Issue/959 cleanup sampling stmts

src/functions-reference/binary_distributions.qmd

@@ -29,7 +29,7 @@ Increment target log probability density with `bernoulli_lupmf(y | theta)`.
 {{< since 2.0 >}}
 
 <!-- real; bernoulli ~; -->
-\index{{\tt \bfseries bernoulli }!sampling statement|hyperpage}
+\index{{\tt \bfseries bernoulli }!distribution statement|hyperpage}
 
 ### Stan Functions
 
@@ -109,7 +109,7 @@ Increment target log probability density with `bernoulli_logit_lupmf(y | alpha)`
 {{< since 2.0 >}}
 
 <!-- real; bernoulli_logit ~; -->
-\index{{\tt \bfseries bernoulli\_logit }!sampling statement|hyperpage}
+\index{{\tt \bfseries bernoulli\_logit }!distribution statement|hyperpage}
 
 ### Stan Functions
 
@@ -168,7 +168,7 @@ Increment target log probability density with `bernoulli_logit_glm_lupmf(y | x,
 {{< since 2.25 >}}
 
 <!-- real; bernoulli_logit_glm ~; -->
-\index{{\tt \bfseries bernoulli\_logit\_glm }!sampling statement|hyperpage}
+\index{{\tt \bfseries bernoulli\_logit\_glm }!distribution statement|hyperpage}
 
 ### Stan Functions
 

src/functions-reference/bounded_continuous_distributions.qmd

@@ -25,7 +25,7 @@ $y \in [\alpha,\beta]$, \begin{equation*} \text{Uniform}(y|\alpha,\beta) =
 Increment target log probability density with `uniform_lupdf(y | alpha, beta)`.
 {{< since 2.0 >}}
 <!-- real; uniform ~; -->
-\index{{\tt \bfseries uniform }!sampling statement|hyperpage}
+\index{{\tt \bfseries uniform }!distribution statement|hyperpage}
 
 ### Stan functions
 

src/functions-reference/bounded_discrete_distributions.qmd

@@ -37,7 +37,7 @@ Increment target log probability density with `binomial_lupmf(n | N, theta)`.
 {{< since 2.0 >}}
 
 <!-- real ; binomial ~; -->
-\index{{\tt \bfseries binomial }!sampling statement|hyperpage}
+\index{{\tt \bfseries binomial }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -127,7 +127,7 @@ n}{\text{logit}^{-1}(\alpha)} \end{equation*}
 Increment target log probability density with `binomial_logit_lupmf(n | N, alpha)`.
 {{< since 2.0 >}}
 <!-- real; binomial_logit ~; -->
-\index{{\tt \bfseries binomial\_logit }!sampling statement|hyperpage}
+\index{{\tt \bfseries binomial\_logit }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -173,7 +173,7 @@ Increment target log probability density with `binomial_logit_glm_lupmf(n | N, x
 {{< since 2.34 >}}
 
 <!-- real; binomial_logit_glm ~; -->
-\index{{\tt \bfseries binomial\_logit\_glm }!sampling statement|hyperpage}
+\index{{\tt \bfseries binomial\_logit\_glm }!distribution statement|hyperpage}
 
 ### Stan Functions
 
@@ -293,7 +293,7 @@ If $N \in \mathbb{N}$, $\alpha \in \mathbb{R}^+$, and $\beta \in
 Increment target log probability density with `beta_binomial_lupmf(n | N, alpha, beta)`.
 {{< since 2.0 >}}
 <!-- real; beta_binomial ~; -->
-\index{{\tt \bfseries beta\_binomial }!sampling statement|hyperpage}
+\index{{\tt \bfseries beta\_binomial }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -369,7 +369,7 @@ If $a \in \mathbb{N}$, $b \in \mathbb{N}$, and $N \in
 Increment target log probability density with `hypergeometric_lupmf(n | N, a, b)`.
 {{< since 2.0 >}}
 <!-- real; hypergeometric ~; -->
-\index{{\tt \bfseries hypergeometric }!sampling statement|hyperpage}
+\index{{\tt \bfseries hypergeometric }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -419,7 +419,7 @@ Increment target log probability density with `categorical_lupmf(y | theta)`
 dropping constant additive terms.
 {{< since 2.0 >}}
 <!-- real; categorical ~; -->
-\index{{\tt \bfseries categorical }!sampling statement|hyperpage}
+\index{{\tt \bfseries categorical }!distribution statement|hyperpage}
 
