typo fixes

Author: avehtari

src/stan-users-guide/finite-mixtures.qmd

@@ -469,11 +469,8 @@ used for mixing proportions because $\lambda$ is the traditional
 notation for a Poisson mean parameter). Given the probability $\theta$
 and the intensity $\lambda$, the distribution for $y_n$ can be written as
 \begin{align*}
-y_n & = 0 \quad\text{with probability } \theta, \text{ and}\\
-y_n & \sim \textsf{Poisson}(y_n \mid \lambda) \quad\text{with probability } 1-\theta.
-\begin{cases}
- 
- 
+y_n & = 0 & \quad\text{with probability } \theta, \text{ and}\\
+y_n & \sim \textsf{Poisson}(y_n \mid \lambda) & \quad\text{with probability } 1-\theta.
 \end{align*}
 
 
@@ -582,7 +579,7 @@ $$
 \begin{align*}
 y_n & = 0 \quad\text{with probability } \theta, \text{ and}\\
 y_n & \sim \textsf{Poisson}_{x\neq 0}(y_n \mid \lambda) \quad\text{with probability } 1-\theta,
-\end{cases}
+\end{align*}
 $$
 Where $\textsf{Poisson}_{x\neq 0}$ is a truncated Poisson distribution, truncated at $0$.
 

src/stan-users-guide/measurement-error.qmd

@@ -131,7 +131,7 @@ $$
 z_n \sim \textsf{normal}(\mu, \sigma).
 $$
 
-The rounding process entails that $z_n \in (y_n - 0.5, y_n + 0.5)$^{There are several different rounding rules (see, e.g., [Wikipedia: Rounding](https://en.wikipedia.org/wiki/Rounding)), which affect which interval ends are open and which are closed, but these do not matter here as for continuous $z_n$ $p(z_n=y_n-0.5)=p(z_n=y_n+0.5)=0$.}.
+The rounding process entails that $z_n \in (y_n - 0.5, y_n + 0.5)$^[There are several different rounding rules (see, e.g., [Wikipedia: Rounding](https://en.wikipedia.org/wiki/Rounding)), which affect which interval ends are open and which are closed, but these do not matter here as for continuous $z_n$ $p(z_n=y_n-0.5)=p(z_n=y_n+0.5)=0$.].
 The probability mass function for the discrete observation $y$ is then given
 by marginalizing out the unrounded measurement, producing the likelihood
 \begin{align*}

src/stan-users-guide/survival.qmd

@@ -505,9 +505,9 @@ function $h_0(t)$ is unmodeled; if the baseline hazard were known,
 failure times could be generated.  Cox's proportional hazards model is
 generative for the ordering of failures conditional on a number of
 censored items. Proportional hazard models may also include parametric
-or non-parametric model for the baseline hazard function^{Cox mentioned
+or non-parametric model for the baseline hazard function^[Cox mentioned
 in his seminal paper that modeling the baseline hazard function would improve
-statistical efficiency, but he did not do it for computational reasons.}.
+statistical efficiency, but he did not do it for computational reasons.].
 
 
 ### Partial likelihood function {-}

src/stan-users-guide/truncation-censoring.qmd

@@ -201,7 +201,7 @@ that $y_{\mathrm{cens},m}>U$.
 With $M$ censored observations, the likelihood on the log scale
 is
 \begin{align*}
-\log \prod_{m=1}^M \Pr[y_m > U]
+\log \prod_{m=1}^M \Pr[y_{\mathrm{cens},m} > U]
   &= \log \left( 1 - \Phi\left(\left(\frac{U - \mu}{\sigma}\right)\right)^{M}\right) \\
   &= M \times \texttt{normal}\mathtt{\_}\texttt{lccdf}\left(U \mid \mu, \sigma \right),
 \end{align*}