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4 changes: 2 additions & 2 deletions docs/source/learn/core_notebooks/pymc_overview.ipynb
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"\n",
"This is a more realistic problem than the first regression example, as we are now dealing with a **multivariate regression** model. However, while there are several potential predictors in the LSL-DR dataset, it is difficult *a priori* to determine which ones are relevant for constructing an effective statistical model. There are a number of approaches for conducting variable selection, but a popular automated method is *regularization*, whereby ineffective covariates are shrunk towards zero via regularization (a form of penalization) if they do not contribute to predicting outcomes. \n",
"\n",
"You may have heard of regularization from machine learning or classical statistics applications, where methods like the lasso or ridge regression shrink parameters towards zero by applying a penalty to the size of the regression parameters. In a Bayesian context, we apply an appropriate prior distribution to the regression coefficients. One such prior is the *hierarchical regularized horseshoe*, which uses two regularization strategies, one global and a set of local local parameters, one for each coefficient. The key to making this work is by selecting a long-tailed distribution as the shrinkage priors, which allows some to be nonzero, while pushing the rest towards zero.\n",
"You may have heard of regularization from machine learning or classical statistics applications, where methods like the lasso or ridge regression shrink parameters towards zero by applying a penalty to the size of the regression parameters. In a Bayesian context, we apply an appropriate prior distribution to the regression coefficients. One such prior is the *hierarchical regularized horseshoe*, which uses two regularization strategies, one global and a set of local parameters, one for each coefficient. The key to making this work is by selecting a long-tailed distribution as the shrinkage priors, which allows some to be nonzero, while pushing the rest towards zero.\n",
"\n",
"The horeshoe prior for each regression coefficient $\\beta_i$ looks like this:\n",
"\n",
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"source": [
"### Model Specification\n",
"\n",
"Specifying the model in PyMC mirrors its statistical specification. This model employs a couple of new distributions: the {class}`~pymc.HalfStudentT` distribution for the $\\tau$ and $\\lambda$ priors, and the `InverseGamma` distribution for the $c2$ variable.\n",
"Specifying the model in PyMC mirrors its statistical specification. This model employs a couple of new distributions: the {class}`~pymc.HalfStudentT` distribution for the $\\tau$ and $\\lambda$ priors, and the `InverseGamma` distribution for the $c^2$ variable.\n",
"\n",
"In PyMC, variables with purely positive priors like {class}`~pymc.InverseGamma` are transformed with a log transform. This makes sampling more robust. Behind the scenes, a variable in the unconstrained space (named `<variable-name>_log`) is added to the model for sampling. Variables with priors that constrain them on two sides, like {class}`~pymc.Beta` or {class}`~pymc.Uniform`, are also transformed to be unconstrained but with a log odds transform. \n",
"\n",
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