diff --git a/GPy/testing/inference_tests.py b/GPy/testing/inference_tests.py
new file mode 100644
index 00000000..c7efa821
--- /dev/null
+++ b/GPy/testing/inference_tests.py
@@ -0,0 +1,71 @@
+
+"""
+The test cases for various inference algorithms
+"""
+
+import unittest, itertools
+import numpy as np
+import GPy
+
+
+class InferenceXTestCase(unittest.TestCase):
+    
+    def genData(self):
+        D1,D2,N = 12,12,50
+        np.random.seed(1234)
+    
+        x = np.linspace(0, 4 * np.pi, N)[:, None]
+        s1 = np.vectorize(lambda x: np.sin(x))
+        s2 = np.vectorize(lambda x: np.cos(x)**2)
+        s3 = np.vectorize(lambda x:-np.exp(-np.cos(2 * x)))
+        sS = np.vectorize(lambda x: np.cos(x))
+    
+        s1 = s1(x)
+        s2 = s2(x)
+        s3 = s3(x)
+        sS = sS(x)
+    
+        s1 -= s1.mean(); s1 /= s1.std(0)
+        s2 -= s2.mean(); s2 /= s2.std(0)
+        s3 -= s3.mean(); s3 /= s3.std(0)
+        sS -= sS.mean(); sS /= sS.std(0)
+    
+        S1 = np.hstack([s1, sS])
+        S2 = np.hstack([s3, sS])
+    
+        P1 = np.random.randn(S1.shape[1], D1)
+        P2 = np.random.randn(S2.shape[1], D2)
+    
+        Y1 = S1.dot(P1)
+        Y2 = S2.dot(P2)
+    
+        Y1 += .01 * np.random.randn(*Y1.shape)
+        Y2 += .01 * np.random.randn(*Y2.shape)
+    
+        Y1 -= Y1.mean(0)
+        Y2 -= Y2.mean(0)
+        Y1 /= Y1.std(0)
+        Y2 /= Y2.std(0)
+
+        slist = [s1, s2, s3, sS]
+        slist_names = ["s1", "s2", "s3", "sS"]
+        Ylist = [Y1, Y2]
+        
+        return Ylist
+    
+    def test_inferenceX_BGPLVM(self):
+        Ys = self.genData()
+        m = GPy.models.BayesianGPLVM(Ys[0],5,kernel=GPy.kern.Linear(5,ARD=True))
+        
+        x,mi = m.infer_newX(m.Y, optimize=False)
+        self.assertTrue(mi.checkgrad())
+        
+        m.optimize(max_iters=10000)
+        x,mi = m.infer_newX(m.Y)
+
+        self.assertTrue(np.allclose(m.X.mean, mi.X.mean))
+        self.assertTrue(np.allclose(m.X.variance, mi.X.variance))
+        
+
+if __name__ == "__main__":
+    unittest.main()
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