12,517 research outputs found
Bayesian estimation of orientation preference maps
Imaging techniques such as optical imaging of intrinsic signals, 2-photon calcium imaging and voltage sensitive dye imaging can be used to measure the functional organization of visual cortex across different spatial and temporal scales. Here, we present Bayesian methods based on Gaussian processes for extracting topographic maps from functional imaging data. In particular, we focus on the estimation of orientation preference maps (OPMs) from intrinsic signal imaging data. We model the underlying map as a bivariate Gaussian process, with a prior covariance function that reflects known properties of OPMs, and a noise covariance adjusted to the data. The posterior mean can be interpreted as an optimally smoothed estimate of the map, and can be used for model based interpolations of the map from sparse measurements. By sampling from the posterior distribution, we can get error bars on statistical properties such as preferred orientations, pinwheel locations or pinwheel counts. Finally, the use of an explicit probabilistic model facilitates interpretation of parameters and quantitative model comparisons. We demonstrate our model both on simulated data and on intrinsic signaling data from ferret visual cortex
Determining the population properties of spinning black holes
There are at least two formation scenarios consistent with the first
gravitational-wave observations of binary black hole mergers. In field models,
black hole binaries are formed from stellar binaries that may undergo common
envelope evolution. In dynamic models, black hole binaries are formed through
capture events in globular clusters. Both classes of models are subject to
significant theoretical uncertainties. Nonetheless, the conventional wisdom
holds that the distribution of spin orientations of dynamically merging black
holes is nearly isotropic while field-model black holes prefer to spin in
alignment with the orbital angular momentum. We present a framework in which
observations of black hole mergers can be used to measure ensemble properties
of black hole spin such as the typical black hole spin misalignment. We show
how to obtain constraints on population hyperparameters using minimal
assumptions so that the results are not strongly dependent on the uncertain
physics of formation models. These data-driven constraints will facilitate
tests of theoretical models and help determine the formation history of binary
black holes using information encoded in their observed spins. We demonstrate
that the ensemble properties of binary detections can be used to search for and
characterize the properties of two distinct populations of black hole mergers.Comment: 10 pages, 5 figures, 1 table. Minor revisions, published in PR
Bayesian Analysis of the Polarization of Distant Radio Sources: Limits on Cosmological Birefringence
A recent study of the rotation of the plane of polarization of light from 160
cosmological sources claims to find significant evidence for cosmological
anisotropy. We point out methodological weaknesses of that study, and reanalyze
the same data using Bayesian methods that overcome these problems. We find that
the data always favor isotropic models for the distribution of observed
polarizations over counterparts that have a cosmological anisotropy of the type
advocated in the earlier study. Although anisotropic models are not completely
ruled out, the data put strong lower limits on the length scale (in
units of the Hubble length) associated with the anisotropy; the lower limits of
95% credible regions for lie between 0.43 and 0.62 in all anisotropic
models we studied, values several times larger than the best-fit value of
found in the earlier study. The length scale is not
constrained from above. The vast majority of sources in the data are at
distances closer than 0.4 Hubble lengths (corresponding to a redshift of
0.8); the results are thus consistent with there being no significant
anisotropy on the length scale probed by these data.Comment: 8 pages, 3 figures; submitted to Phys. Rev.
Markov chain Monte Carlo analysis of Bianchi VII_h models
We have extended the analysis of Jaffe et al. to a complete Markov chain
Monte Carlo (MCMC) study of the Bianchi type models including a
dark energy density, using 1-year and 3-year Wilkinson Microwave Anisotropy
Probe (WMAP) cosmic microwave background (CMB) data. Since we perform the
analysis in a Bayesian framework our entire inference is contained in the
multidimensional posterior distribution from which we can extract marginalised
parameter constraints and the comparative Bayesian evidence. Treating the
left-handed Bianchi CMB anisotropy as a template centred upon the `cold-spot'
in the southern hemisphere, the parameter estimates derived for the total
energy density, `tightness' and vorticity from 3-year data are found to be:
, , with orientation ). This template is preferred by a factor of roughly
unity in log-evidence over a concordance cosmology alone. A Bianchi type
template is supported by the data only if its position on the sky is heavily
restricted. The low total energy density of the preferred template, implies a
geometry that is incompatible with cosmologies inferred from recent CMB
observations. Jaffe et al. found that extending the Bianchi model to include a
term in creates a degeneracy in the plane. We explore this region fully by MCMC and find that the
degenerate likelihood contours do not intersect areas of parameter space that 1
or 3 year WMAP data would prefer at any significance above . Thus we
can confirm that a physical Bianchi model is not responsible for
this signature.Comment: 8 pages, 10 figures, significant update to include more accurate
results and conclusions to match version accepted by MNRA
Dynamic filtering of static dipoles in magnetoencephalography
We consider the problem of estimating neural activity from measurements
of the magnetic fields recorded by magnetoencephalography. We exploit
the temporal structure of the problem and model the neural current as a
collection of evolving current dipoles, which appear and disappear, but whose
locations are constant throughout their lifetime. This fully reflects the physiological
interpretation of the model.
