fix links in MLDA Page

Author: HimanshuSainani

examples/samplers/MLDA_introduction.ipynb

@@ -65,9 +65,9 @@
     "\n",
     "[Variance reduction 1](./MLDA_variance_reduction_linear_regression.ipynb) and [Variance reduction 2](https://github.com/alan-turing-institute/pymc/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_variance_reduction_groundwater.ipynb) (external link): Those two notebooks demonstrate the variance reduction feature in a linear regression model and a groundwater flow model. This feature allows the user to define a quantity of interest that they need to estimate using the MCMC samples. It then collects those quantities of interest, as well as differences of these quantities between levels, during MLDA sampling. The collected quentities can then be used to produce an estimate which has lower variance than a standard estimate that uses samples from the fine chain only. The first notebook does not have external dependencies, while the second one requires FEniCS. Note that the second notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency.\n",
     "\n",
-    "[Adaptive error model](https://github.com/alan-turing-institute/pymc/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_adaptive_error_model.ipynb) (external link): In this notebook we use MLDA to tackle another inverse problem; groundwarer flow modeling. The aim is to infer the posterior distribution of model parameters (hydraulic conductivity) given data (measurements of hydraulic head). In this example we make use of PyTensor Ops in order to define a \"black box\" likelihood, i.e. a likelihood that uses external code. Specifically, our likelihood uses the [FEniCS](https://fenicsproject.org/) library to solve a PDE. This is a common scenario, as PDEs of this type are slow to solve with scipy or other standard libraries. Note that this notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency. We employ the adaptive error model (AEM) feature and compare the performance of basic MLDA with AEM-enhanced MLDA. The idea of Adaptive Error Model (AEM) is to estimate the mean and variance of the forward-model error between adjacent levels, i.e. estimate the bias of the coarse forward model compared to the fine forward model, and use those estimates to correct the coarse model. Using the technique should improve ESS/sec on the fine level.\n",
+    "[Adaptive error model](https://github.com/alan-turing-institute/pymc3/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_adaptive_error_model.ipynb) (external link): In this notebook we use MLDA to tackle another inverse problem; groundwarer flow modeling. The aim is to infer the posterior distribution of model parameters (hydraulic conductivity) given data (measurements of hydraulic head). In this example we make use of PyTensor Ops in order to define a \"black box\" likelihood, i.e. a likelihood that uses external code. Specifically, our likelihood uses the [FEniCS](https://fenicsproject.org/) library to solve a PDE. This is a common scenario, as PDEs of this type are slow to solve with scipy or other standard libraries. Note that this notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency. We employ the adaptive error model (AEM) feature and compare the performance of basic MLDA with AEM-enhanced MLDA. The idea of Adaptive Error Model (AEM) is to estimate the mean and variance of the forward-model error between adjacent levels, i.e. estimate the bias of the coarse forward model compared to the fine forward model, and use those estimates to correct the coarse model. Using the technique should improve ESS/sec on the fine level.\n",
     "\n",
-    "[Benchmarks and tuning](https://github.com/alan-turing-institute/pymc/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_benchmarks_tuning.ipynb) (external link): In this notebook we benchmark MLDA against other samplers using different parameterizations of the groundwater flow model. We also give some advice on tuning MLDA. Note that this notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency."
+    "[Benchmarks and tuning](https://github.com/alan-turing-institute/pymc3/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_benchmarks_tuning.ipynb) (external link): In this notebook we benchmark MLDA against other samplers using different parameterizations of the groundwater flow model. We also give some advice on tuning MLDA. Note that this notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency."
    ]
   },
   {

examples/samplers/MLDA_introduction.myst.md

@@ -59,9 +59,9 @@ Please note that the MLDA sampler is new in PyMC. The user should be extra criti
 
 [Variance reduction 1](./MLDA_variance_reduction_linear_regression.ipynb) and [Variance reduction 2](https://github.com/alan-turing-institute/pymc/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_variance_reduction_groundwater.ipynb) (external link): Those two notebooks demonstrate the variance reduction feature in a linear regression model and a groundwater flow model. This feature allows the user to define a quantity of interest that they need to estimate using the MCMC samples. It then collects those quantities of interest, as well as differences of these quantities between levels, during MLDA sampling. The collected quentities can then be used to produce an estimate which has lower variance than a standard estimate that uses samples from the fine chain only. The first notebook does not have external dependencies, while the second one requires FEniCS. Note that the second notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency.
 
-[Adaptive error model](https://github.com/alan-turing-institute/pymc/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_adaptive_error_model.ipynb) (external link): In this notebook we use MLDA to tackle another inverse problem; groundwarer flow modeling. The aim is to infer the posterior distribution of model parameters (hydraulic conductivity) given data (measurements of hydraulic head). In this example we make use of PyTensor Ops in order to define a "black box" likelihood, i.e. a likelihood that uses external code. Specifically, our likelihood uses the [FEniCS](https://fenicsproject.org/) library to solve a PDE. This is a common scenario, as PDEs of this type are slow to solve with scipy or other standard libraries. Note that this notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency. We employ the adaptive error model (AEM) feature and compare the performance of basic MLDA with AEM-enhanced MLDA. The idea of Adaptive Error Model (AEM) is to estimate the mean and variance of the forward-model error between adjacent levels, i.e. estimate the bias of the coarse forward model compared to the fine forward model, and use those estimates to correct the coarse model. Using the technique should improve ESS/sec on the fine level.
+[Adaptive error model](https://github.com/alan-turing-institute/pymc3/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_adaptive_error_model.ipynb) (external link): In this notebook we use MLDA to tackle another inverse problem; groundwarer flow modeling. The aim is to infer the posterior distribution of model parameters (hydraulic conductivity) given data (measurements of hydraulic head). In this example we make use of PyTensor Ops in order to define a "black box" likelihood, i.e. a likelihood that uses external code. Specifically, our likelihood uses the [FEniCS](https://fenicsproject.org/) library to solve a PDE. This is a common scenario, as PDEs of this type are slow to solve with scipy or other standard libraries. Note that this notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency. We employ the adaptive error model (AEM) feature and compare the performance of basic MLDA with AEM-enhanced MLDA. The idea of Adaptive Error Model (AEM) is to estimate the mean and variance of the forward-model error between adjacent levels, i.e. estimate the bias of the coarse forward model compared to the fine forward model, and use those estimates to correct the coarse model. Using the technique should improve ESS/sec on the fine level.
 
-[Benchmarks and tuning](https://github.com/alan-turing-institute/pymc/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_benchmarks_tuning.ipynb) (external link): In this notebook we benchmark MLDA against other samplers using different parameterizations of the groundwater flow model. We also give some advice on tuning MLDA. Note that this notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency.
+[Benchmarks and tuning](https://github.com/alan-turing-institute/pymc3/blob/mlda_all_notebooks/docs/source/notebooks/MLDA_benchmarks_tuning.ipynb) (external link): In this notebook we benchmark MLDA against other samplers using different parameterizations of the groundwater flow model. We also give some advice on tuning MLDA. Note that this notebook is outside the core PyMC repository because FEniCS is not a PyMC dependency.
 
 ```{code-cell} ipython3
 %load_ext watermark