AR and MA representation of partial autocorrelation functions, with applications

We prove a representation of the partial autocorrelation function (PACF), or the Verblunsky coefficients, of a stationary process in terms of the AR and MA coefficients. We apply it to show the asymptotic behaviour of the PACF. We also propose a new definition of short and long memory in terms of the PACF.Comment: Published in Probability Theory and Related Field

Cosmological parameters from SDSS and WMAP

We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a ``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1 sigma constraints on the Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.Comment: Minor revisions to match accepted PRD version. SDSS data and ppt figures available at http://www.hep.upenn.edu/~max/sdsspars.htm

Influence of birth cohort on age of onset cluster analysis in bipolar I disorder

PURPOSE: Two common approaches to identify subgroups of patients with bipolar disorder are clustering methodology (mixture analysis) based on the age of onset, and a birth cohort analysis. This study investigates if a birth cohort effect will influence the results of clustering on the age of onset, using a large, international database. METHODS: The database includes 4037 patients with a diagnosis of bipolar I disorder, previously collected at 36 collection sites in 23 countries. Generalized estimating equations (GEE) were used to adjust the data for country median age, and in some models, birth cohort. Model-based clustering (mixture analysis) was then performed on the age of onset data using the residuals. Clinical variables in subgroups were compared. RESULTS: There was a strong birth cohort effect. Without adjusting for the birth cohort, three subgroups were found by clustering. After adjusting for the birth cohort or when considering only those born after 1959, two subgroups were found. With results of either two or three subgroups, the youngest subgroup was more likely to have a family history of mood disorders and a first episode with depressed polarity. However, without adjusting for birth cohort (three subgroups), family history and polarity of the first episode could not be distinguished between the middle and oldest subgroups. CONCLUSION: These results using international data confirm prior findings using single country data, that there are subgroups of bipolar I disorder based on the age of onset, and that there is a birth cohort effect. Including the birth cohort adjustment altered the number and characteristics of subgroups detected when clustering by age of onset. Further investigation is needed to determine if combining both approaches will identify subgroups that are more useful for research

Does the "Silver bullet" lose its shine over the time? Assessment of loss of lithium response in a preliminary sample of bipolar disorder outpatients

Background: Though often perceived as a "silver bullet" treatment for bipolar disorder (BD), lithium has seldom reported to lose its efficacy over the time. Objective: The aim of the present study was to assess cases of refractoriness toward restarted lithium in BD patients who failed to preserve maintenance. Method: Treatment trajectories associated with re-instituted lithium following loss of achieved lithium-based maintenance in BD were retrospectively reviewed for 37 BD-I patients (median age 52 years; F: M=17: 20 or 46% of the total) over an 8.1-month period on average. Results: In our sample only 4 cases (roughly 11% of the total, of whom F: M=2: 2) developed refractoriness towards lithium after its discontinuation. Thirty-three controls (F: M=15: 18) maintained lithium response at the time of re-institution. No statistically significant difference between cases and controls was observed with respect to a number of demographic and clinical features but for time spent before first trial ever with lithium in life (8.5 vs. 3 years; U=24.5, Z=-2.048, p=.041) and length of lithium discontinuation until new therapeutic attempt (5.5 vs. 2 years; U=8, Z=-2.927, p=.003) between cases vs. controls respectively. Tapering off of lithium was significantly faster among cases vs. controls (1 vs. 7 days; U=22, Z=-2.187), though both subgroups had worrisome high rates of poor adherence overall. Conclusion: Although intrinsic limitations of the present preliminary assessment hamper the validity and generalizability of overall results, stating the clinical relevance of the topic further prospective research is warranted. The eventual occurrence of lithium refractoriness may indeed be associated with peculiar course trajectories and therapeutic outcomes ultimately urging the prescribing clinicians to put efforts in preserving maintenance of BD in the absence of any conclusive research insight on the matter. © Fornaro et al

Sampling Properties of U-statistics for a Class of Stationary Nonlinear Processes

Stationary nonlinear processes, U-statistics, Large sample properties,