Stellar evolution models are fundamental tools in astrophysics; these models exhibit complex, nonstationary behavior, particularly in late evolutionary stages. This makes direct calibration to observational data challenging and computationally expensive. We develop a statistical framework for emulation and calibration of stellar evolution models using Deep Gaussian Processes (DeepGPs). To efficiently incorporate the high-dimensional and non-stationary simulator response surface, we fit a DeepGP emulator trained on simulated stellar evolution data. The emulator takes as inputs physical properties of a star and outputs the expected brightness in several wide wavelength bands of light. We adopt a multi-stage, modular approach to both emulation and calibration, allowing for pragmatic inference while retaining uncertainty quantification. Results demonstrate a robust framework, confirming that DeepGP emulation facilitates the capture of non-stationary structures in stellar evolution tracks.

Implemented a GPT-style transformer from scratch in JAX and Flax, without using any high-level model libraries. The architecture includes multi-head causal self-attention, learned positional embeddings, and stacked transformer blocks with pre-norm residual connections. Training uses a JIT-compiled loop with jax.value_and_grad, AdamW, and cosine learning rate decay. Trained a character-level model on the Tiny Shakespeare corpus (~1M tokens); loss drops from 4.96 to 2.63 over 3000 steps with no significant overfitting.

This project is a simple example that I was exploring while I was learning about SMC. It demonstrates how to use Sequential Monte Carlo with annealing to sample from posterior distributions of logistic regression coefficients. The algorithm gradually transitions from the prior distribution (β=0) to the posterior distribution (β=1), making it particularly effective for complex, multimodal posteriors.

This project examines the performance of three bias reduction techniques for Maximum Likelihood Estimation in GLMs: Asymptotic Bias Correction (adjusts MLE estimates using first-order bias approximation), Firth's Method (modifies the score function to reduce bias while preserving invariance properties), and Log-F Prior Method (a Bayesian-inspired technique that allows incorporation of prior information).