  We present an approach to Bayesian mean estimation of quantum states using
hyperspherical parametrization and an experiment-specific likelihood which
allows utilization of all available data, even when qubits are lost. With this
method, we report the first closed-form Bayesian mean estimate for the ideal
single qubit. Due to computational constraints, we utilize numerical sampling
to determine the Bayesian mean estimate for a photonic two-qubit experiment in
which our novel analysis reduces burdens associated with experimental
asymmetries and inefficiencies. This method can be applied to quantum states of
any dimension and experimental complexity.
