 Award ID(s):
 1812063
 NSFPAR ID:
 10390267
 Date Published:
 Journal Name:
 Annual Review of Statistics and Its Application
 Volume:
 10
 Issue:
 1
 ISSN:
 23268298
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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A bstract It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting randommatrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infiniterange quantum spin glass, the quantum p spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations — the exponential of the spin glass “complexity” as obtained from the quantum ThoulessAndersonPalmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicitybreaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semiclassical limit.more » « less

Abstract Meta‐analysis is a statistical methodology for combining information from diverse sources so that a more reliable and efficient conclusion can be reached. It can be conducted by either synthesizing study‐level summary statistics or drawing inference from an overarching model for individual participant data (IPD) if available. The latter is often viewed as the “gold standard.” For random‐effects models, however, it remains not fully understood whether the use of IPD indeed gains efficiency over summary statistics. In this paper, we examine the relative efficiency of the two methods under a general likelihood inference setting. We show theoretically and numerically that summary‐statistics‐based analysis is
at most as efficient as IPD analysis, provided that the random effects follow the Gaussian distribution, and maximum likelihood estimation is used to obtain summary statistics. More specifically, (i) the two methods are equivalent in an asymptotic sense; and (ii) summary‐statistics‐based inference can incur an appreciable loss of efficiency if the sample sizes are not sufficiently large. Our results are established under the assumption that the between‐study heterogeneity parameter remains constant regardless of the sample sizes, which is different from a previous study. Our findings are confirmed by the analyses of simulated data sets and a real‐world study of alcohol interventions. 
Tabulated statistics of road networks at the level of intersections and for builtup areas for each decade from 1900 to 2010, and for 2015, for each corebased statistical area (CBSA, i.e., metropolitan and micropolitan statistical area) in the conterminous United States. These areas are derived from historical road networks developed by Johannes Uhl. See Burghardt et al. (2022) for details on the data processing.
Spatial coverage: all CBSAs that are covered by the HISDACUS historical settlement layers.
This dataset includes around 2,700 U.S. counties. In the remaining counties, construction year coverage in the underlying ZTRAX data (Zillow Transaction and Assessment Dataset) is low. See Uhl et al. (2021) for details.
All data created by Keith A. Burghardt, USC Information Sciences Institute, USA
Codebook: these CBSA statistics are stratified by degree of aggregation.
 CBSA_stats_diffFrom1950: Change in CBSAaggregated patch statistics between 1950 and 2015
 CBSA_stats_by_decade: CBSAaggregated patch statistics for each decade from 19002010 plus 2015
 CBSA_stats_by_decade: CBSAaggregated cumulative patch statistics for each decade from 19002010 plus 2015. All roads created up to a given decade are used for calculating statistics.
 Patch_stats_by_decade: Individual patch statistics for each decade from 19002010 plus 2015
 Patch_stats_by_decade: Individual cumulative patch statistics for each decade from 19002010 plus 2015. All roads created up to a given decade are used for calculating statistics.
The statistics are the following:
 msaid: CBSA code
 id: (if patch statistics) arbitrary int unique to each patch within the CBSA that year
 year: year of statistics
 pop: population within all CBSA counties
 patch_bupr: built up property records (BUPR) within a patch (or sum of patches within CBSA)
 patch_bupl: built up property l (BUPL) within a patch (or sum of patches within CBSA)
 patch_bua: built up area (BUA) within a patch (or sum of patches within CBSA)
 all_bupr: Same as above but for all data in 2015 regardless of whether properties were in patches
 all_bupl: Same as above but for all data in 2015 regardless of whether properties were in patches
 all_bua: Same as above but for all data in 2015 regardless of whether properties were in patches
 num_nodes: number of nodes (intersections)
 num_edges: number of edges (roads between intersections)
 distance: total road length in km
 k_mean: mean number of undirected roads per intersection
 k1: fraction of nodes with degree 1
 k4plus: fraction of nodes with degree 4+
 bearing: histogram of different bearings between intersections
 entropy: entropy of bearing histogram
 mean_local_gridness: Griddedness used in text
 mean_local_gridness_max: Same as griddedness used in text but assumes we can have up to 3 quadrilaterals for degree 3 (maximum possible, although intersections will not necessarily create right angles)
Code available at https://github.com/johannesuhl/USRoadNetworkEvolution.
References:
Burghardt, K., Uhl, J., Lerman, K., & Leyk, S. (2022). Road Network Evolution in the Urban and Rural United States Since 1900. Computers, Environment and Urban Systems.

Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra, and computational algebra), geometry, and combinatorics to provide insight into knotty problems in mathematical statistics. In this review, we illustrate this on three problems related to networks: network models for relational data, causal structure discovery, and phylogenetics. For each problem, we give an overview of recent results in algebraic statistics, with emphasis on the statistical achievements made possible by these tools and their practical relevance for applications to other scientific disciplines.more » « less

The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions – both in theory and from observations. Despite promising findings on the topic of fractal geometries in turbulence, there is no accepted image for the physical flow features corresponding to this statistical signature in the inertial subrange. The present study uses boundary layer turbulence measurements to evaluate the selfsimilar geometric properties of velocity isosurfaces and investigate their influence on statistics for the velocity signal. The fractal dimension of streamwise velocity isosurfaces, indicating statistical selfsimilarity in the size of ‘wrinkles’ along each isosurface, is shown to be constant only within the inertial subrange of scales. For the transition between the inertial subrange and production range, it is inferred that the largest wrinkles become increasingly confined by the overall size of largescale coherent velocity regions such as uniform momentum zones. The selfsimilarity of isosurfaces yields powerlaw trends in subsequent onedimensional statistics. For instance, the theoretical 2/3 powerlaw exponent for the structure function can be recovered by considering the collective behaviour of numerous isosurface level sets. The results suggest that the physical presence of inertial subrange eddies is manifested in the selfsimilar wrinkles of isosurfaces.more » « less