Time series prediction via aggregation : an oracle bound including numerical cost

We address the problem of forecasting a time series meeting the Causal Bernoulli Shift model, using a parametric set of predictors. The aggregation technique provides a predictor with well established and quite satisfying theoretical properties expressed by an oracle inequality for the prediction risk. The numerical computation of the aggregated predictor usually relies on a Markov chain Monte Carlo method whose convergence should be evaluated. In particular, it is crucial to bound the number of simulations needed to achieve a numerical precision of the same order as the prediction risk. In this direction we present a fairly general result which can be seen as an oracle inequality including the numerical cost of the predictor computation. The numerical cost appears by letting the oracle inequality depend on the number of simulations required in the Monte Carlo approximation. Some numerical experiments are then carried out to support our findings

CLTs and asymptotic variance of time-sampled Markov chains

For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel Pμ = Σkμ(k)Pk. In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance

Bayesian computation: a summary of the current state, and samples backwards and forwards

© 2015, The Author(s). Recent decades have seen enormous improvements in computational inference for statistical models; there have been competitive continual enhancements in a wide range of computational tools. In Bayesian inference, first and foremost, MCMC techniques have continued to evolve, moving from random walk proposals to Langevin drift, to Hamiltonian Monte Carlo, and so on, with both theoretical and algorithmic innovations opening new opportunities to practitioners. However, this impressive evolution in capacity is confronted by an even steeper increase in the complexity of the datasets to be addressed. The difficulties of modelling and then handling ever more complex datasets most likely call for a new type of tool for computational inference that dramatically reduces the dimension and size of the raw data while capturing its essential aspects. Approximate models and algorithms may thus be at the core of the next computational revolution

Journal of political marketing : political campaigns in the new millennium

We introduce an adaptive output-sensitive Metropolis-Hastings algorithm for probabilistic models expressed as programs, Adaptive Lightweight Metropolis-Hastings (AdLMH). This algorithm extends Lightweight Metropolis-Hastings (LMH) by adjusting the probabilities of proposing random variables for modification to improve convergence of the program output. We show that AdLMH converges to the correct equilibrium distribution and compare convergence of AdLMH to that of LMH on several test problems to highlight different aspects of the adaptation scheme. We observe consistent improvement in convergence on the test problems

The differences in sleep profile changes under continuous positive airway pressure (CPAP) therapy between non-obese, obese and severely obese sleep apnea patients

Sleep disturbances in obstructive sleep apnea are caused mainly by repetitive apneas and hypopneas. An alternative factor contributing to disordered sleep may be the obesity, which is frequently associated with sleep apnea. The sleep disturbing effect of obesity was found previously in obese nonapneic subjects. The aim of this study was to evaluate the effect of obesity on sleep quality in sleep apnea patients in particular in patients under continuous positive airway pressure (CPAP) with successfully normalized respiration. We reviewed the archive data of 18 non-obese, 18 obese and 17 severely obese age and gender matched sleep apnea patients treated with CPAP. The polysomnographic parameters from the diagnostic night, from the second night under CPAP and from the follow up night (after three months of CPAP use) were compared. Before CPAP the apnea hypopnea index was worse in obese and in severely obese group and it normalised under CPAP in all groups. The severely obese group showed more light sleep and less REM sleep before CPAP and inversely - less light and more REM sleep in the second night under CPAP than the non-obese group. In the follow up, there was no differences in sleep profile between groups. This study indicates obesity does not affect the sleep independently of respiratory disorders. Before therapy it is associated with more severe sleep apnea and indirectly with worse sleep quality

CLTs and asymptotic variance of time-sampled Markov chains

For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel Pμ = ∑k μ(k)Pk. In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker's and Metropolis algorithms in terms of asymptotic variance