We consider the inventory management problem of a firm reacting to potential change points in demand, which we define as known epochs at which the demand distribution may (or may not) abruptly change. Motivating examples include global news events (e.g., the 9/11 terrorist attacks), local events (e.g., the opening of a nearby attraction), or internal events (e.g., a product redesign). In the periods following such a potential change point in demand, a manager is torn between using a possibly obsolete demand model estimated from a long data history and using a model estimated from a short, recent history. We formulate a Bayesian inventory problem just after a potential change point. We pursue heuristic policies coupled with cost lower bounds, including a new lower bounding approach to non-perishable Bayesian inventory problems that relaxes the dependence between physical demand and demand signals and that can be applied for a broad set of belief and demand distributions. Our numerical studies reveal small gaps between the costs implied by our heuristic solutions and our lower bounds. We also provide analytical and numerical sensitivity results suggesting that a manager worried about downside profit risk should err on the side of underestimating demand at a potential change point.