Error compiling equation

Question

My document (subfile in documentclass book) compiles perfectly, untill I add the following equation:

\begin{equation} 
\label{beliefupdate}
\begin{split}
b_{t+1}(s') & = \Pr(s'|o',a,b) \\
            & = \frac{\Pr(o'|s',a,b)\Pr(s'|a,b)}{\Pr(o'|a,b} \\
            & = \frac{\Pr(o'|s',a) \sum_{s\in\S}\Pr(s'|a,b,s)\Pr(s|a,b)}{\Pr(o'|a,b)} \\
            & = \frac{O(o',a,s') \sum_{s\in\S}T(s,a,s')b_t(s)}{\Pr(o'|a,b)}
\end{split}
\end{equation}

I have loaded the packages:

\usepackage{amsmath}  
\usepackage{amsfonts}
\usepackage{amssymb} 
\usepackage{physics}

\renewcommand{\S}{\mathcal{S}}

\usepackage{graphicx}
\usepackage{wrapfig}

Now, Latex starts giving me warnings in two locations of the document. The first few are in this piece of code, way before the location where I enter the equation

\begin{wrapfigure}{r}
    \centering
    \includegraphics[scale = 0.25]{images/MDP.jpg}
\end{wrapfigure}

I get the error: 'missing number, treated as zero' and also 'Illegal unit of measure (pt inserted)' both about the line \centering

The second batch of errors is about the line \end{split} in the equation.

errors:

FIRST ERROR:

Argument of \opbraces has an extra }.

\par l.151 \end{split}

---

SECOND ERROR:

Runaway argument?

(o'|a,b ! Paragraph ended before \opbraces was complete. \par l.151 \end{split}

---

THIRD ERROR: Missing $ inserted.

---

I honestly don't see where I go wrong

Answer 1

Well, you're missing ) at the end of the second line in split:

        & = \frac{\Pr(o'|s',a,b)\Pr(s'|a,b)}{\Pr(o'|a,b} \\

should be

        & = \frac{\Pr(o'|s',a,b)\Pr(s'|a,b)}{\Pr(o'|a,b)} \\

The missing parenthesis goes unnoticed when physics is not loaded, but it becomes essential when it is, because the package (re)defines \Pr to look for an argument enclosed in (...) (which is a bad thing to do, in my opinion).

Check your input more closely. And don't do \renewcommand\S{\mathcal{S}}.

_{Personal opinion. I cannot recommend using the physics package, because it has a very convoluted syntax and makes disputable typesetting decisions.}