Homeowners insurers haven’t always been in the vanguard of technology. But they have been relatively quick to catch on to the possibilities of big data created by the combination of powerful computers and vast new troves of information— from the internet, mobile apps and sensing devices to thousands of federal agency databases made public by the Obama administration.

Sorting and using that data has not been a simple process, for technological and cultural reasons, but acceptance is speeding up, said Lori Sherer, a partner at Bain & Company in San Francisco.