A Parzen-based distance between probability measures as an alternative of summary statistics in Approximate Bayesian Computation

Approximate Bayesian Computation (ABC) are likelihood-free Monte Carlo methods. ABC methods use a comparison between simulated data, using different parameters drew from a prior distribution, and observed data. This comparison process is based on computing a distance between the summary statistics from the simulated data and the observed data. For complex models, it is usually difficult to define a methodology for choosing or constructing the summary statistics. Recently, a nonparametric ABC has been proposed, that uses a dissimilarity measure between discrete distributions based on empirical kernel embeddings as an alternative for summary statistics. The nonparametric ABC outperforms other methods including ABC, kernel ABC or synthetic likelihood ABC. However, it assumes that the probability distributions are discrete, and it is not robust when dealing with few observations. In this paper, we propose to apply kernel embeddings using an smoother density estimator or Parzen estimator for comparing the empirical data distributions, and computing the ABC posterior. Synthetic data and real data were used to test the Bayesian inference of our method. We compare our method with respect to state-of-the-art methods, and demonstrate that our method is a robust estimator of the posterior distribution in terms of the number of observations

CP Violating Rate Difference Relations for B→PPB\to PP and B→PVB \to PV in Broken SU(3)

Within the standard model there exist certain relations between CP violating rate differences in B decays in the SU(3) limit. We study SU(3) breaking corrections to these relations in the case of charmless, hadronic, two body $B$ decays using the improved factorization model of Ref.\cite{3}. We consider the cases $B \to PP$ and $B \to PV$ for both $B_d$ and $B_s$ mesons. We present an estimate for $A_{CP}(\pi^- \pi^+)$ in terms of $A_{CP}(K^- \pi^+)$.Comment: Latex 13 pages, no figure

Short-term time series prediction using Hilbert space embeddings of autoregressive processes

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on kernel methods. Motivated by the powerful framework of Hilbert space embeddings of distributions, in this paper we apply this methodology for the kernel embedding of an autoregressive process of order p. By doing so, we provide a non-linear version of an autoregressive process, that shows increased performance over the linear model in highly complex time series. We use the method proposed for one-step ahead forecasting of different time-series, and compare its performance against other non-linear methods

Short-term time series prediction using Hilbert space embeddings of autoregressive processes

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on kernel methods. Motivated by the powerful framework of Hilbert space embeddings of distributions, in this paper we apply this methodology for the kernel embedding of an autoregressive process of order p. By doing so, we provide a non-linear version of an autoregressive process, that shows increased performance over the linear model in highly complex time series. We use the method proposed for one-step ahead forecasting of different time-series, and compare its performance against other non-linear methods

Modeling and behavior of the simulation of electric propagation during deep brain stimulation

Deep brain stimulation (DBS) is an effective treatment for Parkinson's disease. In the literature, there are a wide variety of mathematical and computational models to describe electric propagation during DBS; however unfortunately, there is no clarity about the reasons that justify the use of a specific model. In this work, we present a detailed mathematical formulation of the DBS electric propagation that supports the use of a model based on the Laplace Equation. Moreover, we performed DBS simulations for several geometrical models of the brain in order to determine whether geometry size, shape and ground location influence electric stimulation prediction by using the Finite Element Method (FEM). Theoretical and experimental analysis show, firstly, that under the correct assumptions, the Laplace equation is a suitable alternative to describe the electric propagation, and secondly, that geometrical structure, size and grounding of the head volume affect the magnitude of the electric potential, particularly for monopolar stimulation. Results show that, for monopolar stimulation, basic and more realistic models can differ more than 2900%

