## 3 Background  
The growing demand for synthetic data across industries has spurred the emergence of companies providing tailored solutions. Notable organisations like 'Gretel.ai', 'Hazy', and 'MOSTLY AI' focus on structured and unstructured synthetic data generation. These companies employ a variety of methods, including advanced statistical models and deep learning architectures, to address specific applications such as NLP and computer vision ([[https://mostly.ai/blog/synthetic-data-companies](https://mostly.ai/blog/synthetic-data-companies)]([https://mostly.ai/blog/synthetic-data-companies](https://mostly.ai/blog/synthetic-data-companies)) accessed on 4 January 2025). For instance, 'Gretel.ai' offers models like DoppelGANger (DGAN) and LSTM, while 'Hazy' uses DGAN, Synthetic Data Vault (SDW), and Bayesian models ([[https://hazy.com/docs/models](https://hazy.com/docs/models)]([https://hazy.com/docs/models](https://hazy.com/docs/models)) accessed on 4 January 2025). Similarly, 'Datacebo' provides tools like DeepEcho and SDV, specifically designed for time-series data ([[https://sdv.dev/](https://sdv.dev/)]([https://sdv.dev/](https://sdv.dev/)) accessed on 4 January 2025). These diverse approaches allow organisations to tackle challenges in various domains, balancing accuracy, scalability, and complexity. Naive Bayesian models are foundational statistical techniques that belong to the family of generative classifiers. They operate by applying [PERSON] theorem to compute posterior probabilities, assuming conditional independence among features. Despite their simplicity and restrictive assumptions, Naive Bayes models are effective, particularly in scenarios with small sample sizes or when rapid probabilistic predictions are required [15]. The model's formula is expressed as per the equation:  
\[P(C_{k}|\mathbf{x})=\frac{P(C_{k})\prod_{i=1}^{n}P(x_{i}|C_{k})}{P(\mathbf{x})} \tag{1}\] \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Algorithm Name** & **Model Basis** & **Strenghts** & **Limitations** \\ \hline \multirow{2}{*}{Fintech-kMC} & \multirow{2}{*}{Monte Carlo} & Tailored for financial context; simple to implement & Limited scalability; less faithful to original data \\ \hline \multirow{2}{*}{TimeGAN} & \multirow{2}{*}{GAN} & Captures temporal dynamics; robust across data types & High training complexity; requires extensive data \\ \hline RTSGAN & \multirow{2}{*}{GAN} & Handles missing data; simplifies latent space & Computationally intensive; requires hyperparameter tuning \\ \hline TimeVAE & \multirow{2}{*}{VAE} & Fast training; high interpretability & Limited handling of volatile data \\ \hline VAE-GAN & \multirow{2}{*}{GAN and VAE} & Balances diversity and accuracy; flexible & High computational cost; potential mode collapse \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the discussed models. Here, \(P(C_{k})\) is the prior probability, \(P(x_{i}|C_{k})\) is the likelihood of a feature given a class, and \(P(\mathbf{x})\) is the evidence. Naive Bayes classifiers are widely used for tasks like spam detection and text classification due to their efficiency and straightforward implementation. Bayesian networks extend Bayesian principles by modelling relationships between variables using directed acyclic graphs (DAGs). Nodes represent variables, while directed edges capture conditional dependencies. Each node is associated with a conditional probability table (CPT) that quantifies these dependencies [16]. Bayesian networks excel in situations where understanding interdependencies and managing uncertainty are critical, such as risk analysis and decision support systems. Their ability to handle missing data and integrate external knowledge further enhances their utility, although challenges such as variable discretisation and the need for expert input persist. Hidden Markov Models (HMMs) are powerful tools for modelling sequential data.