39,999 research outputs found
Bayesian Methods for Exoplanet Science
Exoplanet research is carried out at the limits of the capabilities of
current telescopes and instruments. The studied signals are weak, and often
embedded in complex systematics from instrumental, telluric, and astrophysical
sources. Combining repeated observations of periodic events, simultaneous
observations with multiple telescopes, different observation techniques, and
existing information from theory and prior research can help to disentangle the
systematics from the planetary signals, and offers synergistic advantages over
analysing observations separately. Bayesian inference provides a
self-consistent statistical framework that addresses both the necessity for
complex systematics models, and the need to combine prior information and
heterogeneous observations. This chapter offers a brief introduction to
Bayesian inference in the context of exoplanet research, with focus on time
series analysis, and finishes with an overview of a set of freely available
programming libraries.Comment: Invited revie
Quantum Bayesian methods and subsequent measurements
After a derivation of the quantum Bayes theorem, and a discussion of the
reconstruction of the unknown state of identical spin systems by repeated
measurements, the main part of this paper treats the problem of determining the
unknown phase difference of two coherent sources by photon measurements. While
the approach of this paper is based on computing correlations of actual
measurements (photon detections), it is possible to derive indirectly a
probability distribution for the phase difference. In this approach, the
quantum phase is not an observable, but a parameter of an unknown quantum
state. Photon measurements determine a probability distribution for the phase
difference. The approach used in this paper takes into account both photon
statistics and the finite efficiency of the detectors.Comment: Expanded and corrected version. 13 pages, 1 figur
Bayesian methods of astronomical source extraction
We present two new source extraction methods, based on Bayesian model
selection and using the Bayesian Information Criterion (BIC). The first is a
source detection filter, able to simultaneously detect point sources and
estimate the image background. The second is an advanced photometry technique,
which measures the flux, position (to sub-pixel accuracy), local background and
point spread function. We apply the source detection filter to simulated
Herschel-SPIRE data and show the filter's ability to both detect point sources
and also simultaneously estimate the image background. We use the photometry
method to analyse a simple simulated image containing a source of unknown flux,
position and point spread function; we not only accurately measure these
parameters, but also determine their uncertainties (using Markov-Chain Monte
Carlo sampling). The method also characterises the nature of the source
(distinguishing between a point source and extended source). We demonstrate the
effect of including additional prior knowledge. Prior knowledge of the point
spread function increase the precision of the flux measurement, while prior
knowledge of the background has onlya small impact. In the presence of higher
noise levels, we show that prior positional knowledge (such as might arise from
a strong detection in another waveband) allows us to accurately measure the
source flux even when the source is too faint to be detected directly. These
methods are incorporated in SUSSEXtractor, the source extraction pipeline for
the forthcoming Akari FIS far-infrared all-sky survey. They are also
implemented in a stand-alone, beta-version public tool that can be obtained at
http://astronomy.sussex.ac.uk/rss23/sourceMiner\_v0.1.2.0.tar.gzComment: Accepted for publication by ApJ (this version compiled used
emulateapj.cls
What do Bayesian methods offer population forecasters?
The Bayesian approach has a number of attractive properties for probabilistic forecasting. In this paper, we apply Bayesian time series models to obtain future population estimates with uncertainty for England and Wales. To account for heterogeneity found in the historical data, we add parameters to represent the stochastic volatility in the error terms. Uncertainty in model choice is incorporated through Bayesian model averaging techniques. The resulting predictive distributions from Bayesian forecasting models have two main advantages over those obtained using traditional stochastic models. Firstly, data and uncertainties in the parameters and model choice are explicitly included using probability distributions. As a result, more realistic probabilistic population forecasts can be obtained. Second, Bayesian models formally allow the incorporation of expert opinion, including uncertainty, into the forecast. Our results are discussed in relation to classical time series methods and existing cohort component projections. This paper demonstrates the flexibility of the Bayesian approach to simple population forecasting and provides insights into further developments of more complicated population models that include, for example, components of demographic change
Bayesian Methods for Measuring Operational Risk
The likely imposition by regulators of minimum standards for capital to cover 'other risks' has been a driving force behind the recent interest in operational risk management. Much discussion has been centered on the form of capital charges for other risks. At the same time major banks are developing models to improve internal management of operational processes, new insurance products for operational risks are being designed and there is growing interest in alternative risk transfer, through OR-linked products.
Bayesian Methods
Probabilistic Bayesian methods enable combination of information from various sources. The Bayes theorem is explained and its use is illustrated on several examples of practical importance, such as revealing the cause of an accident or reliability increasing of non-destructive testing. Also its use for continuous quantities and for increasing the reliability of the parameters of normal or Weibull distribution is shown
Bayesian Methods in Nonlinear Time Series
This paper reviews the analysis of the threshold autoregressive, smooth threshold autoregressive, and Markov switching autoregressive models from the Bayesian perspective. For each model we start by describing a baseline model and discussing possible extensions and applications. Then we review the choice of prior, inference, tests against the linear hypothesis, and conclude with models selection. A short discussion of recent progress in incorporating regime changes into theoretical macroeconomic models concludes our survey.Threshold, Smooth Threshold, Markov-switching
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