This article develops a “borrowed strength” methodology for estimating local probability densities in a random field. Under a piecewise stationarity condition similarities between the densities in different regions of the field can be exploited by estimating a global mixture density and imposing the parameter-space support of this borrowed strength estimate on the local estimation problems. The local estimates are then used in an analysis of the homogeneity of the field, which is shown to benefit from the method of borrowing strength.