Gray-crowned Rosy-Finches usually inhabit remote rocky highland terrain, but on the Aleutians they occur down to sea-level where they are largely resident. This species can be divided into gray-cheeked and brown-cheeked groups. This is a member of the gray-cheeked group, L. t. griseonucha, sometimes called the Aleutian Rosy-Finch. It is the largest subspecies, but similar to L. t. umbrina of the Pribiloff's. It is supposedly paler on breast and back and dusky throat blends with brown breast. However differences are slight and the two races are reportedly almost identical in the field. None of the supposed differences are evident to me from in this photo. Formerly lumped with Asian Rosy-Finch (L. arctoa) but split by the AOU in 1993 with the unusual rationale that they were originally lumped in the 6th edition of the checklist without good cause. The anticipated peer reviewed paper was never published. Canon PowerShot SX50 HS.
References:
Clement, P. (2017). Grey-crowned Rosy-finch (Leucosticte tephrocotis). In: del Hoyo, J., Elliott, A., Sargatal, J., Christie, D.A. & de Juana, E. (eds.). Handbook of the Birds of the World Alive. Lynx Edicions, Barcelona. (retrieved from http://www.hbw.com/node/61374 on 4 July 2017).
Clement, P., A. Harris, and J. Davis. 1993. Finches and Sparrows: An Identification Guide. Princeton Univ. Press, Princeton, N. J.
Macdougall-Shackleton, Scott A., Richard E. Johnson and Thomas P. Hahn.(2000).Gray-crowned Rosy-Finch (Leucosticte tephrocotis), The Birds of North America (P. G. Rodewald, Ed.). Ithaca: Cornell Lab of Ornithology; Retrieved from the Birds of North America: https://birdsna.org/Species-Account/bna/species/gcrfin