14,551 research outputs found
Cluster membership probabilities from proper motions and multiwavelength photometric catalogues: I. Method and application to the Pleiades cluster
We present a new technique designed to take full advantage of the high
dimensionality (photometric, astrometric, temporal) of the DANCe survey to
derive self-consistent and robust membership probabilities of the Pleiades
cluster. We aim at developing a methodology to infer membership probabilities
to the Pleiades cluster from the DANCe multidimensional astro-photometric data
set in a consistent way throughout the entire derivation. The determination of
the membership probabilities has to be applicable to censored data and must
incorporate the measurement uncertainties into the inference procedure.
We use Bayes' theorem and a curvilinear forward model for the likelihood of
the measurements of cluster members in the colour-magnitude space, to infer
posterior membership probabilities. The distribution of the cluster members
proper motions and the distribution of contaminants in the full
multidimensional astro-photometric space is modelled with a
mixture-of-Gaussians likelihood. We analyse several representation spaces
composed of the proper motions plus a subset of the available magnitudes and
colour indices. We select two prominent representation spaces composed of
variables selected using feature relevance determination techniques based in
Random Forests, and analyse the resulting samples of high probability
candidates. We consistently find lists of high probability (p > 0.9975)
candidates with 1000 sources, 4 to 5 times more than obtained in the
most recent astro-photometric studies of the cluster.
The methodology presented here is ready for application in data sets that
include more dimensions, such as radial and/or rotational velocities, spectral
indices and variability.Comment: 14 pages, 4 figures, accepted by A&
Multivariate Design of Experiments for Engineering Dimensional Analysis
We consider the design of dimensional analysis experiments when there is more
than a single response. We first give a brief overview of dimensional analysis
experiments and the dimensional analysis (DA) procedure. The validity of the DA
method for univariate responses was established by the Buckingham -Theorem
in the early 20th century. We extend the theorem to the multivariate case,
develop basic criteria for multivariate design of DA and give guidelines for
design construction. Finally, we illustrate the construction of designs for DA
experiments for an example involving the design of a heat exchanger
Approximate Inference in Continuous Determinantal Point Processes
Determinantal point processes (DPPs) are random point processes well-suited
for modeling repulsion. In machine learning, the focus of DPP-based models has
been on diverse subset selection from a discrete and finite base set. This
discrete setting admits an efficient sampling algorithm based on the
eigendecomposition of the defining kernel matrix. Recently, there has been
growing interest in using DPPs defined on continuous spaces. While the
discrete-DPP sampler extends formally to the continuous case, computationally,
the steps required are not tractable in general. In this paper, we present two
efficient DPP sampling schemes that apply to a wide range of kernel functions:
one based on low rank approximations via Nystrom and random Fourier feature
techniques and another based on Gibbs sampling. We demonstrate the utility of
continuous DPPs in repulsive mixture modeling and synthesizing human poses
spanning activity spaces
On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression
In logistic regression, separation occurs when a linear combination of the
predictors can perfectly classify part or all of the observations in the
sample, and as a result, finite maximum likelihood estimates of the regression
coefficients do not exist. Gelman et al. (2008) recommended independent Cauchy
distributions as default priors for the regression coefficients in logistic
regression, even in the case of separation, and reported posterior modes in
their analyses. As the mean does not exist for the Cauchy prior, a natural
question is whether the posterior means of the regression coefficients exist
under separation. We prove theorems that provide necessary and sufficient
conditions for the existence of posterior means under independent Cauchy priors
for the logit link and a general family of link functions, including the probit
link. We also study the existence of posterior means under multivariate Cauchy
priors. For full Bayesian inference, we develop a Gibbs sampler based on
Polya-Gamma data augmentation to sample from the posterior distribution under
independent Student-t priors including Cauchy priors, and provide a companion R
package in the supplement. We demonstrate empirically that even when the
posterior means of the regression coefficients exist under separation, the
magnitude of the posterior samples for Cauchy priors may be unusually large,
and the corresponding Gibbs sampler shows extremely slow mixing. While
alternative algorithms such as the No-U-Turn Sampler in Stan can greatly
improve mixing, in order to resolve the issue of extremely heavy tailed
posteriors for Cauchy priors under separation, one would need to consider
lighter tailed priors such as normal priors or Student-t priors with degrees of
freedom larger than one
Spanning Tests for Markowitz Stochastic Dominance
We derive properties of the cdf of random variables defined as saddle-type
points of real valued continuous stochastic processes. This facilitates the
derivation of the first-order asymptotic properties of tests for stochastic
spanning given some stochastic dominance relation. We define the concept of
Markowitz stochastic dominance spanning, and develop an analytical
representation of the spanning property. We construct a non-parametric test for
spanning based on subsampling, and derive its asymptotic exactness and
consistency. The spanning methodology determines whether introducing new
securities or relaxing investment constraints improves the investment
opportunity set of investors driven by Markowitz stochastic dominance. In an
application to standard data sets of historical stock market returns, we reject
market portfolio Markowitz efficiency as well as two-fund separation. Hence, we
find evidence that equity management through base assets can outperform the
market, for investors with Markowitz type preferences
Forecasts of non-Gaussian parameter spaces using Box-Cox transformations
Forecasts of statistical constraints on model parameters using the Fisher
matrix abound in many fields of astrophysics. The Fisher matrix formalism
involves the assumption of Gaussianity in parameter space and hence fails to
predict complex features of posterior probability distributions. Combining the
standard Fisher matrix with Box-Cox transformations, we propose a novel method
that accurately predicts arbitrary posterior shapes. The Box-Cox
transformations are applied to parameter space to render it approximately
multivariate Gaussian, performing the Fisher matrix calculation on the
transformed parameters. We demonstrate that, after the Box-Cox parameters have
been determined from an initial likelihood evaluation, the method correctly
predicts changes in the posterior when varying various parameters of the
experimental setup and the data analysis, with marginally higher computational
cost than a standard Fisher matrix calculation. We apply the Box-Cox-Fisher
formalism to forecast cosmological parameter constraints by future weak
gravitational lensing surveys. The characteristic non-linear degeneracy between
matter density parameter and normalisation of matter density fluctuations is
reproduced for several cases, and the capabilities of breaking this degeneracy
by weak lensing three-point statistics is investigated. Possible applications
of Box-Cox transformations of posterior distributions are discussed, including
the prospects for performing statistical data analysis steps in the transformed
Gaussianised parameter space.Comment: 14 pages, 7 figures; minor changes to match version published in
MNRA
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