127,679 research outputs found
On the density distribution across space: a probabilistic approach
This paper aims at providing a Bayesian parametric framework to tackle the accessibility problem across space in urban theory. Adopting continuous variables in a probabilistic setting we are able to associate with the distribution density to the Kendall's tau index and replicate the general issues related to the role of proximity in a more general context. In addition, by referring to the Beta and Gamma distribution, we are able to introduce a differentiation feature in each spatial unit without incurring in any a-priori definition of territorial units. We are also providing an empirical application of our theoretical setting to study the density distribution of the population across Massachusetts.Agglomerations, Bayesian inference, Distance, Gibbs sampling, Kendall's tau index, Population density.
Inferring Synaptic Structure in presence of Neural Interaction Time Scales
Biological networks display a variety of activity patterns reflecting a web
of interactions that is complex both in space and time. Yet inference methods
have mainly focused on reconstructing, from the network's activity, the spatial
structure, by assuming equilibrium conditions or, more recently, a
probabilistic dynamics with a single arbitrary time-step. Here we show that,
under this latter assumption, the inference procedure fails to reconstruct the
synaptic matrix of a network of integrate-and-fire neurons when the chosen time
scale of interaction does not closely match the synaptic delay or when no
single time scale for the interaction can be identified; such failure,
moreover, exposes a distinctive bias of the inference method that can lead to
infer as inhibitory the excitatory synapses with interaction time scales longer
than the model's time-step. We therefore introduce a new two-step method, that
first infers through cross-correlation profiles the delay-structure of the
network and then reconstructs the synaptic matrix, and successfully test it on
networks with different topologies and in different activity regimes. Although
step one is able to accurately recover the delay-structure of the network, thus
getting rid of any \textit{a priori} guess about the time scales of the
interaction, the inference method introduces nonetheless an arbitrary time
scale, the time-bin used to binarize the spike trains. We therefore
analytically and numerically study how the choice of affects the inference
in our network model, finding that the relationship between the inferred
couplings and the real synaptic efficacies, albeit being quadratic in both
cases, depends critically on for the excitatory synapses only, whilst
being basically independent of it for the inhibitory ones
Density-Based Semantics for Reactive Probabilistic Programming
Synchronous languages are now a standard industry tool for critical embedded
systems. Designers write high-level specifications by composing streams of
values using block diagrams. These languages have been extended with Bayesian
reasoning to program state-space models which compute a stream of distributions
given a stream of observations. However, the semantics of probabilistic models
is only defined for scheduled equations -- a significant limitation compared to
dataflow synchronous languages and block diagrams which do not require any
ordering.
In this paper we propose two schedule agnostic semantics for a probabilistic
synchronous language. The key idea is to interpret probabilistic expressions as
a stream of un-normalized density functions which maps random variable values
to a result and positive score. The co-iterative semantics interprets programs
as state machines and equations are computed using a fixpoint operator. The
relational semantics directly manipulates streams and is thus a better fit to
reason about program equivalence. We use the relational semantics to prove the
correctness of a program transformation required to run an optimized inference
algorithm for state-space models with constant parameters
DPO - Denoising, Deconvolving, and Decomposing Photon Observations
The analysis of astronomical images is a non-trivial task. The D3PO algorithm
addresses the inference problem of denoising, deconvolving, and decomposing
photon observations. Its primary goal is the simultaneous but individual
reconstruction of the diffuse and point-like photon flux given a single photon
count image, where the fluxes are superimposed. In order to discriminate
between these morphologically different signal components, a probabilistic
algorithm is derived in the language of information field theory based on a
hierarchical Bayesian parameter model. The signal inference exploits prior
information on the spatial correlation structure of the diffuse component and
the brightness distribution of the spatially uncorrelated point-like sources. A
maximum a posteriori solution and a solution minimizing the Gibbs free energy
of the inference problem using variational Bayesian methods are discussed.
Since the derivation of the solution is not dependent on the underlying
position space, the implementation of the D3PO algorithm uses the NIFTY package
to ensure applicability to various spatial grids and at any resolution. The
fidelity of the algorithm is validated by the analysis of simulated data,
including a realistic high energy photon count image showing a 32 x 32 arcmin^2
observation with a spatial resolution of 0.1 arcmin. In all tests the D3PO
algorithm successfully denoised, deconvolved, and decomposed the data into a
diffuse and a point-like signal estimate for the respective photon flux
components.Comment: 22 pages, 8 figures, 2 tables, accepted by Astronomy & Astrophysics;
refereed version, 1 figure added, results unchanged, software available at
http://www.mpa-garching.mpg.de/ift/d3po
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