In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
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Question: Sampling from hierarchical Bayesian models is often difficult for MCMC methods, because of the strong correlations between the model parameters and the hyperparameters. Recent Riemannian manifold Hamiltonian Monte Carlo (RMHMC) methods have significant potential advantages in this setting, but are computationally expensive. We introduce a new RMHMC method, which we call semi-separable Hamiltonian Monte Carlo, which uses a specially designed mass matrix that allows the joint Hamiltonian over model parameters and hyperparameters to decompose into two simpler Hamiltonians. This structure is exploited by a new integrator which we call the alternating blockwise leapfrog algorithm. The resulting method can mix faster than simpler Gibbs sampling while being simpler and more efficient than previous instances of RMHMC.

Answer: Semi-Separable Hamiltonian Monte Carlo for Inference in Bayesian Hierarchical Models

Question: Proposed methods for prediction interval estimation so far focus on cases where input variables are numerical. In datasets with solely nominal input variables, we observe records with the exact same input x, but different real valued outputs due to the inherent noise in the system. Existing prediction interval estimation methods do not use representations that can accurately model such inherent noise in the case of nominal inputs. We propose a new prediction interval estimation method tailored for this type of data, which is prevalent in biology and medicine. We call this method Distribution Adaptive Prediction Interval Estimation given Nominal inputs (DAPIEN) and has four main phases. First, we select a distribution function that can best represent the inherent noise of the system for all unique inputs. Then we infer the parameters i (e.g. i = [meani, variancei]) of the selected distribution function for all unique input vectors xi and generate a new corresponding training set using pairs of xi , i. III). Then, we train a model to predict given a new xu. Finally, we calculate the prediction interval for a new sample using the inverse of the cumulative distribution function once the parameters is predicted by the trained model. We compared DAPIEN to the commonly used Bootstrap method on three synthetic datasets. Our results show that DAPIEN provides tighter prediction intervals while preserving the requested coverage when compared to Bootstrap. This work can facilitate broader usage of regression methods in medicine and biology where it is necessary to provide tight prediction intervals while preserving coverage when input variables are nominal.

Answer: DICTION INTERVAL ESTIMATION USING NOMINAL VARIABLES

Question: The report presents the process of planning, designing and the development of a database of spoken children's speech whose native language is Bulgarian. The proposed model is designed for children between the age of 4 and 6 without speech disorders, and reflects their specific capabilities. At this age most children cannot read, there is no sustained concentration, they are emotional, etc. The aim is to unite all the media information accompanying the recording and processing of spoken speech, thereby to facilitate the work of researchers in the field of speech recognition. This database will be used for the development of systems for children's speech recognition, children's speech synthesis systems, games which allow voice control, etc. As a result of the proposed model a prototype system for speech recognition is presented.

Answer:
Design and development a children's speech database