 ### Distribution statement
 
@@ -428,7 +428,7 @@ dropping constant additive terms.
 Increment target log probability density with `categorical_logit_lupmf(y | beta)`.
 {{< since 2.4 >}}
 <!-- real; categorical_logit ~; -->
-\index{{\tt \bfseries categorical\_logit }!sampling statement|hyperpage}
+\index{{\tt \bfseries categorical\_logit }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -522,7 +522,7 @@ See [the definition of softmax](matrix_operations.qmd#softmax) for the definitio
 Increment target log probability density with `categorical_logit_glm_lupmf(y | x, alpha, beta)`.
 {{< since 2.23 >}}
 <!-- real; categorical_logit_glm ~; -->
-\index{{\tt \bfseries categorical\_logit\_glm }!sampling statement|hyperpage}
+\index{{\tt \bfseries categorical\_logit\_glm }!distribution statement|hyperpage}
 
 
 ### Stan functions
@@ -612,7 +612,7 @@ Increment the target log probability density with `discrete_range_lupmf(y | l, u
 dropping constant additive terms.
 {{< since 2.26 >}}
 <!-- real; discrete_range ~; -->
-\index{{\tt \bfseries discrete\_range }!sampling statement|hyperpage}
+\index{{\tt \bfseries discrete\_range }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -695,7 +695,7 @@ $\text{logit}^{-1}(\infty) = 1$.
 Increment target log probability density with `ordered_logistic_lupmf(k | eta, c)`.
 {{< since 2.0 >}}
 <!-- real; ordered_logistic ~; -->
-\index{{\tt \bfseries ordered\_logistic }!sampling statement|hyperpage}
+\index{{\tt \bfseries ordered\_logistic }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -754,7 +754,7 @@ $\text{logit}^{-1}(\infty) = 1$.
 Increment target log probability density with `ordered_logistic_lupmf(y | x, beta, c)`.
 {{< since 2.23 >}}
 <!-- real; ordered_logistic ~; -->
-\index{{\tt \bfseries ordered\_logistic\_glm }!sampling statement|hyperpage}
+\index{{\tt \bfseries ordered\_logistic\_glm }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -851,7 +851,7 @@ $\Phi(\infty) = 1$.
 Increment target log probability density with `ordered_probit_lupmf(k | eta, c)`.
 {{< since 2.19 >}}
 <!-- real; ordered_probit ~; -->
-\index{{\tt \bfseries ordered\_probit }!sampling statement|hyperpage}
+\index{{\tt \bfseries ordered\_probit }!distribution statement|hyperpage}
 
 ### Stan functions
 

src/functions-reference/circular_distributions.qmd

@@ -43,7 +43,7 @@ of the values of $y$ or $\mu$).
 Increment target log probability density with `von_mises_lupdf(y | mu, kappa)`.
 {{< since 2.0 >}}
 <!-- real; von_mises ~; -->
-\index{{\tt \bfseries von\_mises }!sampling statement|hyperpage}
+\index{{\tt \bfseries von\_mises }!distribution statement|hyperpage}
 
 ### Stan functions
 

src/functions-reference/continuous_distributions_on_0_1.qmd

@@ -30,7 +30,7 @@ distribution requires strictly positive parameters, $\alpha, \beta >
 Increment target log probability density with `beta_lupdf(theta | alpha, beta)`.
 {{< since 2.0 >}}
 <!-- real; beta ~; -->
-\index{{\tt \bfseries beta }!sampling statement|hyperpage}
+\index{{\tt \bfseries beta }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -111,7 +111,7 @@ parameter, $\kappa > 0$.
 Increment target log probability density with `beta_proportion_lupdf(theta | mu, kappa)`.
 {{< since 2.19 >}}
 <!-- real; beta_proportion ~; -->
-\index{{\tt \bfseries beta\_proportion }!sampling statement|hyperpage}
+\index{{\tt \bfseries beta\_proportion }!distribution statement|hyperpage}
 
