This paper studies two-class (or binary) classification of elements X in R k that allows for a reject option. Based on n independent copies of the pair of random variables (X, Y ) with X ∈ R k and Y ∈ {0, 1}, we consider classifiers f (X) that render three possible outputs: 0, 1 and R. The option R expresses doubt and is to be used for few observations that are hard to classify in an automatic way.Chow ( where misclassifying a sick patient as healthy is worse than the opposite.Running title: Classification with reject option MSC2000 Subject classification: Primary 62C05 ; secondary 62G05, 62G08.
This paper introduces a Bayesian inversion approach to estimating steady state ocean circulation and tracer fields. It is based on a quasi-horizontal flow model and a PDE solver for the forward problem of computing solutions to the tracer field advection-diffusion equations. A typical feature of existing ocean circulation inverse methods is a preprocessing stage in which the tracer data are interpolated over a regular grid and the interpolation error is ignored in the subsequent inversion. Our approach only uses interpolated data at those grid points that have neighboring hydrographic stations. By exploiting physically-based models in an integrated fashion, the method provides a statistically unified inversion and tracer field reconstruction with minimal data smoothing. Solving the problem consists of finding information about the circulation and tracer fields in the presence of a number of assumptions (prior information); the resulting posterior probability distribution summarizes what we can know about these fields. We develop a Markov chain Monte Carlo simulation procedure to extract information from the (analytically intractable) posterior distribution of all the parameters in the model; uncertainty about the "solution" is represented by variation in the output of the simulation runs. Our approach is aimed at finding the time-averaged quasi-horizontal flow and tracer fields for an abyssal neutral density layer in the South Atlantic.
This paper describes a quasi-3D Bayesian inversion of oceanographic tracer data from the South Atlantic Ocean. Initially, one active neutral-density layer is considered with an upper and lower boundary. The available hydrographic data are linked to model parameters (water velocities, diffusion coefficients) via a 3D advection-diffusion equation. A robust solution to the inverse problem can be obtained by introducing prior information about parameters and modeling the observation error. This approach estimates both horizontal and vertical flow as well as diffusion coefficients. A system of alternating zonal jets is found at the depths of the North Atlantic Deep Water, consistent with direct measurements of flow and concentration maps. A uniqueness analysis of the model is performed in terms of the oxygen consumption rate. The vertical mixing coefficient bears some relation to the bottom topography even though the authors do not incorporate topography into their model. The method is extended to a multilayer model, using thermal wind relations weakly in a local fashion (as opposed to integrating the entire water column) to connect layers vertically. Results suggest that the estimated deep zonal jets extend vertically, with a clear depth-dependent structure. The vertical structure of the flow field is modified by the tracer fields relative to the a priori flow field defined by thermal wind. The velocity estimates are consistent with independent observed flow at the depths of the Antarctic Intermediate Water; at still shallower depths, above the layers considered here, the subtropical gyre is a significant feature of the horizontal flow.
Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led to the development of exact, or perfect, sampling algorithms which convert a Markov chain into an algorithm that produces i.i.d. samples from the stationary distribution. Unfortunately, very few of these algorithms have been developed for the distributions that arise in statistical applications, which typically have uncountable support. Here we study an exact sampling algorithm using a geometrically ergodic Markov chain on a general state space. Our work provides a significant reduction to the number of input draws necessary for the Bernoulli factory, which enables exact sampling via a rejection sampling approach. We illustrate the algorithm on a univariate Metropolis-Hastings sampler and a bivariate Gibbs sampler, which provide a proof of concept and insight into hyper-parameter selection. Finally, we illustrate the algorithm on a Bayesian version of the one-way random effects model with data from a styrene exposure study.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.