)
+
+        # setting a StudentT prior on non-negative parameters
+        # should raise an assertionerror.
+        self.assertRaises(AssertionError, m.rbf.set_prior, studentT)
+        
+        # The gradients need to be checked
+        self.assertTrue(m.checkgrad())
+        
+        # Check the singleton pattern:
+        self.assertIs(studentT, GPy.priors.StudentT(1,2,4))
+        self.assertIsNot(studentT, GPy.priors.StudentT(2,2,4))
+    
     def test_lognormal(self):
         xmin, xmax = 1, 2.5*np.pi
         b, C, SNR = 1, 0, 0.1
@@ -74,7 +97,7 @@ class PriorTests(unittest.TestCase):
         # setting a Gaussian prior on non-negative parameters
         # should raise an assertionerror.
         #self.assertRaises(AssertionError, m.Z.set_prior, gaussian)
-
+        self.assertTrue(m.checkgrad())
 
 
     def test_fixed_domain_check(self):
@@ -107,8 +130,6 @@ class PriorTests(unittest.TestCase):
         # should raise an assertionerror.
         self.assertRaises(AssertionError, m.rbf.set_prior, gaussian)
 
-
-
 if __name__ == "__main__":
     print("Running unit tests, please be (very) patient...")
     unittest.main()