 ### Stan functions
 <!-- real; beta_proportion_lpdf; (reals theta | reals mu, reals kappa); -->

src/functions-reference/conventions_for_probability_functions.qmd

@@ -224,7 +224,7 @@ is just a more efficient way to write
  }
 ```
 
-With the same arguments, the vectorized sampling statement
+With the same arguments, the vectorized distribution statement
 
 ```stan
  y ~ normal(mu, sigma);

src/functions-reference/correlation_matrix_distributions.qmd

@@ -61,7 +61,7 @@ practice.
 Increment target log probability density with `lkj_corr_lupdf(y | eta)`.
 {{< since 2.3 >}}
 <!-- real; lkj_corr ~; -->
-\index{{\tt \bfseries lkj\_corr }!sampling statement|hyperpage}
+\index{{\tt \bfseries lkj\_corr }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -139,7 +139,7 @@ unit Euclidean length.
 Increment target log probability density with `lkj_corr_cholesky_lupdf(L | eta)`.
 {{< since 2.4 >}}
 <!-- real; lkj_corr_cholesky ~; -->
-\index{{\tt \bfseries lkj\_corr\_cholesky }!sampling statement|hyperpage}
+\index{{\tt \bfseries lkj\_corr\_cholesky }!distribution statement|hyperpage}
 
 ### Stan functions
 

src/functions-reference/covariance_matrix_distributions.qmd

@@ -36,7 +36,7 @@ Gamma function,
 Increment target log probability density with `wishart_lupdf(W | nu, Sigma)`.
 {{< since 2.0 >}}
 <!-- real; wishart ~; -->
-\index{{\tt \bfseries wishart }!sampling statement|hyperpage}
+\index{{\tt \bfseries wishart }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -150,7 +150,7 @@ for symmetric and positive-definite $W \in \mathbb{R}^{K \times K}$,
 Increment target log probability density with `inv_wishart_lupdf(W | nu, Sigma)`.
 {{< since 2.0 >}}
 <!-- real; inv_wishart ~; -->
-\index{{\tt \bfseries inv\_wishart }!sampling statement|hyperpage}
+\index{{\tt \bfseries inv\_wishart }!distribution statement|hyperpage}
 
