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Split conformal prediction techniques are applied to regression problems with circular responses by introducing a suitable conformity score, leading to prediction sets with adaptive arc length and finite-sample coverage guarantees for any circular predictive model under exchangeable data. Leveraging the high performance of existing predictive models designed for linear responses, we analyze a general projection procedure that converts any linear response regression model into one suitable for circular responses. When random forests serve as basis models in this projection procedure, we harness the out-of-bag dynamics to eliminate the necessity for a separate calibration sample in the construction of prediction sets. For synthetic and real datasets the resulting projected random forests model produces more efficient out-of-bag conformal prediction sets, with shorter median arc length, when compared to the split conformal prediction sets generated by two existing alternative models., Comment: 7 pages; 4 figures

We present a model-agnostic framework for the construction of prediction intervals of insurance claims, with finite sample statistical guarantees, extending the technique of split conformal prediction to the domain of two-stage frequency-severity modeling. The framework effectiveness is showcased with simulated and real datasets using classical parametric models and contemporary machine learning methods. When the underlying severity model is a random forest, we extend the two-stage split conformal prediction algorithm, showing how the out-of-bag mechanism can be leveraged to eliminate the need for a calibration set in the conformal procedure.

When split conformal prediction operates in batch mode with exchangeable data, we determine the exact distribution of the empirical coverage of prediction sets produced for a finite batch of future observables, as well as the exact distribution of its almost sure limit when the batch size goes to infinity. Both distributions are universal, being determined solely by the nominal miscoverage level and the calibration sample size, thereby establishing a criterion for choosing the minimum required calibration sample size in applications., Comment: 6 pages, 1 table

We show that the byproducts of the standard training process of a random forest yield not only the well known and almost computationally free out-of-bag point estimate of the model generalization error, but also give a direct path to compute confidence intervals for the generalization error which avoids processes of data splitting and model retraining. Besides the low computational cost involved in their construction, these confidence intervals are shown through simulations to have good coverage and appropriate shrinking rate of their width in terms of the training sample size., Comment: 10 pages

We develop a Bayesian hierarchical semiparametric model for phenomena related to time series of counts. The main feature of the model is its capability to learn a latent pattern of heterogeneity in the distribution of the process innovation rates, which are softly clustered through time with the help of a Dirichlet process placed at the top of the model hierarchy. The probabilistic forecasting capabilities of the model are put to test in the analysis of crime data in Pittsburgh, with favorable results.

Microarray gene expression data are analyzed by means of a Bayesian nonparametric model, with emphasis on prediction of future observables, yielding a method for selection of differentially expressed genes and a classifier.

We describe briefly in this note a procedure for consistently estimating the marginal likelihood of a statistical model through a sample from the posterior distribution of the model parameters.

A tractable nonparametric prior over densities is introduced which is closed under sampling and exhibits proper posterior asymptotics., Comment: 19 pages; 6 figures