Update case studies to use new language syntax

With Stan 2.33+ several old language syntax features produce errors. All the case studies would be good to update to use the latest syntax. Many case studies are in external repos and the authors have submitted only the rendered html and short md-part for the case study contents page. Only the html needs to be updated in users/documentation/case-studies/.

It would be good o contact the original authors and ask them if they are willing to update their repos and submit a new html. If the authors disagree or don't respond, we may consider updating just the syntax on html.

To start the process, I'm listing here all the case studies, and we can start tracking which have been fixed. Tagging also some authors that were easily found by github id autocomplete @mitzimorris, @WardBrian, @bob-carpenter, @charlesm93, @bbbales2, @imadmali

• Bayesian Structural Equation Modeling using blavaan: Feng Ji, Xingyao Xiao, Aybolek Amanmyradova, Sophia Rabe-Hesketh
• Multilevel regression modeling with CmdStanPy and plotnine: Mitzi Morris
• HoloML in Stan: Low-photon Image Reconstruction: Brian Ward, Bob Carpenter, and David Barmherzig
• Bayesian Latent Class Models and Handling of Label Switching: Feng Ji, Aybolek Amanmyradova, Sophia Rabe-Hesketh
• Bayesian model of planetary motion: exploring ideas for a modeling workflow: Charles Margossian and Andrew Gelman
• HMM Interface Example: Ben Bales
• Spatial models for plant neighborhood dynamics in Stan: Cristina Barber, Andrii Zaiats, Cara Applestein and T.Trevor Caughlin
• Predicting Engine Failure with Hierarchical Gaussian Process: Hyunji Moon, Jungin Choi
• Upgrading to the new ODE interface: Ben Bales, Sebastian Weber
• Bayesian Workflow for disease transmission modeling in Stan: Leo Grinsztajn, Elizaveta Semenova, Charles C. Margossian, and Julien Riou
• Reduce Sum Example: parallelization of a single chain across multiple cores: Ben Bales
• Stan Notebooks in the Cloud: Mitzi Morris
• Model-based Inference for Causal Effects in Completely Randomized Experimen: JoonHo Lee, Avi Feller and Sophia Rabe-Hesketh
• Tagging Basketball Events with HMM in Stan: Imad Ali
• Model building and expansion for golf putting: Andrew Gelman
• A Dyadic Item Response Theory Model: Stan Case Study: Nicholas Sim, Brian Gin, Anders Skrondal and Sophia Rabe-Hesketh (note: source link points to fork of example-models)
• Multilevel Linear Models using Rstanarm: JoonHo Lee, Nicholas Sim, Feng Ji, and Sophia Rabe-Hesketh
• Predator-Prey Population Dynamics: the Lotka-Volterra model in Stan: Bob Carpenter
• Nearest neighbor Gaussian process (NNGP) models in Stan: Lu Zhang
• Extreme value analysis and user defined probability functions in Stan: Aki Vehtari
• Modelling Loss Curves in Insurance with RStan: Mick Cooney
• Splines in Stan: Milad Kharratzadeh
• Spatial Models in Stan: Intrinsic Auto-Regressive Models for Areal Data: Mitzi Morris
• The QR Decomposition for Regression Models: Michael Betancourt
• Robust RStan Workflow: Michael Betancourt
• Robust PyStan Workflow: Michael Betancourt (also uses PyStan 2 which is no longer supported)
• Typical Sets and the Curse of Dimensionality: Bob Carpenter
• Diagnosing Biased Inference with Divergences: Michael Betancourt
• Identifying Bayesian Mixture Models: Michael Betancourt
• How the Shape of a Weakly Informative Prior Affects Inferences: Michael Betancourt
• Exact Sparse CAR Models in Stan: Max Joseph
• A Primer on Bayesian Multilevel Modeling using PyStan: Chris Fonnesbeck (also: rendered HTML was deleted?)
• The Impact of Reparameterization on Point Estimates: Bob Carpenter
• Hierarchical Two-Parameter Logistic Item Response Model: Daniel C. Furr
• Rating Scale and Generalized Rating Scale Models with Latent Regression: Daniel C. Furr
• Partial Credit and Generalized Partial Credit Models with Latent Regression: Daniel C. Furr
• Rasch and Two-Parameter Logistic Item Response Models with Latent Regression: Daniel C. Furr
• Two-Parameter Logistic Item Response Model: Daniel C. Furr, Seung Yeon Lee, Joon-Ho Lee, and Sophia Rabe-Hesketh
• Cognitive Diagnosis Model: DINA model with independent attributes: Seung Yeon Lee
• Pooling with Hierarchical Models for Repeated Binary Trials: Bob Carpenter
• Multiple Species-Site Occupancy Model: Bob Carpenter
• Soil Carbon Modeling with RStan: Bob Carpenter

首先检查 users/documentation/case-studies/ 下未勾选的案例研究，并确定哪些渲染后的 HTML 页面在 Stan 2.33+ 下包含语法错误。在决定是请求更新后的 HTML，还是在本地进行语法更改之前，先检查列出的作者和仓库信息。完成的标准是受影响的案例研究已更新，并且清单反映了它们的状态。