 ### Stan functions
 

src/functions-reference/distributions_over_unbounded_vectors.qmd

@@ -31,7 +31,7 @@ where $|\Sigma|$ is the absolute determinant of $\Sigma$.
 Increment target log probability density with `multi_normal_lupdf(y | mu, Sigma)`.
 {{< since 2.0 >}}
 <!-- real; multi_normal ~; -->
-\index{{\tt \bfseries multi\_normal }!sampling statement|hyperpage}
+\index{{\tt \bfseries multi\_normal }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -165,7 +165,7 @@ for $y \in \mathbb{R}^K$, \begin{equation*} \text{MultiNormalPrecision}(y|\mu,\O
 Increment target log probability density with `multi_normal_prec_lupdf(y | mu, Omega)`.
 {{< since 2.3 >}}
 <!-- real; multi_normal_prec ~; -->
-\index{{\tt \bfseries multi\_normal\_prec }!sampling statement|hyperpage}
+\index{{\tt \bfseries multi\_normal\_prec }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -258,7 +258,7 @@ probability functions will raise errors.
 Increment target log probability density with `multi_normal_cholesky_lupdf(y | mu, L)`.
 {{< since 2.0 >}}
 <!-- real; multi_normal_cholesky ~; -->
-\index{{\tt \bfseries multi\_normal\_cholesky }!sampling statement|hyperpage}
+\index{{\tt \bfseries multi\_normal\_cholesky }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -391,7 +391,7 @@ function does not take into account the mean prediction.
 Increment target log probability density with `multi_gp_lupdf(y | Sigma, w)`.
 {{< since 2.3 >}}
 <!-- real; multi_gp ~; -->
-\index{{\tt \bfseries multi\_gp }!sampling statement|hyperpage}
+\index{{\tt \bfseries multi\_gp }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -436,7 +436,7 @@ account the mean prediction.
 Increment target log probability density with `multi_gp_cholesky_lupdf(y | L, w)`.
 {{< since 2.5 >}}
 <!-- real; multi_gp_cholesky ~; -->
-\index{{\tt \bfseries multi\_gp\_cholesky }!sampling statement|hyperpage}
+\index{{\tt \bfseries multi\_gp\_cholesky }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -479,7 +479,7 @@ K)/2\right)}      {\Gamma(\nu/2)} \ \frac{1}{\sqrt{\left| \Sigma
 Increment target log probability density with `multi_student_t_lupdf(y | nu, mu, Sigma)`.
 {{< since 2.0 >}}
 <!-- real; multi_student_t ~; -->
-\index{{\tt \bfseries multi\_student\_t }!sampling statement|hyperpage}
+\index{{\tt \bfseries multi\_student\_t }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -615,7 +615,7 @@ L^{-T}L^{-1} \, \left(y - \mu\right) \right)^{-(\nu + K)/2} \! .
 Increment target log probability density with `multi_student_t_cholesky_lupdf(y | nu, mu, L)`.
 {{< since 2.30 >}}
 <!-- real; multi_student_t_cholesky ~; -->
-\index{{\tt \bfseries multi\_student\_t\_cholesky }!sampling statement|hyperpage}
+\index{{\tt \bfseries multi\_student\_t\_cholesky }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -696,14 +696,14 @@ processes observations and avoids a matrix inversions can be used
 Increment target log probability density with `gaussian_dlm_obs_lupdf(y | F, G, V, W, m0, C0)`.
 {{< since 2.0 >}}
 <!-- real; gaussian_dlm_obs ~; -->
-\index{{\tt \bfseries gaussian\_dlm\_obs }!sampling statement|hyperpage}
+\index{{\tt \bfseries gaussian\_dlm\_obs }!distribution statement|hyperpage}
 
 ### Stan functions
 
 The following two functions differ in the type of their V, the first
 taking a full observation covariance matrix V\ and the second a vector
 V\ representing the diagonal of the observation covariance matrix.
-The sampling statement defined in the previous section works with
+The distribution statement defined in the previous section works with
 either type of observation V.
 
 <!-- real; gaussian_dlm_obs_lpdf; (matrix y | matrix F, matrix G, matrix V, matrix W, vector m0, matrix C0); -->

src/functions-reference/embedded_laplace.qmd

@@ -366,15 +366,15 @@ group the $i^\text{th}$ observation belongs to.
 * `m`: a vector of offsets or prior means for $\theta$.
 
 <!-- real; laplace_marginal_poisson_log ~; -->
-\index{{\tt \bfseries laplace\_marginal\_poisson\_log }!sampling statement|hyperpage}
+\index{{\tt \bfseries laplace\_marginal\_poisson\_log }!distribution statement|hyperpage}
 
 `y ~ ` **`laplace_marginal_poisson_log`**`(y_index, m, hessian_block_size, covariance_function, covariance_arguments)`<br>\newline
 
 Increment target log probability density with `laplace_marginal_poisson_log_lupmf(y | y_index, m, hessian_block_size, covariance_function, covariance_arguments`.
 {{< since 2.39 >}}
 
 <!-- real; laplace_marginal_tol_poisson_log ~; -->
-\index{{\tt \bfseries laplace\_marginal\_tol\_poisson\_log }!sampling statement|hyperpage}
+\index{{\tt \bfseries laplace\_marginal\_tol\_poisson\_log }!distribution statement|hyperpage}
 
 `y ~ ` **`laplace_marginal_tol_poisson_log`**`(y_index, m, hessian_block_size, covariance_function, covariance_arguments, tolerances)`<br>\newline
 
@@ -464,15 +464,15 @@ group the $i^\text{th}$ observation belongs to.
 * `m`: a vector of offsets or prior means for $\theta$.
 