In order to conduct inference under this proposed model, it was necessary
to develop an algorithm based around state-of-the-art sequential Monte
Carlo methods employing carefully designed importance distributions. Previous
work employed a bootstrap filter and an artificial dynamic structure
where dipoles performed a random walk in space, yielding nonphysical artefacts
in the reconstructions; such artefacts are not observed when using the
proposed model. The algorithm is validated with simulated data, in which
it provided an average localisation error which is approximately half that of
the bootstrap filter. An application to complex real data derived from a somatosensory
experiment is presented. Assessment of model fit via marginal
likelihood showed a clear preference for the proposed model and the associated
reconstructions show better localisation
A framework for testing isotropy with the cosmic microwave background
We present a new framework for testing the isotropy of the Universe using
cosmic microwave background data, building on the nested-sampling ANICOSMO
code. Uniquely, we are able to constrain the scalar, vector and tensor degrees
of freedom alike; previous studies only considered the vector mode (linked to
vorticity). We employ Bianchi type VII cosmologies to model the anisotropic
Universe, from which other types may be obtained by taking suitable limits. In
a separate development, we improve the statistical analysis by including the
effect of Bianchi power in the high-, as well as the low-,
likelihood. To understand the effect of all these changes, we apply our new
techniques to WMAP data. We find no evidence for anisotropy, constraining shear
in the vector mode to (95% CL). For the
first time, we place limits on the tensor mode; unlike other modes, the tensor
shear can grow from a near-isotropic early Universe. The limit on this type of
shear is (95% CL).Comment: 11 pages, 6 figures, v3: minor modifications to match version
accepted by MNRA
The intrinsic shapes of starless cores in Ophiuchus
Using observations of cores to infer their intrinsic properties requires the
solution of several poorly constrained inverse problems. Here we address one of
these problems, namely to deduce from the projected aspect ratios of the cores
in Ophiuchus their intrinsic three-dimensional shapes. Four models are
proposed, all based on the standard assumption that cores are randomly
orientated ellipsoids, and on the further assumption that a core's shape is not
correlated with its absolute size. The first and simplest model, M1, has a
single free parameter, and assumes that the relative axes of a core are drawn
randomly from a log-normal distribution with zero mean and standard deviation
\sigma o. The second model, M2a, has two free parameters, and assumes that the
log-normal distribution (with standard deviation \sigma o) has a finite mean,
\mu o, defined so that \mu o<0 means elongated (prolate) cores are favoured,
whereas \mu o>0 means flattened (oblate) cores are favoured. Details of the
third model (M2b, two free parameters) and the fourth model (M4, four free
parameters) are given in the text. Markov chain Monte Carlo sampling and
Bayesian analysis are used to map out the posterior probability density
functions of the model parameters, and the relative merits of the models are
compared using Bayes factors. We show that M1 provides an acceptable fit to the
Ophiuchus data with \sigma o ~ 0.57+/-0.06; and that, although the other models
sometimes provide an improved fit, there is no strong justification for the
introduction of their additional parameters.Comment: 10 pages, 8 figures. Accepted by MNRA
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Low-rank graphical models and Bayesian inference in the statistical analysis of noisy neural data
We develop new methods of Bayesian inference, largely in the context of analysis of neuroscience data. The work is broken into several parts. In the first part, we introduce a novel class of joint probability distributions in which exact inference is tractable. Previously it has been difficult to find general constructions for models in which efficient exact inference is possible, outside of certain classical cases. We identify a class of such models that are tractable owing to a certain "low-rank" structure in the potentials that couple neighboring variables. In the second part we develop methods to quantify and measure information loss in analysis of neuronal spike train data due to two types of noise, making use of the ideas developed in the first part. Information about neuronal identity or temporal resolution may be lost during spike detection and sorting, or precision of spike times may be corrupted by various effects. We quantify the information lost due to these effects for the relatively simple but sufficiently broad class of Markovian model neurons. We find that decoders that model the probability distribution of spike-neuron assignments significantly outperform decoders that use only the most likely spike assignments. We also apply the ideas of the low-rank models from the first section to defining a class of prior distributions over the space of stimuli (or other covariate) which, by conjugacy, preserve the tractability of inference. In the third part, we treat Bayesian methods for the estimation of sparse signals, with application to the locating of synapses in a dendritic tree. We develop a compartmentalized model of the dendritic tree. Building on previous work that applied and generalized ideas of least angle regression to obtain a fast Bayesian solution to the resulting estimation problem, we describe two other approaches to the same problem, one employing a horseshoe prior and the other using various spike-and-slab priors. In the last part, we revisit the low-rank models of the first section and apply them to the problem of inferring orientation selectivity maps from noisy observations of orientation preference. The relevant low-rank model exploits the self-conjugacy of the von Mises distribution on the circle. Because the orientation map model is loopy, we cannot do exact inference on the low-rank model by the forward backward algorithm, but block-wise Gibbs sampling by the forward backward algorithm speeds mixing. We explore another von Mises coupling potential Gibbs sampler that proves to effectively smooth noisily observed orientation maps
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