Update Bayesian_Gaussian_Mixture_Model.ipynb

Fixed broken link in line 482

Author: synandi

tensorflow_probability/examples/jupyter_notebooks/Bayesian_Gaussian_Mixture_Model.ipynb

@@ -114,7 +114,7 @@
         "\n",
         "It is not possible to directly sample from this distribution owing to a computationally intractable normalization term.\n",
         "\n",
-        "[Metropolis-Hastings algorithms](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) are technique for for sampling from intractable-to-normalize distributions.\n",
+        "[Metropolis-Hastings algorithms](https://en.wikipedia.org/wiki/Metropolis%E2%80%93Hastings_algorithm) are techniques for sampling from intractable-to-normalize distributions.\n",
         "\n",
         "TensorFlow Probability offers a number of MCMC options, including several based on Metropolis-Hastings. In this notebook, we'll use [Hamiltonian Monte Carlo](https://en.wikipedia.org/wiki/Hamiltonian_Monte_Carlo)  (`tfp.mcmc.HamiltonianMonteCarlo`). HMC is often a good choice because it can converge rapidly, samples the state space jointly (as opposed to coordinatewise), and leverages one of TF's virtues: automatic differentiation. That said, sampling from a BGMM posterior might actually be better done by other approaches, e.g., [Gibb's sampling](https://en.wikipedia.org/wiki/Gibbs_sampling)."
       ]
@@ -154,7 +154,7 @@
         "id": "Uj9uHZN2yUqz"
       },
       "source": [
-        "Before actually building the model, we'll need to define a new type of distribution.  From the model specification above, its clear we're parameterizing the MVN with an inverse covariance matrix, i.e.,  [precision matrix](https://en.wikipedia.org/wiki/Precision_(statistics%29).  To accomplish this in TF,  we'll need to roll out our `Bijector`.  This `Bijector` will use the forward transformation:\n",
+        "Before actually building the model, we'll need to define a new type of distribution.  From the model specification above, it's clear we're parameterizing the MVN with an inverse covariance matrix, i.e.,  [precision matrix](https://en.wikipedia.org/wiki/Precision_(statistics%29).  To accomplish this in TF,  we'll need to roll out our `Bijector`.  This `Bijector` will use the forward transformation:\n",
         "\n",
         "- `Y =  tf.linalg.triangular_solve((tf.linalg.matrix_transpose(chol_precision_tril), X, adjoint=True) + loc`.\n",
         "\n",
@@ -459,7 +459,7 @@
         "id": "JS8XOsxiyiBV"
       },
       "source": [
-        "Hamiltonian Monte Carlo (HMC) requires the target log-probability function be differentiable with respect to its arguments.  Furthermore, HMC can exhibit dramatically higher statistical efficiency if the state-space is unconstrained.\n",
+        "Hamiltonian Monte Carlo (HMC) requires the target log-probability function to be differentiable with respect to its arguments.  Furthermore, HMC can exhibit dramatically higher statistical efficiency if the state-space is unconstrained.\n",
         "\n",
         "This means we'll have to work out two main issues when sampling from the BGMM posterior:\n",
         "\n",
@@ -479,11 +479,11 @@
         "2. run the MCMC in unconstrained space\n",
         "3. transform the unconstrained variables back to the constrained space.\n",
         "\n",
-        "As with `MVNCholPrecisionTriL`, we'll use [`Bijector`s](https://www.tensorflow.org/api_docs/python/tf/distributions/bijectors/Bijector) to transform random variables to unconstrained space.\n",
+        "As with `MVNCholPrecisionTriL`, we'll use [`Bijector`s](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Bijector) to transform random variables to unconstrained space.\n",
         "\n",
         "- The [`Dirichlet`](https://en.wikipedia.org/wiki/Dirichlet_distribution) is transformed to unconstrained space via the [softmax function](https://en.wikipedia.org/wiki/Softmax_function).\n",
         "\n",
-        "- Our precision random variable is a distribution over postive semidefinite matrices. To unconstrain these we'll use the `FillTriangular` and `TransformDiagonal` bijectors.  These convert vectors to lower-triangular matrices and ensure the diagonal is positive. The former is useful because it enables sampling only $d(d+1)/2$ floats rather than $d^2$."
+        "- Our precision random variable is a distribution over positive semidefinite matrices. To unconstrain these we'll use the `FillTriangular` and `TransformDiagonal` bijectors.  These convert vectors to lower-triangular matrices and ensure the diagonal is positive. The former is useful because it enables sampling only $d(d+1)/2$ floats rather than $d^2$."
       ]
     },
     {