7,382 research outputs found
A Bayesian Periodogram Finds Evidence for Three Planets in 47 Ursae Majoris
A Bayesian analysis of 47 Ursae Majoris (47 UMa) radial velocity data
confirms and refines the properties of two previously reported planets with
periods of 1079 and 2325 days and finds evidence for an additional long period
planet with a period of approximately 10000 days. The three planet model is
found to be 10^5 times more probable than the next most probable model which is
a two planet model. The nonlinear model fitting is accomplished with a new
hybrid Markov chain Monte Carlo (HMCMC) algorithm which incorporates parallel
tempering, simulated annealing and genetic crossover operations. Each of these
features facilitate the detection of a global minimum in chi-squared. By
combining all three, the HMCMC greatly increases the probability of realizing
this goal. When applied to the Kepler problem it acts as a powerful
multi-planet Kepler periodogram. The measured periods are 1078 \pm 2,
2391{+100}{-87}, and 14002{+4018}{-5095}d, and the corresponding eccentricities
are 0.032 \pm 0.014, 0.098{+.047}{-.096}, and 0.16{+.09}{-.16}. The results
favor low eccentricity orbits for all three. Assuming the three signals (each
one consistent with a Keplerian orbit) are caused by planets, the corresponding
limits on planetary mass (M sin i) and semi-major axis are (2.53{+.07}{-.06}MJ,
2.10\pm0.02au), (0.54\pm0.07MJ, 3.6\pm0.1au), and (1.6{+0.3}{-0.5}MJ,
11.6{+2.1}{-2.9}au), respectively. We have also characterized a noise induced
eccentricity bias and designed a correction filter that can be used as an
alternate prior for eccentricity, to enhance the detection of planetary orbits
of low or moderate eccentricity
A Bayesian method for detecting stellar flares
We present a Bayesian-odds-ratio-based algorithm for detecting stellar flares
in light curve data. We assume flares are described by a model in which there
is a rapid rise with a half-Gaussian profile, followed by an exponential decay.
Our signal model also contains a polynomial background model. This is required
to fit underlying light curve variations that are expected in the data, which
could otherwise partially mimic a flare. We characterise the false alarm
probability and efficiency of this method and compare it with a simpler
thresholding method based on that used in Walkowicz et al (2011). We find our
method has a significant increase in detection efficiency for low
signal-to-noise ratio (S/N) flares. For a conservative false alarm probability
our method can detect 95% of flares with S/N less than ~20, as compared to S/N
of ~25 for the simpler method. As an example we have applied our method to a
selection of stars in Kepler Quarter 1 data. The method finds 687 flaring stars
with a total of 1873 flares after vetos have been applied. For these flares we
have characterised their durations and and signal-to-noise ratios.Comment: Accepted for MNRAS. The code used for the analysis can be found at
https://github.com/BayesFlare/bayesflare/releases/tag/v1.0.
Fast Exact Bayesian Inference for Sparse Signals in the Normal Sequence Model
We consider exact algorithms for Bayesian inference with model selection
priors (including spike-and-slab priors) in the sparse normal sequence model.
Because the best existing exact algorithm becomes numerically unstable for
sample sizes over n=500, there has been much attention for alternative
approaches like approximate algorithms (Gibbs sampling, variational Bayes,
etc.), shrinkage priors (e.g. the Horseshoe prior and the Spike-and-Slab LASSO)
or empirical Bayesian methods. However, by introducing algorithmic ideas from
online sequential prediction, we show that exact calculations are feasible for
much larger sample sizes: for general model selection priors we reach n=25000,
and for certain spike-and-slab priors we can easily reach n=100000. We further
prove a de Finetti-like result for finite sample sizes that characterizes
exactly which model selection priors can be expressed as spike-and-slab priors.
The computational speed and numerical accuracy of the proposed methods are
demonstrated in experiments on simulated data, on a differential gene
expression data set, and to compare the effect of multiple hyper-parameter
settings in the beta-binomial prior. In our experimental evaluation we compute
guaranteed bounds on the numerical accuracy of all new algorithms, which shows
that the proposed methods are numerically reliable whereas an alternative based
on long division is not
Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis
Modeling nonstationary processes is of paramount importance to many
scientific disciplines including environmental science, ecology, and finance,
among others. Consequently, flexible methodology that provides accurate
estimation across a wide range of processes is a subject of ongoing interest.
We propose a novel approach to model-based time-frequency estimation using
time-varying autoregressive models. In this context, we take a fully Bayesian
approach and allow both the autoregressive coefficients and innovation variance
to vary over time. Importantly, our estimation method uses the lattice filter
and is cast within the partial autocorrelation domain. The marginal posterior
distributions are of standard form and, as a convenient by-product of our
estimation method, our approach avoids undesirable matrix inversions. As such,
estimation is extremely computationally efficient and stable. To illustrate the
effectiveness of our approach, we conduct a comprehensive simulation study that
compares our method with other competing methods and find that, in most cases,
our approach performs superior in terms of average squared error between the
estimated and true time-varying spectral density. Lastly, we demonstrate our
methodology through three modeling applications; namely, insect communication
signals, environmental data (wind components), and macroeconomic data (US gross
domestic product (GDP) and consumption).Comment: 49 pages, 16 figure
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