  Measuring the temperature structure of the solar atmosphere is critical to
understanding how it is heated to high temperatures. Unfortunately, the
temperature of the upper atmosphere cannot be observed directly, but must be
inferred from spectrally resolved observations of individual emission lines
that span a wide range of temperatures. Such observations are "inverted" to
determine the distribution of plasma temperatures along the line of sight. This
inversion is ill-posed and, in the absence of regularization, tends to produce
wildly oscillatory solutions. We introduce the application of sparse Bayesian
inference to the problem of inferring the temperature structure of the solar
corona. Within a Bayesian framework a preference for solutions that utilize a
minimum number of basis functions can be encoded into the prior and many ad hoc
assumptions can be avoided. We demonstrate the efficacy of the Bayesian
approach by considering a test library of 40 assumed temperature distributions.
