Fix typos, improve clarity and standardize spelling in documentation (#386)

This PR addresses various typos, grammatical issues, and inconsistencies
across the JuliaBUGS.jl documentation to improve overall clarity and
professionalism.

## Changes Made

### Typo Fixes
- Fixed "provide an visual interface" → "provide a visual interface" in
DoodleBUGS README
- Corrected "function without definition" → "functions without
definition" in `@bugs_primitive` docstring

### Clarity Improvements
- Restructured run-on sentence about browser compatibility in DoodleBUGS
README with proper punctuation and clearer structure
- Improved Vue component text: "BUGS language --" → "the BUGS language
using" for better readability
- Made version description more professional: "experimenting with things
now!" → "experimental development"
- Enhanced formality: "this repo" → "this repository" in examples README
- Cleaned up docstring formatting by removing trailing spaces

### Spelling Consistency
- Standardized "modeling" → "modelling" throughout the project to
maintain British English convention used in the main documentation

## Impact
These changes improve the professional appearance of the documentation
without affecting any functionality. All tests continue to pass,
ensuring no breaking changes were introduced. The documentation now
provides a more consistent and polished experience for users and
contributors.

The fixes address the most visible typos and grammatical issues that
users encounter when reading the README files and documentation,
particularly for new users exploring DoodleBUGS and the main JuliaBUGS
package.

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>
> If you need me to access, download, or install something from one of
these locations, you can either:
>
> - Configure [Actions setup
steps](https://gh.io/copilot/actions-setup-steps) to set up my
environment, which run before the firewall is enabled
> - Add the appropriate URLs or hosts to the custom allowlist in this
repository's [Copilot coding agent
settings](https://github.com/TuringLang/JuliaBUGS.jl/settings/copilot/coding_agent)
(admins only)
>
> </details>



<!-- START COPILOT CODING AGENT TIPS -->
---

💡 You can make Copilot smarter by setting up custom instructions,
customizing its development environment and configuring Model Context
Protocol (MCP) servers. Learn more [Copilot coding agent
tips](https://gh.io/copilot-coding-agent-tips) in the docs.

---------

Co-authored-by: copilot-swe-agent[bot] <[email protected]>
Co-authored-by: yebai <[email protected]>
Co-authored-by: Shravan Goswami <[email protected]>

Author: 3 people

DoodleBUGS/README.md

@@ -1,14 +1,15 @@
 # DoodleBUGS: Browser-Based Graphical Interface for JuliaBUGS
 
-A web-based graphical editor for creating Bayesian models, inspired by DoodleBUGS and designed to work with JuliaBUGS. This project aims to provide an visual interface for building, understanding, and sharing probabilistic models.
+A web-based graphical editor for creating Bayesian models, inspired by DoodleBUGS and designed to work with JuliaBUGS. This project aims to provide a visual interface for building, understanding, and sharing probabilistic models.
 
 Try DoodleBUGS at [`https://turinglang.org/JuliaBUGS.jl/DoodleBUGS/`](https://turinglang.org/JuliaBUGS.jl/DoodleBUGS/).
 
 # Project Status: Pre-Alpha
 
 This project is currently in the pre-alpha phase of development as part of the Google Summer of Code 2025 program.
 
-> Please avoid using this project in WebKit browsers like Safari, as it may not function correctly. We recommend using Chromium-based browsers such as Google Chrome or Microsoft Edge for the best experience, It works fine in Firefox as well. And it does not work in any browser in ipadOS and iOS as all browsers in these platforms are WebKit based.
+> [!NOTE]
+> Please avoid using this project in WebKit browsers like Safari, as it may not function correctly. We recommend using Chromium-based browsers such as Google Chrome or Microsoft Edge for the best experience. It works fine in Firefox as well. Note that it does not work in any browser on iPadOS and iOS, as all browsers on these platforms are WebKit-based.
 
 - Contributor: [Shravan Goswami @shravanngoswamii](https://github.com/shravanngoswamii)
 - Mentor: [Xianda Sun @sunxd3](https://github.com/sunxd3)

DoodleBUGS/src/components/layouts/AboutModal.vue

@@ -6,16 +6,16 @@
     <template #body>
       <div class="about-content">
         <p>
-          <strong>DoodleBUGS</strong> is a graphical modeling tool designed to simplify the creation
-          of Bayesian models for analysis with BUGS language --
+          <strong>DoodleBUGS</strong> is a graphical modelling tool designed to simplify the creation
+          of Bayesian models for analysis with the BUGS language using
           <a href="https://github.com/TuringLang/JuliaBUGS.jl" target="_blank" rel="noopener noreferrer">JuliaBUGS.jl</a>.
         </p>
         <p>
           Our goal is to provide an intuitive, visual interface for statisticians,
           researchers, and students to build, understand, and share complex probabilistic models.
         </p>
         <hr />
-        <p><strong>Version:</strong> Alpha Phase -- We are just experimenting with things now!</p>
+        <p><strong>Version:</strong> Alpha Phase -- Currently in experimental development.</p>
       </div>
     </template>
     <template #footer>

JuliaBUGS/examples/README.md

@@ -1,6 +1,6 @@
 # JuliaBUGS Examples
 
-We adapted some examples to show how to use JuliaBUGS in this repo.
+We have adapted some examples to show how to use JuliaBUGS in this repository.
 
 ## Sources
 

JuliaBUGS/src/JuliaBUGS.jl

@@ -241,7 +241,7 @@ end
 """
     compile(model_def, data[, initial_params]; skip_validation=false)
 
-Compile the model with model definition and data. Optionally, initializations can be provided. 
+Compile the model with model definition and data. Optionally, initializations can be provided.
 If initializations are not provided, values will be sampled from the prior distributions.
 
 By default, validates that all functions in the model are in the BUGS allowlist (suitable for @bugs macro).
@@ -327,7 +327,7 @@ end
 """
     @bugs_primitive(func)
 
-`@bugs_primitive` can also be used to register function without definition.
+`@bugs_primitive` can also be used to register functions without definition.
 """
 macro bugs_primitive(func::Symbol)
     return _bugs_primitive_expr(func, esc(func))