A Bayesian multinomial regression model for palaeoclimate reconstruction with time uncertainty

Estimating chronological uncertainty is a critical but often neglected prerequisite in palaeoclimatological reconstructions and core comparisons. We describe a hierarchical Bayesian multinomial regression model for temperature reconstruction
that allows uncertainty in the sediment core sample dates. Climate model output is used as pseudodata to provide prior information about the overall variability of past temperatures. Including time uncertainty in the model can make usual
summaries such as the posterior mean temperature less useful.We therefore recommend considering also fixed chronology reconstructions and exploration of individual temperature history realizations. This can be particularly relevant for tracking
short-lived events.We demonstrate the proposed model by reconstructing the past temperature from fossil pollen data obtained from three cores in Estonia and southern Sweden.