Nelder-Mead started at exactly 0 cannot leave a symmetric stationary point

scipy's Nelder-Mead builds its initial simplex by perturbing nonzero coordinates by 5% and zero coordinates by only 0.00025. If a likelihood is symmetric in a parameter (e.g. a sign-folded model invariant to mu -> -mu) and you warm-start bootstrap refits at an MLE where that parameter is 0, nearly every refit stays pinned at 0 even when the resample's optimum is elsewhere. This silently shrinks parametric-bootstrap intervals. Add a second start with the symmetric parameter offset from 0, or pass initial_simplex explicitly.