## 4 Dataset Generation and Simulation Environment
### Comparative Benchmarking Framework  
To objectively assess the MHMM's performance, its two variants (Expert System and Trained) were benchmarked against a suite of established temporal models, chosen to represent different classes of sequence modeling approaches. This comprehensive comparison evaluates the benefits of multimodal fusion and the MHMM's interpretability against state-of-the-art black-box and discriminative models.  
* MHMM (Expert System): This variant of our Multimodal Hidden Markov Model uses pre-defined, expert-informed parameters. It represents an ideal scenario where domain knowledge is perfectly integrated, and it uniquely leverages contextual metadata (task complexity, fatigue events) to dynamically adjust its predictions, showcasing the full potential of a context-aware system.
* MHMM (Trained): This is a standard MHMM that learns its parameters (initial state probabilities, transition probabilities, and emission distributions) directly from the training data using the Baum-Welch algorithm. Its inclusion evaluates the MHMM's ability to discover proficiency dynamics from raw observation sequences without prior expert knowledge, providing a more realistic benchmark for data-driven applications.
* Unimodal HMMs (TCT, HRV, or TLX): Three separate Hidden Markov Models were implemented, each trained exclusively on a single data modality (Task Completion Time, Heart Rate Variability, or NASA Task Load Index). These serve as crucial baselines to empirically demonstrate the advantage of multimodal data fusion over relying on any single physiological, behavioral, or subjective indicator.
* Long Short-Term Memory (LSTM) Network: As a type of recurrent neural network, LSTM models are state-of-the-art in sequence learning, capable of capturing complex long-range dependencies in data. They serve as a powerful \"black-box\" performance benchmark, often achieving high accuracy but lacking the inherent interpretability of probabilistic models like HMMs.
* Transformer Model: This advanced neural architecture, known for its use of self-attention mechanisms, excels in capturing global dependencies within sequences, making it highly effective for sequence-to-sequence tasks. Its inclusion provides a contemporary benchmark from the deep learning domain to assess how advanced neural architectures perform in modeling temporal proficiency dynamics.
* Hybrid HMM-LSTM Model: This model combines the strengths of both HMMs and LSTMs. It uses the MHMM's emission probabilities (representing the likelihood of observations given each hidden state) as additional features for an LSTM network.  
This hybrid approach explores whether integrating probabilistic insights from HMMs can enhance the predictive power of neural sequence processing.
* Conditional Random Field (CRF): Unlike generative models such as HMMs, CRFs are discriminative models that focus on directly modeling the conditional probability of a sequence of labels given a sequence of observations. They are powerful for sequence labeling tasks and avoid some of the strong independence assumptions of HMMs, offering an alternative probabilistic modeling approach for comparison.