Shrinkage Estimation in Multilevel Normal Models

This review traces the evolution of theory that started when Charles Stein in 1955 [In Proc. 3rd Berkeley Sympos. Math. Statist. Probab. I (1956) 197--206, Univ. California Press] showed that using each separate sample mean from $k\ge3$ Normal populations to estimate its own population mean $\mu_i$ can be improved upon uniformly for every possible $\mu=(\mu_1,...,\mu_k)'$. The dominating estimators, referred to here as being "Model-I minimax," can be found by shrinking the sample means toward any constant vector. Admissible minimax shrinkage estimators were derived by Stein and others as posterior means based on a random effects model, "Model-II" here, wherein the $\mu_i$ values have their own distributions. Section 2 centers on Figure 2, which organizes a wide class of priors on the unknown Level-II hyperparameters that have been proved to yield admissible Model-I minimax shrinkage estimators in the "equal variance case." Putting a flat prior on the Level-II variance is unique in this class for its scale-invariance and for its conjugacy, and it induces Stein's harmonic prior (SHP) on $\mu_i$.Comment: Published in at http://dx.doi.org/10.1214/11-STS363 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bound States in n Dimensions (Especially n = 1 and n = 2)

We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two dimensions, examples of weak potentials with one or infinitely many bound states. We derive bounds for one and two dimensions which have the "right" coupling constant behaviour for large coupling.Comment: Talk given by A. Martin at Les Houches, October 2001, to appear in "Few-Body Problems

Enabling transition into higher education for students with asperger syndrome

This project report provides an insight into the lives of students with Asperger Syndrome (AS) during their transition into higher education. It details the experiences of eight students with AS. Students were interviewed multiple times at various junctures throughout their first academic year. Although they told stories of everyday disabling barriers, they also shared experiences of academic and social successes. The project was primarily focused on students with AS; however, its findings will hopefully help inform inclusive policy and practice within higher education institutions

When adolescents stop psychological therapy: rupture-repair in the therapeutic alliance and association with therapy ending

therapeutic alliance consistently predicts dropout from psychological therapy, and ruptures in the therapeutic alliance may also predict dropout, yet there is a dearth of research with adolescents. This study investigated whether markers of rupturerepair in the therapeutic alliance were indicative of different types of treatment ending in adolescents who received psychological treatment for depression. Data were from the IMPACT study, a trial investigating the effectiveness of therapies for adolescent depression. Participants were randomly allocated to receive a psychological therapy: Brief Psychosocial Intervention, Cognitive-Behavioural Therapy or Short-Term Psychoanalytic Psychotherapy. The sample (N=35) comprised adolescents who had either completed their treatment (n=14) or dropped out (n=21) according to their therapist. Dropout cases were further classified as dissatisfied (n=14) or got-whatthey- needed (n=7) based on post-therapy interviews with the adolescent and therapist. Selected audio-recordings of therapy sessions were rated using the Rupture Resolution Rating System and Working Alliance Inventory (observer-version). Therapeutic alliance and rupture-repair during therapy were similar for completers and got-what-they-needed dropouts, while dissatisfied dropouts had poorer therapeutic alliance, more ruptures, ruptures were frequently unresolved, and therapists contributed to ruptures to a greater extent. Qualitative analysis of the sessions led to the construction of three categories of therapist contribution to ruptures: therapist minimal response; persisting with a therapeutic activity; and focus on risk. Results suggest that ruptures, especially when unresolved, could be regarded as warning signs of disengagement and dropout from psychological treatment. Future research should investigate how ruptures may be effectively identified and resolved in treatment with adolescents

Self-interaction errors in nuclear energy density functionals

When applied to a single nucleon, nuclear energy density functionals may yield a non-vanishing internal energy thus implying that the nucleon is interacting with itself. It is shown how to avoid this unphysical feature for semi-local phenomenological functionals containing all possible bilinear combinations of local densities and currents up to second order in the derivatives. The method outlined in this Rapid Communication could be easily extended to functionals containing higher order terms, and could serve as a guide for constraining the time-odd part of the functional

Diffusion with resetting in arbitrary spatial dimension

We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the non-equilibrium stationary state which exhibits non-Gaussian behaviour. We then consider the presence of an absorbing target centred at the origin and compute the survival probability and mean time to absorption of the diffusive particle by the target. The mean absorption time is finite and has a minimum value at an optimal resetting rate $r^*$ which depends on dimension. Finally we consider the problem of a finite density of diffusive particles, each resetting to its own initial position. While the typical survival probability of the target at the origin decays exponentially with time regardless of spatial dimension, the average survival probability decays asymptotically as $\exp -A (\log t)^d$ where $A$ is a constant. We explain these findings using an interpretation as a renewal process and arguments invoking extreme value statistics.Comment: 21 pages, 3 figures, submitted to Journal of Physics

Comparison of habitat-based indices of abundance with fishery-independent biomass estimates from bottom trawl surveys

Rockfish species are notoriously difficult to sample with multispecies bottom trawl survey methods. Typically, biomass estimates have high coefficients of variation and can fluctuate outside the bounds of biological reality from year to year. This variation may be due in part to their patchy distribution related to very specific habitat preferences. We successfully modeled the distribution of five commercially important and abundant rockf ish species. A two-stage modeling method (modeling both presence-absence and abundance) and a collection of important habitat variables were used to predict bottom trawl survey catch per unit of effort. The resulting models explained between 22% and 66% of the variation in rockfish distribution. The models were largely driven by depth, local slope, bottom temperature, abundance of coral and sponge, and measures of water column productivity (i.e., phytoplankton and zooplankton). A year-effect in the models was back-transformed and used as an index of the time series of abundance. The abundance index trajectories of three of five species were similar to the existing estimates of their biomass. In the majority of cases the habitat-based indices exhibited less interannual variability and similar precision when compared with stratified survey-based biomass estimates. These indices may provide for stock assessment models a more stable alternative to current biomass estimates produced by the multispecies bottom trawl survey in the Gulf of Alaska