Exploring Photometric Redshifts as an Optimization Problem: An Ensemble MCMC and Simulated Annealing-Driven Template-Fitting Approach

Using a grid of $\sim 2$ million elements ($\Delta z = 0.005$) adapted from COSMOS photometric redshift (photo-z) searches, we investigate the general properties of template-based photo-z likelihood surfaces. We find these surfaces are filled with numerous local minima and large degeneracies that generally confound rapid but "greedy" optimization schemes, even with additional stochastic sampling methods. In order to robustly and efficiently explore these surfaces, we develop BAD-Z [Brisk Annealing-Driven Redshifts (Z)], which combines ensemble Markov Chain Monte Carlo (MCMC) sampling with simulated annealing to sample arbitrarily large, pre-generated grids in approximately constant time. Using a mock catalog of 384,662 objects, we show BAD-Z samples $\sim 40$ times more efficiently compared to a brute-force counterpart while maintaining similar levels of accuracy. Our results represent first steps toward designing template-fitting photo-z approaches limited mainly by memory constraints rather than computation time.