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Add distribution statements
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src/functions-reference/embedded_laplace.qmd

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@@ -219,6 +219,22 @@ The arguments required to compute this likelihood are:
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* `y_index`: an array whose $i^\text{th}$ element indicates to which
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group the $i^\text{th}$ observation belongs to.
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<!-- real; laplace_marginal_poisson_log ~; -->
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\index{{\tt \bfseries laplace\_marginal\_poisson\_log }!sampling statement|hyperpage}
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`y ~ ` **`laplace_marginal_poisson_log`**`(y_index, theta0, K_function, (...))`<br>\newline
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Increment target log probability density with `laplace_marginal_poisson_log_lupmf(y | y_index, theta0, K_function, (...))`.
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{{< since 2.37 >}}
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<!-- real; laplace_marginal_tol_poisson_log ~; -->
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\index{{\tt \bfseries laplace\_marginal\_tol\_poisson\_log }!sampling statement|hyperpage}
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`y ~ ` **`laplace_marginal_tol_poisson_log`**`(y_index, theta0, K_function, (...), tol, max_steps, hessian_block_size, solver, max_steps_linesearch)`<br>\newline
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Increment target log probability density with `laplace_marginal_tol_poisson_log_lupmf(y | y_index, theta0, K_function, (...), tol, max_steps, hessian_block_size, solver, max_steps_linesearch)`.
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{{< since 2.37 >}}
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The signatures for the embedded Laplace approximation function with a Poisson
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likelihood are
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@@ -259,6 +275,24 @@ to the rate parameter of the Poisson. The likelihood is then,
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$$
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p(y \mid \theta, \phi) = \prod_i\text{Poisson} (y_i \mid \exp(\theta_{g(i)}) x_i).
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$$
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<!-- real; laplace_marginal_poisson_2_log ~; -->
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\index{{\tt \bfseries laplace\_marginal\_poisson\_2\_log }!sampling statement|hyperpage}
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`y ~ ` **`laplace_marginal_poisson_2_log`**`(y_index, x, theta0, K_function, (...))`<br>\newline
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Increment target log probability density with `laplace_marginal_poisson_2_log_lupmf(y | y_index, x, theta0, K_function, (...))`.
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{{< since 2.37 >}}
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<!-- real; laplace_marginal_tol_poisson_2_log ~; -->
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\index{{\tt \bfseries laplace\_marginal\_tol\_poisson\_2\_log }!sampling statement|hyperpage}
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`y ~ ` **`laplace_marginal_tol_poisson_2_log`**`(y_index, x, theta0, K_function, (...), tol, max_steps, hessian_block_size, solver, max_steps_linesearch)`<br>\newline
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Increment target log probability density with `laplace_marginal_tol_poisson_2_log_lupmf(y | y_index, x, theta0, K_function, (...), tol, max_steps, hessian_block_size, solver, max_steps_linesearch)`.
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{{< since 2.37 >}}
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The signatures for this function are:
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<!-- real; laplace_marginal_poisson_2_log_lpmf; (array[] int y | array[] int y_index, vector x, vector theta0, function K_function, tuple(...)); -->
@@ -313,6 +347,23 @@ The arguments for the likelihood function are:
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group the $i^\text{th}$ observation belongs to.
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* `eta`: the overdispersion parameter.
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<!-- real; laplace_marginal_neg_binomial_2_log ~; -->
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\index{{\tt \bfseries laplace\_marginal\_neg\_binomial\_2\_log }!sampling statement|hyperpage}
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`y ~ ` **`laplace_marginal_neg_binomial_2_log`**`(y_index, eta, theta0, K_function, (...))`<br>\newline
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Increment target log probability density with `laplace_marginal_neg_binomial_2_log_lupmf(y | y_index, eta, theta0, K_function, (...))`.
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{{< since 2.37 >}}
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<!-- real; laplace_marginal_tol_neg_binomial_2_log ~; -->
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\index{{\tt \bfseries laplace\_marginal\_tol\_neg\_binomial\_2\_log }!sampling statement|hyperpage}
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`y ~ ` **`laplace_marginal_tol_neg_binomial_2_log`**`(y_index, eta, theta0, K_function, (...), tol, max_steps, hessian_block_size, solver, max_steps_linesearch)`<br>\newline
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Increment target log probability density with `laplace_marginal_tol_neg_binomial_2_log_lupmf(y | y_index, eta, theta0, K_function, (...), tol, max_steps, hessian_block_size, solver, max_steps_linesearch)`.
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{{< since 2.37 >}}
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The function signatures for the embedded Laplace approximation with a negative
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Binomial likelihood are
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<!-- real; laplace_marginal_neg_binomial_2_log_lpmf; (array[] int y | array[] int y_index, real eta, vector theta0, function K_function, tuple(...)); -->
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* `y_index`: an array whose $i^\text{th}$ element indicates to which
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group the $i^\text{th}$ observation belongs to.
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<!-- real; laplace_marginal_bernoulli_logit ~; -->
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\index{{\tt \bfseries laplace\_marginal\_bernoulli\_logit }!sampling statement|hyperpage}
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`y ~ ` **`laplace_marginal_bernoulli_logit`**`(y_index, theta0, K_function, (...))`<br>\newline
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Increment target log probability density with `laplace_marginal_bernoulli_logit_lupmf(y | y_index, theta0, K_function, (...))`.
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{{< since 2.37 >}}
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<!-- real; laplace_marginal_tol_bernoulli_logit ~; -->
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\index{{\tt \bfseries laplace\_marginal\_tol\_bernoulli\_logit }!sampling statement|hyperpage}
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`y ~ ` **`laplace_marginal_tol_bernoulli_logit`**`(y_index, theta0, K_function, (...), tol, max_steps, hessian_block_size, solver, max_steps_linesearch)`<br>\newline
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Increment target log probability density with `laplace_marginal_tol_bernoulli_logit_lupmf(y | y_index, theta0, K_function, (...), tol, max_steps, hessian_block_size, solver, max_steps_linesearch)`.
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{{< since 2.37 >}}
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The function signatures for the embedded Laplace approximation with a Bernoulli likelihood are
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<!-- real; laplace_marginal_bernoulli_logit_lpmf; (array[] int y | array[] int y_index, vector theta0, function K_function, tuple(...)); -->

src/functions-reference/functions_index.qmd

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