Tag: Bayesian analysis
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Kernel-Embedded Gaussian Processes for Bayesian Computation and Model Evaluation
(Work in Progress) It had been a while since I had worked on a technical blog post, so I wanted to get something out there. I have been playing around with a lot of concepts in my head centering on Gaussian processes and using them for Bayesian computation. Most of the time when I write…
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A Few Results on Spatial Dirichlet Processes
The author reflects on unfinished work regarding Spatial Dirichlet Process models and their convolutions with white noise, expressing a desire to improve clarity in exposition. Key concepts include Gaussian processes, Hilbert spaces, and Dirichlet processes. Despite the complex mathematics involved, the author presents theorems and proof strategies in a more accessible manner.
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Decision Theory for Large-Scale Outlier Detection Using Aleatoric Uncertainty
The content discusses aleatoric uncertainty in Bayesian neural networks and its application to outlier detection. By leveraging decision theory, the author explores how modeling uncertainties in parameters and data generating mechanisms can enhance outlier classification. This involves formulating loss functions and employing Bayesian false discovery rate strategies for effective threshold setting.
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Bayesian Decision Theory for Gaussian Process (GP) Models with an Application Towards Approximate Evaluation of Source Functions Generating the GP as a Solution to a Differential Equation.
The author explores the integration of decision theory within the framework of Gaussian processes, focusing on nonparametric models. They highlight the relevance of selecting appropriate loss functions when applying Bayesian decision principles, particularly in the context of ordinary differential equations. Applications and future exploration in financial modeling and clustering are also suggested.
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Dirichlet Process Projections
The blog post explores hierarchical modeling using Dirichlet processes combined with projections onto orthogonal random vectors. The author discusses the challenges of maintaining orthogonality while developing a Bayesian nonparametric framework and introduces a new modeling approach that incorporates dimension changing, MCMC algorithms, and potential applications in function spaces with Gaussian processes as base measures.