 <!-- real; laplace_marginal_neg_binomial_2_log ~; -->
-\index{{\tt \bfseries laplace\_marginal\_neg\_binomial\_2\_log }!sampling statement|hyperpage}
+\index{{\tt \bfseries laplace\_marginal\_neg\_binomial\_2\_log }!distribution statement|hyperpage}
 
 `y ~ ` **`laplace_marginal_neg_binomial_2_log`**`(y_index, eta, m, hessian_block_size, covariance_function, covariance_arguments)`<br>\newline
 
 Increment target log probability density with `laplace_marginal_neg_binomial_2_log_lupmf(y | y_index, eta, m, hessian_block_size, covariance_function, covariance_arguments)`.
 {{< since 2.39 >}}
 
 <!-- real; laplace_marginal_tol_neg_binomial_2_log ~; -->
-\index{{\tt \bfseries laplace\_marginal\_tol\_neg\_binomial\_2\_log }!sampling statement|hyperpage}
+\index{{\tt \bfseries laplace\_marginal\_tol\_neg\_binomial\_2\_log }!distribution statement|hyperpage}
 
 `y ~ ` **`laplace_marginal_tol_neg_binomial_2_log`**`(y_index, eta, m, hessian_block_size, covariance_function, covariance_arguments, tolerances)`<br>\newline
 
@@ -560,15 +560,15 @@ group the $i^\text{th}$ observation belongs to.
 * `m`: a vector of offsets or prior means for $\theta$.
 
 <!-- real; laplace_marginal_bernoulli_logit ~; -->
-\index{{\tt \bfseries laplace\_marginal\_bernoulli\_logit }!sampling statement|hyperpage}
+\index{{\tt \bfseries laplace\_marginal\_bernoulli\_logit }!distribution statement|hyperpage}
 
 `y ~ ` **`laplace_marginal_bernoulli_logit`**`(y_index, m, hessian_block_size, covariance_function, covariance_arguments)`<br>\newline
 
 Increment target log probability density with `laplace_marginal_bernoulli_logit_lupmf(y | y_index, m, hessian_block_size, covariance_function, covariance_arguments)`.
 {{< since 2.39 >}}
 
 <!-- real; laplace_marginal_tol_bernoulli_logit ~; -->
-\index{{\tt \bfseries laplace\_marginal\_tol\_bernoulli\_logit }!sampling statement|hyperpage}
+\index{{\tt \bfseries laplace\_marginal\_tol\_bernoulli\_logit }!distribution statement|hyperpage}
 
 `y ~ ` **`laplace_marginal_tol_bernoulli_logit`**`(y_index, m, hessian_block_size, covariance_function, covariance_arguments, tolerances)`<br>\newline
 

src/functions-reference/multivariate_discrete_distributions.qmd

@@ -31,7 +31,7 @@ where the multinomial coefficient is defined by
 Increment target log probability density with `multinomial_lupmf(y | theta)`.
 {{< since 2.0 >}}
 <!-- real; multinomial ~; -->
-\index{{\tt \bfseries multinomial }!sampling statement|hyperpage}
+\index{{\tt \bfseries multinomial }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -92,7 +92,7 @@ where the multinomial coefficient is defined by
 Increment target log probability density with `multinomial_logit_lupmf(y | gamma)`.
 {{< since 2.24 >}}
 <!-- real; multinomial_logit ~; -->
-\index{{\tt \bfseries multinomial\_logit }!sampling statement|hyperpage}
+\index{{\tt \bfseries multinomial\_logit }!distribution statement|hyperpage}
 
 ### Stan functions
 
@@ -148,7 +148,7 @@ where $\alpha_0$ is defined as $\alpha_0 = \sum_{k=1}^K \alpha_k$.
 Increment target log probability density with `dirichlet_multinomial_lupmf(y | alpha)`.
 {{< since 2.34 >}}
 <!-- real; dirichlet_multinomial ~; -->
-\index{{\tt \bfseries dirichlet\_multinomial }!sampling statement|hyperpage}
+\index{{\tt \bfseries dirichlet\_multinomial }!distribution statement|hyperpage}
 
 ### Stan functions