Above are papers related to the following paper: [Paper_ID] Paper #1127551. 	[Title] COMPUTING DISTRIBUTIONS OF ORDER STATISTICS [Abstract] Recurrence relationships among the distribution functions of order statistics of independent, but not identically distributed, random quantities are derived. These results extend known theory and provide computationally practicable algorithms for a variety of problems. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #561674. 	[Title] Studies of Neurological Transmission Analysis using Hierarchical Bayesian Mixture Models [Abstract] Hierarchically structured mixture models are studied in the context of data analysis and inference on neural synaptic transmission characteristics in mammalian, and other, central nervous systems. Mixture structures arise due to uncertainties about the stochastic mechanisms governing the responses to electro-chemical stimulation of individual neuro-transmitter release sites at nerve junctions. Models attempt to capture scientific features such as the sensitivity of individual synaptic transmission sites to electro-chemical stimuli, and the extent of their electro-chemical responses when stimulated. This is done via suitably structured classes of prior distributions for parameters describing these features. Such priors may be structured to permit assessment of currently topical scientific hypotheses about fundamental neural function. Posterior analysis is implemented via stochastic simulation. Several data analyses are described to illustrate the approach, with resulting neurophysiological insights in some recently generated experimental contexts. Further developments and open questions, both neurophysiological and statistical, are noted. Research partially supported by the NSF under grants DMS-9024793, DMS-9305699 and DMS-9304250. This work represents part of a collaborative project with Dr Dennis A Turner, of Duke University Medical Center and Durham VA. Data was provided by Dr Turner and by Dr Howard V Wheal of Southampton University. A slightly revised version of this paper is published in the Journal of the American Statistical Association (vol 92, pp587-606), under the modified title Hierarchical Mixture Models in Neurological Transmission Analysis. The author is the recipient of the 1997 Mitchell Prize for "the Bayesian analysis of a substantive and concrete problem" based on the work reported in this paper. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #562067. 	[Title] Computing Nonparametric Hierarchical Models [Abstract] Bayesian models involving Dirichlet process mixtures are at the heart of the modern nonparametric Bayesian movement. Much of the rapid development of these models in the last decade has been a direct result of advances in simulation-based computational methods. Some of the very early work in this area, circa 1988-1991, focused on the use of such nonparametric ideas and models in applications of otherwise standard hierarchical models. This chapter provides some historical review and perspective on these developments, with a prime focus on the use and integration of such nonparametric ideas in hierarchical models. We illustrate the ease with which the strict parametric assumptions common to most standard Bayesian hierarchical models can be relaxed to incorporate uncertainties about functional forms using Dirichlet process components, partly enabled by the approach to computation using MCMC methods. The resulting methology is illustrated with two examples taken from an unpublished 1992 report on the topic. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #561789. 	[Title] Practical Bayesian Inference Using Mixtures of Mixtures [Abstract] Discrete mixtures of normal distributions are widely used in modeling amplitude fluctuations of electrical potentials at synapses of human, and other animal nervous systems. The usual framework has independent data values y j arising as y j = j + x n 0 +j where the means j come from some discrete prior G() and the unknown x n 0 +j 's and observed x j ; j = 1; : : : ; n 0 are gaussian noise terms. A practically important development of the associated statistical methods is the issue of non-normality of the noise terms, often the norm rather than the exception in the neurological context. We have recently developed models, based on convolutions of Dirichlet process mixtures, for such problems. Explicitly, we model the noise data values x j as arising from a Dirich-let process mixture of normals, in addition to modeling the location prior G() as a Dirichlet process itself. This induces a Dirichlet mixture of mixtures of normals, whose analysis may be developed using Gibbs sampling techniques. We discuss these models and their analysis, and illustrate in the context of neurological response analysis. Please summarise all the given information.

Paper #1127551 has the title `COMPUTING DISTRIBUTIONS OF ORDER STATISTICS  
` and the abstract `Recurrence relationships among the distribution functions of order statistics of independent, but not identically distributed, random quantities are derived. These results extend known theory and provide computationally practicable algorithms for a variety of problems. 
`.
Question: Which category should Paper #1127551 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1127551 has the title `COMPUTING DISTRIBUTIONS OF ORDER STATISTICS  
` and the abstract `Recurrence relationships among the distribution functions of order statistics of independent, but not identically distributed, random quantities are derived. These results extend known theory and provide computationally practicable algorithms for a variety of problems. 
`.
Question: Which category should Paper #1127551 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods