2,038 research outputs found
Theory and Application of Dynamic Spatial Time Series Models
Stochastic economic processes are often characterized by dynamic interactions between variables that are dependent in both space and time. Analyzing these processes raises a number of questions about the econometric methods used that are both practically and theoretically interesting. This work studies econometric approaches to analyze spatial data that evolves dynamically over time. The book provides a background on least squares and maximum likelihood estimators, and discusses some of the limits of basic econometric theory. It then discusses the importance of addressing spatial heterogeneity in policies. The next chapters cover parametric modeling of linear and nonlinear spatial time series, non-parametric modeling of nonlinearities in panel data, modeling of multiple spatial time series variables that exhibit long and short memory, and probabilistic causality in spatial time series settings
Propagation and reconstruction of re-entry uncertainties using continuity equation and simplicial interpolation
This work proposes a continuum-based approach for the propagation of
uncertainties in the initial conditions and parameters for the analysis and
prediction of spacecraft re-entries. Using the continuity equation together
with the re-entry dynamics, the joint probability distribution of the
uncertainties is propagated in time for specific sampled points. At each time
instant, the joint probability distribution function is then reconstructed from
the scattered data using a gradient-enhanced linear interpolation based on a
simplicial representation of the state space. Uncertainties in the initial
conditions at re-entry and in the ballistic coefficient for three
representative test cases are considered: a three-state and a six-state steep
Earth re-entry and a six-state unguided lifting entry at Mars. The paper shows
the comparison of the proposed method with Monte Carlo based techniques in
terms of quality of the obtained marginal distributions and runtime as a
function of the number of samples used
Adaptive MCMC for Bayesian variable selection in generalised linear models and survival models
Developing an efficient computational scheme for high-dimensional Bayesian
variable selection in generalised linear models and survival models has always
been a challenging problem due to the absence of closed-form solutions for the
marginal likelihood. The RJMCMC approach can be employed to samples model and
coefficients jointly, but effective design of the transdimensional jumps of
RJMCMC can be challenge, making it hard to implement. Alternatively, the
marginal likelihood can be derived using data-augmentation scheme e.g.
Polya-gamma data argumentation for logistic regression) or through other
estimation methods. However, suitable data-augmentation schemes are not
available for every generalised linear and survival models, and using
estimations such as Laplace approximation or correlated pseudo-marginal to
derive marginal likelihood within a locally informed proposal can be
computationally expensive in the "large n, large p" settings. In this paper,
three main contributions are presented. Firstly, we present an extended
Point-wise implementation of Adaptive Random Neighbourhood Informed proposal
(PARNI) to efficiently sample models directly from the marginal posterior
distribution in both generalised linear models and survival models. Secondly,
in the light of the approximate Laplace approximation, we also describe an
efficient and accurate estimation method for the marginal likelihood which
involves adaptive parameters. Additionally, we describe a new method to adapt
the algorithmic tuning parameters of the PARNI proposal by replacing the
Rao-Blackwellised estimates with the combination of a warm-start estimate and
an ergodic average. We present numerous numerical results from simulated data
and 8 high-dimensional gene fine mapping data-sets to showcase the efficiency
of the novel PARNI proposal compared to the baseline add-delete-swap proposal
Probing massive neutrinos with the Minkowski functionals of the galaxy distribution
The characteristic signatures of massive neutrinos on large-scale structure
(LSS), if fully captured, can be used to put a stringent constraint on their
mass sum, . Previous work utilizing N-body simulations has shown the
Minkowski functionals (MFs) of LSS can reveal the imprints of massive neutrinos
on LSS, provide important complementary information to two-point statistics and
significantly improve constraints on . In this work, we take a step
forward and apply the statistics to the biased tracers of LSS, i.e. the
galaxies, and in redshift space. We perform a Fisher matrix analysis and
quantify the constraining power of the MFs by using the Molino mock galaxy
catalogs, which are constructed based on the halo occupation distribution (HOD)
framework with parameters for the SDSS and -22 galaxy samples. We
find the MFs give tighter constraints on all of the cosmological parameters
that we consider than the power spectrum. The constraints on
, and from
the MFs are better by a factor of 1.9, 2.9, 3.7, 4.2, 2.5, and 5.7,
respectively, after marginalizing over the HOD parameters. Specifically, for
, we obtain a 1 constraint of 0.059 eV with the MFs alone for
a volume of only .Comment: 33 pages, 5 + 4 figures, 4 tables. To be submitted to JCAP. Comments
welcome. arXiv admin note: text overlap with arXiv:2204.0294
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