2,038 research outputs found

    Theory and Application of Dynamic Spatial Time Series Models

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    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

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    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

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    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

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    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, MνM_{\nu}. 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 MνM_{\nu}. 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 Mr<−21.5M_r < -21.5 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 Ωm,Ωb,h,ns,σ8\Omega_{\mathrm{m}}, \Omega_{\mathrm{b}}, h, n_s, \sigma_8, and MνM_\nu 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 MνM_{\nu}, we obtain a 1σ\sigma constraint of 0.059 eV with the MFs alone for a volume of only (1h−1Gpc)3\left(1 h^{-1} \mathrm{Gpc}\right)^3.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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