Spectral estimation for spatial point patterns

This article determines how to implement spatial spectral analysis of point processes (in two dimensions or more), by establishing the moments of raw spectral summaries of point processes. We establish the first moments of raw direct spectral estimates such as the discrete Fourier transform of a point pattern. These have a number of surprising features that departs from the properties of raw spectral estimates of random fields and time series. As for random fields, the special case of isotropic processes warrants special attention, which we discuss. For time series and random fields white noise plays a special role, mirrored by the Poisson processes in the case of the point process. For random fields bilinear estimators are prevalent in spectral analysis. We discuss how to smooth any bilinear spectral estimator for a point process. We also determine how to taper this bilinear spectral estimator, how to calculate the periodogram, sample the wavenumbers and discuss the correlation of the periodogram. In parts this corresponds to recommending suitable separable as well as isotropic tapers in d dimensions. This, in aggregation, establishes the foundations for spectral analysis of point processes.Comment: 29 pages + 23 pages of supplements, 6 figure

Visualizing the Wavenumber Content of a Point Pattern

Spatial point patterns are a commonly recorded form of data in ecology, medicine, astronomy, criminology, epidemiology and many other application fields. One way to understand their second order dependence structure is via their spectral density function. However, unlike time series analysis, for point patterns such approaches are currently underutilized. In part, this is because the interpretation of the spectral representation of the underlying point processes is challenging. In this letter, we demonstrate how to band-pass filter point patterns, thus enabling us to explore the spectral representation of point patterns in space by isolating the signal corresponding to certain sets of wavenumbers

A multivariate pseudo-likelihood approach to estimating directional ocean wave models

Ocean buoy data in the form of high frequency multivariate time series are routinely recorded at many locations in the world's oceans. Such data can be used to characterise the ocean wavefield, which is important for numerous socio-economic and scientific reasons. This characterisation is typically achieved by modelling the frequency-direction spectrum, which decomposes spatiotemporal variability by both frequency and direction. State-of-the-art methods for estimating the parameters of such models do not make use of the full spatiotemporal content of the buoy observations due to unnecessary assumptions and smoothing steps. We explain how the multivariate debiased Whittle likelihood can be used to jointly estimate all parameters of such frequency-direction spectra directly from the recorded time series. When applied to North Sea buoy data, debiased Whittle likelihood inference reveals smooth evolution of spectral parameters over time. We discuss challenging practical issues including model misspecification, and provide guidelines for future application of the method

Evaluation of outcomes among patients with traumatic intracranial hypertension treated with decompressive craniectomy vs standard medical care at 24 month

Importance Trials often assess primary outcomes of traumatic brain injury at 6 months. Longer-term data are needed to assess outcomes for patients receiving surgical vs medical treatment for traumatic intracranial hypertension. Objective To evaluate 24-month outcomes for patients with traumatic intracranial hypertension treated with decompressive craniectomy or standard medical care. Design, Setting, and Participants Prespecified secondary analysis of the Randomized Evaluation of Surgery With Craniectomy for Uncontrollable Elevation of Intracranial Pressure (RESCUEicp) randomized clinical trial data was performed for patients with traumatic intracranial hypertension (>25 mm Hg) from 52 centers in 20 countries. Enrollment occurred between January 2004 and March 2014. Data were analyzed between 2018 and 2021. Eligibility criteria were age 10 to 65 years, traumatic brain injury (confirmed via computed tomography), intracranial pressure monitoring, and sustained and refractory elevated intracranial pressure for 1 to 12 hours despite pressure-controlling measures. Exclusion criteria were bilateral fixed and dilated pupils, bleeding diathesis, or unsurvivable injury. Interventions Patients were randomly assigned 1:1 to receive a decompressive craniectomy with standard care (surgical group) or to ongoing medical treatment with the option to add barbiturate infusion (medical group). Main Outcomes and Measures The primary outcome was measured with the 8-point Extended Glasgow Outcome Scale (1 indicates death and 8 denotes upper good recovery), and the 6- to 24-month outcome trajectory was examined. Results This study enrolled 408 patients: 206 in the surgical group and 202 in the medical group. The mean (SD) age was 32.3 (13.2) and 34.8 (13.7) years, respectively, and the study population was predominantly male (165 [81.7%] and 156 [80.0%], respectively). At 24 months, patients in the surgical group had reduced mortality (61 [33.5%] vs 94 [54.0%]; absolute difference, −20.5 [95% CI, −30.8 to −10.2]) and higher rates of vegetative state (absolute difference, 4.3 [95% CI, 0.0 to 8.6]), lower or upper moderate disability (4.7 [−0.9 to 10.3] vs 2.8 [−4.2 to 9.8]), and lower or upper severe disability (2.2 [−5.4 to 9.8] vs 6.5 [1.8 to 11.2]; χ27 = 24.20, P = .001). For every 100 individuals treated surgically, 21 additional patients survived at 24 months; 4 were in a vegetative state, 2 had lower and 7 had upper severe disability, and 5 had lower and 3 had upper moderate disability, respectively. Rates of lower and upper good recovery were similar for the surgical and medical groups (20 [11.0%] vs 19 [10.9%]), and significant differences in net improvement (≥1 grade) were observed between 6 and 24 months (55 [30.0%] vs 25 [14.0%]; χ22 = 13.27, P = .001). Conclusions and Relevance At 24 months, patients with surgically treated posttraumatic refractory intracranial hypertension had a sustained reduction in mortality and higher rates of vegetative state, severe disability, and moderate disability. Patients in the surgical group were more likely to improve over time vs patients in the medical group