Algebra in probabilistic reasoning

This short expository paper outlines applications of computer algebra to the implication problem of conditional independence for Gaussian random variables. We touch on certificates for validity and invalidity of inference rules from the perspective of reproducibility of research data, computational complexity of the inference problem and draw a parallel to automated theorem proving in synthetic geometry.Comment: 6 pages, 2 figures; minor update of the published articl

Four-in-Five Adults Are Vaccinated or Intend to Get a Vaccine

In this data snapshot, author Sarah Boege reports that by March 29, one-quarter of U.S. adults reported that they had already received at least one dose of a COVID-19 vaccine. In addition, 39.1 percent hadn’t yet been vaccinated but reported that they will “definitely” get one when available and another 17.4 percent said that they “probably” will. However, 10.1 percent of adults will “probably not” and 8.2 percent will “definitely not” get a vaccine. These data suggest that a large majority of adults could be vaccinated in the coming months, but experts see risks in having a sizeable group remain unvaccinated. COVID-19 vaccines are also not yet widely available to children and youth under 16 years old

Gaussoids are two-antecedental approximations of Gaussian conditional independence structures

The gaussoid axioms are conditional independence inference rules which characterize regular Gaussian CI structures over a three-element ground set. It is known that no finite set of inference rules completely describes regular Gaussian CI as the ground set grows. In this article we show that the gaussoid axioms logically imply every inference rule of at most two antecedents which is valid for regular Gaussians over any ground set. The proof is accomplished by exhibiting for each inclusion-minimal gaussoid extension of at most two CI statements a regular Gaussian realization. Moreover we prove that all those gaussoids have rational positive-definite realizations inside every $\varepsilon$-ball around the identity matrix. For the proof we introduce the concept of algebraic Gaussians over arbitrary fields and of positive Gaussians over ordered fields and obtain the same two-antecedental completeness of the gaussoid axioms for algebraic and positive Gaussians over all fields of characteristic zero as a byproduct.Comment: 24 pages; v3: added Preliminaries section; corrected miscalculations in examples and added source code lin

Selfadhesivity in Gaussian conditional independence structures

Selfadhesivity is a property of entropic polymatroids which guarantees that the polymatroid can be glued to an identical copy of itself along arbitrary restrictions such that the two pieces are independent given the common restriction. We show that positive definite matrices satisfy this condition as well and examine consequences for Gaussian conditional independence structures. New axioms of Gaussian CI are obtained by applying selfadhesivity to the previously known axioms of structural semigraphoids and orientable gaussoids.Comment: 13 pages; v3: minor revisio

No eleventh conditional Ingleton inequality

A rational probability distribution on four binary random variables $X, Y, Z, U$ is constructed which satisfies the conditional independence relations [X \mathrel{\text{\perp\mkern-10mu\perp}} Y], [X \mathrel{\text{\perp\mkern-10mu\perp}} Z \mid U], [Y \mathrel{\text{\perp\mkern-10mu\perp}} U \mid Z] and [Z \mathrel{\text{\perp\mkern-10mu\perp}} U \mid XY] but whose entropy vector violates the Ingleton inequality. This settles a recent question of Studen\'y (IEEE Trans. Inf. Theory vol. 67, no. 11) and shows that there are, up to symmetry, precisely ten inclusion-minimal sets of conditional independence assumptions on four discrete random variables which make the Ingleton inequality hold.Comment: 7 pages, 1 figur

RANGING PATTERNS AND HABITAT UTILIZATION OF NORTHERN RIVER OTTERS, \u3ci\u3eLONTRA CANADENSIS\u3c/i\u3e, IN MISSOURI: IMPLICATIONS FOR THE CONSERVATION OF A REINTRODUCED SPECIES

I studied the spacing patterns and habitat utilization by reintroduced northern river otters, Lontra canadensis, at two sites in Missouri because previous studies of otters indicate, plasticity of a species social structure will likely be due to the tactics employed in acquiring resources in any given area. Seven hypotheses were tested by employing radio-tracking, habitat assessment and geographic information system approaches: (1) home range (HR) and core area (CA) size differ by sex; (2) HR and CA size differ in breeding vs. non-breeding seasons; (3) percent range overlap differs by sex; (4) habitat utilization, as indicated by latrine use, differs seasonally; (5) primary prey type(s) found in scat differ seasonally; (6) environmental characteristics of areas used extensively by otters (latrines, dens, haul-outs) differ from adjacent, unused sites; and (7) stream-order effects and features associated with core area use are similar between two disjointed field sites, and can thus be used along with GIS-driven identifiers to generate predictions regarding suitable habitat for Midwestern river otter populations. Evidence is presented on differences in ranging patterns of otters by location, sex, and seasonality, as well as differences in core area use and accompanying habitat characteristics for the two populations. The following hypotheses were corroborated: (1) male otters had larger HRs and CAs than female otters; (2) female otters maintained small, non-overlapping home ranges; (3) males exhibit a greater percentage of inter- and intra-sexual HR and CA overlap than females; and (4) HR and CA size, and percent overlap differ between a large, riverine ecosystem and a small, meandering stream ecosystem. However, hypotheses examining temporal use of space by otters were not supported. In conclusion, this study suggested that northern river otters exhibit a variety of spacing patterns in different parts of their range, similar to those discovered in other solitary carnivores. Seasonal use of space was different from that typically found in solitary carnivores; differences may be related to habitat characteristics associated with stream order and wetland ecosystems. Overall, although introduced otters came from disjointed regions differing in habitat features and ecological pressures, reintroduced otters have done very well in Missouri

New Data Show One-in-Six Children Were Poor Before COVID-19 Pandemic

New American Community Survey (ACS) data released by the U.S. Census Bureau on September 17, 2020 show child poverty at 16.8 percent in 2019, down from 18 percent in 2018. Sub-national patterns in child poverty remain intact; for example, higher in rural and urban places than in the suburbs. Importantly, 2019 child poverty declines are likely now outdated due to the COVID-19-related recession, the effects of which may last years. For instance, child poverty had still not yet returned to pre-Great Recession rates from 2007 in all states by 2019, illustrating that recovery in child poverty can be a long process