Using Household, Income and Labour Dynamics in Australia (HILDA) data for 2001, 2006, 2010, 2014 and 2017, we compute posterior probabilities for dominance for all pairwise comparisons of income distributions in these years. The dominance criteria considered are Lorenz dominance and first- and second-order stochastic dominance. The income distributions are estimated using an infinite mixture of gamma density functions, with posterior probabilities computed as the proportion of Markov chain Monte Carlo draws that satisfy the inequalities that define the dominance criteria. We find welfare improvements from 2001 to 2006 and qualified improvements from 2006 to the later three years. Evidence of an ordering between 2010, 2014 and 2017 cannot be established.