عنوان

Adaptive Bayesian Nonparametric Smoothing with Markov Random Fields and Shrinkage Priors

شماره

TLpq2305192500

زبان متن نوشتاري يا گفتاري و مانند آن

انگلیسی

عنوان اصلي

Adaptive Bayesian Nonparametric Smoothing with Markov Random Fields and Shrinkage Priors

نام عام مواد

[Thesis]

نام نخستين پديدآور

Faulkner, James Robert

نام ساير پديدآوران

Minin, Vladimir N

نام ناشر، پخش کننده و غيره

University of Washington

تاریخ نشرو بخش و غیره

2019

نام خاص و کميت اثر

177

جزئيات پايان نامه و نوع درجه آن

Ph.D.

کسي که مدرک را اعطا کرده

University of Washington

امتياز متن

2019

متن يادداشت

The need to estimate unknown functions or surfaces arises in many disciplines in science and there are many statistical methods available to do this. Our interest lies in using Bayesian nonparametric approaches to estimate unknown functions. One such approach to nonparametric estimation is based on the Gaussian Markov random field priors. This class of computationally efficient and flexible methods is widely used in applications. There is frequently the need to estimate functions with change points, discontinuities, or abrupt changes, or functions with varying levels of smoothness. Gaussian Markov random fields have limited ability to accurately capture such features. We develop a locally adaptive version of Markov random fields that uses shrinkage priors on the order-k increments of the discretized function and has the flexibility to accommodate a large class of functional behaviors. We show that the horseshoe prior results in superior performance in comparison to other shrinkage priors. The horseshoe prior induces sparsity in the increments, which provides good smoothing properties, and at the same time the heavy tails of the prior allow for jumps and discontinuities in the field. We first apply the method to some standard settings where we use simulated data to compare to other methods and then apply the models to two benchmark data examples frequently used to test nonparametric methods. We use Hamiltonian Monte Carlo to approximate the posterior distribution of model parameters because this method provides superior performance in the presence of the high dimensionality and strong parameter correlations exhibited by our models. We then extend the method to the estimation of effective population sizes using the coalescent process and genetic sequence data. For that application, we develop a custom Markov chain Monte Carlo sampler based on a combination of elliptical slice sampling and Gibbs sampling. We test the method using simulated data and then use it to reconstruct past changes in genetic diversity of human hepatitis C virus in Egypt and to estimate population size changes of ancient and modern steppe bison. Finally, we extend the method for use in the spatial setting, where we apply the method to disease mapping and to the estimation of the intensity of an inhomogeneous spatial point process. Overall, we find that this method is flexible enough to accommodate a variety of data generating models and offers the adaptive properties and computational tractability that make it a useful addition to the Bayesian nonparametric toolbox.

موضوع مستند نشده

Ecology

موضوع مستند نشده

Genetics

موضوع مستند نشده

Resource management

موضوع مستند نشده

Statistics

مستند نام اشخاص تاييد نشده

Faulkner, James Robert

مستند نام اشخاص تاييد نشده

Minin, Vladimir N

نام الکترونيکي

فرمت انتشار

p

نوع ماده

[Thesis]

کد کاربرگه

276903

سطح دسترسي

a

تكميل شده

Y