1,831 research outputs found
Exploring Multi-Modal Distributions with Nested Sampling
In performing a Bayesian analysis, two difficult problems often emerge.
First, in estimating the parameters of some model for the data, the resulting
posterior distribution may be multi-modal or exhibit pronounced (curving)
degeneracies. Secondly, in selecting between a set of competing models,
calculation of the Bayesian evidence for each model is computationally
expensive using existing methods such as thermodynamic integration. Nested
Sampling is a Monte Carlo method targeted at the efficient calculation of the
evidence, but also produces posterior inferences as a by-product and therefore
provides means to carry out parameter estimation as well as model selection.
The main challenge in implementing Nested Sampling is to sample from a
constrained probability distribution. One possible solution to this problem is
provided by the Galilean Monte Carlo (GMC) algorithm. We show results of
applying Nested Sampling with GMC to some problems which have proven very
difficult for standard Markov Chain Monte Carlo (MCMC) and down-hill methods,
due to the presence of large number of local minima and/or pronounced (curving)
degeneracies between the parameters. We also discuss the use of Nested Sampling
with GMC in Bayesian object detection problems, which are inherently
multi-modal and require the evaluation of Bayesian evidence for distinguishing
between true and spurious detections.Comment: Refereed conference proceeding, presented at 32nd International
Workshop on Bayesian Inference and Maximum Entropy Methods in Science and
Engineerin
Entropic criterion for model selection
Model or variable selection is usually achieved through ranking models
according to the increasing order of preference. One of methods is applying
Kullback-Leibler distance or relative entropy as a selection criterion. Yet
that will raise two questions, why uses this criterion and are there any other
criteria. Besides, conventional approaches require a reference prior, which is
usually difficult to get. Following the logic of inductive inference proposed
by Caticha, we show relative entropy to be a unique criterion, which requires
no prior information and can be applied to different fields. We examine this
criterion by considering a physical problem, simple fluids, and results are
promising.Comment: 10 pages. Accepted for publication in Physica A, 200
Relativistic particle acceleration in developing Alfv\'{e}n turbulence
A new particle acceleration process in a developing Alfv\'{e}n turbulence in
the course of successive parametric instabilities of a relativistic pair plasma
is investigated by utilyzing one-dimensional electromagnetic full particle
code. Coherent wave-particle interactions result in efficient particle
acceleration leading to a power-law like energy distribution function. In the
simulation high energy particles having large relativistic masses are
preferentially accelerated as the turbulence spectrum evolves in time. Main
acceleration mechanism is simultaneous relativistic resonance between a
particle and two different waves. An analytical expression of maximum
attainable energy in such wave-particle interactions is derived.Comment: 15 pages, 9 figures, 1 tabl
Analytic Continuation of Quantum Monte Carlo Data by Stochastic Analytical Inference
We present an algorithm for the analytic continuation of imaginary-time
quantum Monte Carlo data which is strictly based on principles of Bayesian
statistical inference. Within this framework we are able to obtain an explicit
expression for the calculation of a weighted average over possible energy
spectra, which can be evaluated by standard Monte Carlo simulations, yielding
as by-product also the distribution function as function of the regularization
parameter. Our algorithm thus avoids the usual ad-hoc assumptions introduced in
similar algortihms to fix the regularization parameter. We apply the algorithm
to imaginary-time quantum Monte Carlo data and compare the resulting energy
spectra with those from a standard maximum entropy calculation
Sovereign Net Worth: An Analytical Framework
The Fiscal Responsibility Act requires the Crown to articulate targets for a series of fiscal variables, including net worth. Given the dramatic improvement in the fiscal position in recent years, a critical policy question relates to how (and which) measures of Crown net worth should be targeted. This paper sets out a framework for targeting Crown net worth. It does so by supplementing the GAAP-based measure with forward-looking information about spending and tax revenue. The paper argues that targeting net worth for the Crown requires the estimation of a path, rather than a static level.
Educational Outcomes and Obstacles for Children and Youth in Foster Care in Hawaiâi.
Ph.D. Thesis. University of HawaiÊ»i at MÄnoa 2018
- âŠ