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We study the stability and instability of Langmuir waves propagating in a hot, unmagnetized plasma modeled by the Vlasov–Poisson system and encompassing a variety of velocity distributions, including perturbations of Lorentzian, Kappa, and incomplete Maxwellian steady states. The influence of both high-frequency spatial perturbations and physical parameters on the rate of growth or decay of the plasma response to the initial perturbation is elucidated. Our methods do not rely upon analytic approximation, but instead feature a numerical approximation of the roots of the associated dielectric function that can be accurately quantified without the need for prior assumptions on the parameter regimes under consideration. In this way, the computational discovery of so-called “active” subspaces in the parameter space allows one to identify and quantify the uncertainty generated by physical parameters on the stability properties of wave-like perturbations in a collisionless plasma.