A CRITICAL THRESHOLD IN SNOWBALL SAMPLING
KARL ROHE – UNIVERSITY OF WISCONSIN-MADISON
In Snowball sampling and Respondent-Driven Sampling, researchers ask participants to refer their friends into the sample. This talk models snowball sampling as a Markov process on a social graph that is indexed by a Galton-Watson tree. Markov dependence decays exponentially in the number of steps (i.e. referrals). However, the Galton-Watson tree (which indexes the dependence) grows exponentially. The first part of the talk discusses the competition between these exponential rates and how they determine a critical threshold. If m is the expected number of referrals provided by each sample and \lambda_2 is the second eigenvalue of the Markov transition matrix, then the rate is determined by whether or not m < 1/\lambda_2^2. The rest of the talk will discuss ways of overcoming that dependence.