Choosing Smoothness Parameters for Smoothing Splines by Minimizing and Estimate of Risk

Smoothing splines are a popular approach for non-parametric regression problems. We use periodic smoothing splines to fit a periodic signal plus noise model to data for which we assume there are underlying circadian patterns. In the smoothing spline methodology, choosing an appropriate smoothness parameter is an important step in practice. In this paper, we draw a connection between smoothing splines and REACT estimators that provides motivation for the creation of criteria for choosing the smoothness parameter. The new criteria are compared to three existing methods, namely cross-validation, generalized cross-validation, and generalization of maximum likelihood criteria, by a Monte Carlo simulation and by an application to the study of circadian patterns. For most of the situations presented in the simulations, including the practical example, the new criteria out-perform the three existing criteria.

Fitting of Mixtures with Unspecified Number of Components Using Cross Validation Distance Estimate

Estimation of the number of mixture components (k) is an unsolved problem. Available methods for estimation of k include bootstrapping the likelihood ratio test statistics and optimizing a variety of validity functionals such as AIC, BIC/MDL, and ICOMP. We investigate the minimization of distance between fitted mixture model and the true density as a method for estimating k. The distances considered are Kullback-Leibler (KL) and “L sub 2”. We estimate these distances using cross validation. A reliable estimate of k is obtained by voting of B estimates of k corresponding to B cross validation estimates of distance. This estimation methods with KL distance is very similar to Monte Carlo cross validated likelihood methods discussed by Smyth (2000). With focus on univariate normal mixtures, we present simulation studies that compare the cross validated distance method with AIC, BIC/MDL, and ICOMP. We also apply the cross validation estimate of distance approach along with AIC, BIC/MDL and ICOMP approach, to data from an osteoporosis drug trial in order to find groups that differentially respond to treatment.

Methodical study of nitrous oxide eddy covariance measurements using quantum cascade laser spectrometery over a Swiss forest

Nitrous oxide fluxes were measured at the Lägeren CarboEurope IP flux site over the multi-species mixed forest dominated by European beech and Norway spruce. Measurements were carried out during a four-week period in October–November 2005 during leaf senescence. Fluxes were measured with a standard ultrasonic anemometer in combination with a quantum cascade laser absorption spectrometer that measured N2O, CO2, and H2O mixing ratios simultaneously at 5 Hz time resolution. To distinguish insignificant fluxes from significant ones it is proposed to use a new approach based on the significance of the correlation coefficient between vertical wind speed and mixing ratio fluctuations. This procedure eliminated roughly 56% of our half-hourly fluxes. Based on the remaining, quality checked N2O fluxes we quantified the mean efflux at 0.8±0.4 μmol m−2 h−1 (mean ± standard error). Most of the contribution to the N2O flux occurred during a 6.5-h period starting 4.5 h before each precipitation event. No relation with precipitation amount could be found. Visibility data representing fog density and duration at the site indicate that wetting of the canopy may have as strong an effect on N2O effluxes as does below-ground microbial activity. It is speculated that above-ground N2O production from the senescing leaves at high moisture (fog, drizzle, onset of precipitation event) may be responsible for part of the measured flux.

Using contingent valuation to estimate willingness to pay for improved water source in rural Uganda

This research was conducted in August of 2011 in the villages of Kigisu and Rubona in rural Uganda while the author was serving as a community health volunteer with the U.S. Peace Corps. The study used the contingent valuation method (CVM) to estimate the populations’ willingness to pay (WTP) for the operation and maintenance of an improved water source. The survey was administered to 122 households out of 400 in the community, gathering demographic information, health and water behaviors, and using an iterative bidding process to estimate WTP. Households indicated a mean WTP of 286 Ugandan Shillings (UGX) per 20 liters for a public tap and 202 UGX per 20 liters from a private tap. The data were also analyzed using an ordered probit model. It was determined that the number of children in the home, and the distance from the existing source were the primary variables influencing households’ WTP.

What do case-control studies estimate? Survey of methods and assumptions in published case-control research

To evaluate strategies used to select cases and controls and how reported odds ratios are interpreted, the authors examined 150 case-control studies published in leading general medicine, epidemiology, and clinical specialist journals from 2001 to 2007. Most of the studies (125/150; 83%) were based on incident cases; among these, the source population was mostly dynamic (102/125; 82%). A minority (23/125; 18%) sampled from a fixed cohort. Among studies with incident cases, 105 (84%) could interpret the odds ratio as a rate ratio. Fifty-seven (46% of 125) required the source population to be stable for such interpretation, while the remaining 48 (38% of 125) did not need any assumptions because of matching on time or concurrent sampling. Another 17 (14% of 125) studies with incident cases could interpret the odds ratio as a risk ratio, with 16 of them requiring the rare disease assumption for this interpretation. The rare disease assumption was discussed in 4 studies but was not relevant to any of them. No investigators mentioned the need for a stable population. The authors conclude that in current case-control research, a stable exposure distribution is much more frequently needed to interpret odds ratios than the rare disease assumption. At present, investigators conducting case-control studies rarely discuss what their odds ratios estimate.

Selection on floral traits through male fertility in a natural plant population

Most studies on selection in plants estimate female fitness components and neglect male mating success, although the latter might also be fundamental to understand adaptive evolution. Information from molecular genetic markers can be used to assess determinants of male mating success through parentage analyses. We estimated paternal selection gradients on floral traits in a large natural population of the herb Mimulus guttatus using a paternity probability model and maximum likelihood methods. This analysis revealed more significant selection gradients than a previous analysis based on regression of estimated male fertilities on floral traits. There were differences between results of univariate and multivariate analyses most likely due to the underlying covariance structure of the traits. Multivariate analysis, which corrects for the covariance structure of the traits, indicated that male mating success declined with distance from and depended on the direction to the mother plants. Moreover, there was directional selection for plants with fewer open flowers which have smaller corollas, a smaller anther-stigma separation, more red dots on the corolla and a larger fluctuating asymmetry therein. For most of these traits, however, there was also stabilizing selection indicating that there are intermediate optima for these traits. The large number of significant selection gradients in this study shows that even in relatively large natural populations where not all males can be sampled, it is possible to detect significant paternal selection gradients, and that such studies can give us valuable information required to better understand adaptive plant evolution.