  In this paper we introduce a binary search algorithm that efficiently finds
initial maximum likelihood estimates for sequential experiments where a binary
response is modeled by a continuous factor. The problem is motivated by
switching measurements on superconducting Josephson junctions. In this quantum
mechanical experiment, the current is the factor controlled by the experimenter
and a binary response indicating the presence or the absence of a voltage
response is measured. The prior knowledge on the model parameters is typically
poor, which may cause the common approaches of initial estimation to fail. The
binary search algorithm is designed to work reliably even when the prior
information is very poor. The properties of the algorithm are studied in
simulations and an advantage over the initial estimation with equally spaced
factor levels is demonstrated. We also study the cost-efficiency of the binary
search algorithm and find the approximately optimal number of measurements per
stage when there is a cost related to the number of stages in the experiment.
  KEY WORDS: optimal design, binary search, logistic regression, complementary
log-log, quantum physics, switching measurement
