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TempoNest performs a Bayesian analysis of pulsar timing data, which allows for the robust determination of the non-linear pulsar timing solution simultaneously with a range of additional stochastic parameters. This includes both red spin noise and dispersion measure variations using either power law descriptions of the noise, or through a model-independent method that parameterizes the power at individual frequencies in the signal. It uses the Bayesian inference tool MultiNest (ascl:1109.006) to explore the joint parameter space, while using Tempo2 (ascl:1210.015) as a means of evaluating the timing model. TempoNest allows for the analysis of additional stochastic signals beyond the white noise described by the TOA error bars that may be present in the data.