  The Metropolis-Hastings (MH) algorithm is the prototype for a class of Markov
chain Monte Carlo methods that propose transitions between states and then
accept or reject the proposal. These methods generate a correlated sequence of
random samples that convey information about the desired probability
distribution. Deciding how this information gets recorded is an important step
in the practical design of MH-class algorithm implementations. Many
implementations discard most of this information in order to reduce demands on
storage capacity and disk writing throughput. Here, we describe how recording a
bit string containing 1's for acceptance and 0's for rejection allows the full
sample sequence to be recorded with no information loss, facilitating
decoupling of simulation design from the constraints of data analysis. The
recording uses only one bit per sample, which is an upper bound on the rate at
which information about the desired distribution is acquired. We also
demonstrate the method and quantify its benefits on a nontrivial colloidal
system of charged particles in the canonical ensemble. The method imposes no
restrictions on the system or simulation design and is compatible with
descendants of the MH algorithm.
