Richard Buery, chief executive of the Children’s Aid Society, has spent the past two years investing in electronic medical records for the 10 health clinics the organization runs. But what he also needs is technology that would help him evaluate the outcomes of the agency’s many programs or, possibly, indicate such things as the likelihood that a child from a particular family will be abused. “Using data to make predictive decisions about people and where to invest resources would be a very powerful next level,” said Mr. Buery. Help may be on the way for Mr. Buery and thousands of other health and human-service nonprofits in the city. One of the state’s largest nonprofits—FEGS Health and Human Services—is putting its muscle behind a new accelerator aimed at nurturing startups that develop or repurpose technology expressly for nonprofits. The effort, dubbed Center4, has an advisory committee that includes representatives from organizations such as the Foundation Center, the Nonprofit Coordinating Committee of New York, Forrester Research and New York Angels. Center4 is envisioned as a kind of fourth sector that combines the efforts of the three others—government, for-profit and nonprofit entities. Hence the name.