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Particle Learning for Fat-tailed DistributionsNick PolsonChicago, USAWe develop a sequential Monte Carlo method known as particle learning (PL) for fat-tailed errordistributions. Fat-tails are a common feature of many economic and financial time series and can beincorporated into state space models with a number of other features such as stochastic volatility. Anatural framework to address fat-tails is in the class of scale mixtures of normals. By doing so this createsa conditionally dynamic Gaussian model resulting in a mixture Kalman filter model. In particular, wefocus on learning the tail behavior of the time series by assuming that the errors follow a t ν -distributionwhere the researcher sequential computes the posterior distribution of the tail thickness p(ν|y t ) as newdata arrives. This framework is flexible enough to entertain infinite variance Cauchy errors on the onehand (ν = 1) to standard Gaussian errors (ν = ∞). Finally, we show how a variant of the Dickey-Savagedensity ratio can be used to calculate a sequential Bayes factor of a fat-tailed error versus the normal.Comparisons are made to standard Monte Carlo and MCMC approaches and approximate inferences forlatent Gaussian processes. This is joint work with Hedibert F. Lopes.19