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Copy file name to clipboardExpand all lines: src/functions-reference/embedded_laplace.qmd
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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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```
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real laplace_marginal_poisson_log_lpmf(array[] int y | array[] int y_index,
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vector theta0, function K_function, tuple(...));
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real laplace_marginal_tol_poisson_log_lpmf(array[] int y | array[] int y_index,
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vector theta0, function K_function, tuple(...),
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real tol, int max_steps, int hessian_block_size,
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int solver, int max_steps_linesearch);
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<!-- real; laplace_marginal_poisson_log_lpmf; (array[] int y \textbar\ array[] int y_index, vector theta0, function K_function, tuple(...)); -->
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\index{{\tt \bfseries laplace\_marginal\_poisson\_log\_lpmf }!{\tt (array[] int y \textbar\ array[] int y\_index, vector theta0, function K\_function, tuple(...)): real}|hyperpage}
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vector laplace_latent_poisson_log_rng(array[] int y, array[] int y_index,
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vector theta0, function K_function, tuple(...));
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`real`**`laplace_marginal_poisson_log_lpmf`**`(array[] int y \textbar\ array[] int y_index, vector theta0, function K_function, tuple(...))`<br>\newline
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vector laplace_latent_tol_poisson_log_rng(array[] int y, array[] int y_index,
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vector theta0, function K_function, tuple(...),
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real tol, int max_steps, int hessian_block_size,
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int solver, int max_steps_linesearch);
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```
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{{< since 2.37 >}}
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<!-- real; laplace_marginal_tol_poisson_log_lpmf; (array[] int y \textbar\ array[] int y_index, vector theta0, function K_function, tuple(...), real tol, int max_steps, int hessian_block_size, int solver, int max_steps_linesearch); -->
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\index{{\tt \bfseries laplace\_marginal\_tol\_poisson\_log\_lpmf }!{\tt (array[] int y \textbar\ array[] int y\_index, vector theta0, function K\_function, tuple(...), real tol, int max\_steps, int hessian\_block\_size, int solver, int max\_steps\_linesearch): real}|hyperpage}
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`real`**`laplace_marginal_tol_poisson_log_lpmf`**`(array[] int y \textbar\ array[] int y_index, vector theta0, function K_function, tuple(...), real tol, int max_steps, int hessian_block_size, int solver, int max_steps_linesearch)`<br>\newline
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{{< since 2.37 >}}
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<!-- vector; laplace_latent_poisson_log_rng; (array[] int y, array[] int y_index, vector theta0, function K_function, tuple(...)); -->
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\index{{\tt \bfseries laplace\_latent\_poisson\_log\_rng }!{\tt (array[] int y, array[] int y\_index, vector theta0, function K\_function, tuple(...)): vector}|hyperpage}
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`vector`**`laplace_latent_poisson_log_rng`**`(array[] int y, array[] int y_index, vector theta0, function K_function, tuple(...))`<br>\newline
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{{< since 2.37 >}}
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<!-- vector; laplace_latent_tol_poisson_log_rng; (array[] int y, array[] int y_index, vector theta0, function K_function, tuple(...), real tol, int max_steps, int hessian_block_size, int solver, int max_steps_linesearch); -->
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\index{{\tt \bfseries laplace\_latent\_tol\_poisson\_log\_rng }!{\tt (array[] int y, array[] int y\_index, vector theta0, function K\_function, tuple(...), real tol, int max\_steps, int hessian\_block\_size, int solver, int max\_steps\_linesearch): vector}|hyperpage}
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`vector`**`laplace_latent_tol_poisson_log_rng`**`(array[] int y, array[] int y_index, vector theta0, function K_function, tuple(...), real tol, int max_steps, int hessian_block_size, int solver, int max_steps_linesearch)`<br>\newline
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{{< since 2.37 >}}
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A similar built-in likelihood lets users specify an offset $x_i \in \mathbb R^+$
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to the rate parameter of the Poisson. The likelihood is then,
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