A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.Comment: Published in at http://dx.doi.org/10.1214/12-STS406 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Fermi Algebra for the Ising Model on an Infinite Lattice

Fermi algebra methods are applied to the two-dimensional Ising model on an infinite lattice. The way in which the phase transition manifests itself is discussed

Effect of Field Trials on Northern Bobwhite Survival and Hunt Quality on Dixie Plantation

The potential negative effects of horseback field trials on survival and post trial hunting quality of northern bobwhites (Colinus virginianus) have long been debated. Recent acquisition of Dixie Plantation (3,650 ha) by Tall Timbers Research Station provided a unique opportunity to evaluate this interaction as Dixie has been home to the Continental Field Trial since 1937. We monitored radio-tagged bobwhites annually (n = 183; ~20 coveys during fall/winter) on a core study area (640 ha) upon which a portion of the field trial was conducted during January 2015 & 2016. We estimated Kaplan-Meier survival of radio-tagged bobwhites on Dixie before, during, and after the field trial event as well as compared seasonal survival to bobwhite (N = 387) on nearby Tall Timbers Research Station (1,570 ha) during the same time period. Additionally, we recorded the number of coveys seen, coveys pointed, and shots fired during each half-day hunt (n = 133) to evaluate hunt quality before and after the field trial. Bobwhite survival on Dixie was similar (P\u3e0.05) during the two weeks prior to (0.89, SE = 0.026), during (0.93, SE = 0.023), and after (0.92, SE = 0.026) the field trial for the two years combined, as were seasonal survival curves between the two study sites for both years monitored. No differences (P\u3e0.05) were observed in the number of coveys seen per half day hunt before (X = 11.78, SE = 0.39) compared to after (X = 12.35, SE = 0.44), covey rises shot before (X = 6.89, SE = 0.28) and after (X = 7.75, SE = 0.37), or number of shots fired before (X = 23.5, SE = 1.19) versus after (X =24.11 SE = 1.26) the field trial. We were unable to detect any evidence that the type of disturbance generated by this field trial had any effect on either bobwhite survival or post trial hunting quality on our study area

Use of Spring Whistle Counts to Predict Northern Bobwhite Relative Abundance

Spring whistle counts are commonly used to index northern bobwhite (Colinus virginianus) breeding populations and make inference about relative autumn abundance. They are relatively cheap and easy to implement and provide the advantage of surveying bobwhite populations from multiple points daily and early in the year. This could prove useful on properties available for potential lease, purchase, or as translocation sites; as well as to monitor population trends. Our objective was to determine whether spring whistle counts reliably forecast autumn covey numbers on a wide range of sites, years, and densities on 6 properties in southwestern Georgia from 2006 to 2015. We conducted spring whistle counts weekly during peak calling activity (late May–early Jun, for 4–6 consecutive years) on an average of 7 points/property (range = 5–9). We conducted autumn covey counts using these same sampling points as an index of relative abundance. Peak number of males heard in spring and number of coveys heard in autumn was strongly correlated (R2 = 0.791, n = 198) for all points combined, indicating that spring whistle counts are a reliable tool for assessing bobwhite relative abundance on sites where autumn covey counts are precluded or the information is needed prior to autumn