Human Cerebral Activation during Steady-State Visual-Evoked Responses

Flicker stimuli of variable frequency (2-90 Hz) elicit a steady-state visual-evoked response (SSVER) in the electroencephalogram (EEG) with the same frequency as the stimulus. In humans, the amplitude of this response peaks at approximately 15 Hz, decreasing at higher stimulation frequencies. It was not known whether this peak response corresponds to increased synaptic activity in the visual cortex or to other mechanisms [for instance, the temporal coherence (phase summation) of evoked responses]. We studied the SSVER in 16 normal volunteers by means of visual stimulation at 14 different frequencies (from 5 to 60 Hz) while recording the EEG. In nine subjects of the group, we measured regional cerebral blood flow (rCBF) with positron emission tomography (PET)-H2(15)O at rest and during visual stimulation at five different frequencies: 5, 10, 15, 25, and 40 Hz. We confirmed that the amplitude of the SSVER in occipital regions peaks at 15 Hz stimulation. Applying to the PET rCBF data a contrast weighted by the amplitude of the SSVER, we determined that the primary visual cortex rCBF follows an activation pattern similar to the SSVER. This finding suggests that the amplitude of the SSVER corresponds to increased synaptic activity, specifically in Brodmann's area 17. Additionally, this study showed that visual stimulation at 40 Hz causes selective activation of the macular region of the visual cortex, and that a region in the dorsal aspect of the Crus I lobule of the left cerebellar hemisphere is activated during repetitive visual stimulation

Topography of Cortical Activation Differs for Fundamental and Harmonic Frequencies of the Steady-State Visual-Evoked Responses. An EEG and PET H15 2 O Study

In humans, visual flicker stimuli of graded frequency (2--90 Hz) elicit an electroencephalographic (EEG) steady-state visual-evoked response (SSVER) with the same fundamental frequency as the stimulus and, in addition, a series of harmonic responses. The fundamental component of the SSVER is generated by increased synaptic activity in primary visual cortex (V1). We set out to determine the cortical origin of the harmonic responses in humans. For this purpose, we recorded the SSVERs at 5 different frequencies (5, 10, 15, 25, and 40 Hz) and measured regional cerebral blood flow (rCBF) with positron emission tomography-H15 2 O at rest and during visual stimulation at the same frequencies. The rCBF contrast weighted by the amplitude of the SSVERs first harmonics showed activation of a swath of cortex perpendicular to V1, including mostly the inferior half of the parietooccipital sulcus. This area overlapped minimally with the primary visual cortex activated by the fundamental frequency. A different method, estimating EEG cortical source current density with lowresolution brain electromagnetic tomography, gave the same results. Our finding suggests that the inferior portion of the banks of the parieto-occipital sulci contains association visual cortex involved in the procparieto-occipital sulcus

The Mediterranean diet and incidence of hypertension: the Seguimiento Universidad de Navarra (SUN) Study

The Mediterranean diet is receiving increasing attention in cardiovascular epidemiology. The association of adherence to the Mediterranean diet with the incidence of hypertension was evaluated among 9,408 men and women enrolled in a dynamic Spanish prospective cohort study during 1999–2005. Dietary intake was assessed at baseline with a validated semiquantitative food frequency questionnaire, and a 9-point Mediterranean diet score was constructed. During a median follow-up period of 4.2 years (range, 1.9–7.9), 501 incident cases of hypertension were identified. After adjustment for major hypertension risk factors and nutritional covariates, adherence to the Mediterranean diet was not associated with hypertension (the hazard ratio was 1.10 (95% confidence interval (CI): 0.81, 1.41) for moderate adherence and 1.12 (95% CI: 0.79, 1.60) for high adherence). However, it was associated with reduced changes in mean levels of systolic blood pressure (moderate adherence, 2.4 mm Hg (95% CI: 4.0, 0.8); high adherence, 3.1 mm Hg (95% CI: 5.4, 0.8)) and diastolic blood pressure (moderate adherence, 1.3 mm Hg (95% CI: 2.5, 0.1); high adherence, 1.9 mm Hg (95% CI: 3.6, 0.1)) after 6 years of follow-up. These results suggest that adhering to a Mediterranean-type diet could contribute to the prevention of age-related changes in blood pressure

Genome sequences and great expectations

To assess how automatic function assignment will contribute to genome annotation in the next five years, we have performed an analysis of 31 available genome sequences. An emerging pattern is that function can be predicted for almost two-thirds of the 73,500 genes that were analyzed. Despite progress in computational biology, there will always be a great need for large-scale experimental determination of protein function