Functional summary statistics for point processes on the sphere with an application to determinantal point processes

We study point processes on $\mathbb S^d$, the $d$-dimensional unit sphere $\mathbb S^d$, considering both the isotropic and the anisotropic case, and focusing mostly on the spherical case $d=2$. The first part studies reduced Palm distributions and functional summary statistics, including nearest neighbour functions, empty space functions, and Ripley's and inhomogeneous $K$-functions. The second part partly discusses the appealing properties of determinantal point process (DPP) models on the sphere and partly considers the application of functional summary statistics to DPPs. In fact DPPs exhibit repulsiveness, but we also use them together with certain dependent thinnings when constructing point process models on the sphere with aggregation on the large scale and regularity on the small scale. We conclude with a discussion on future work on statistics for spatial point processes on the sphere

Score, Pseudo-Score and Residual Diagnostics for Spatial Point Process Models

We develop new tools for formal inference and informal model validation in the analysis of spatial point pattern data. The score test is generalized to a "pseudo-score" test derived from Besag's pseudo-likelihood, and to a class of diagnostics based on point process residuals. The results lend theoretical support to the established practice of using functional summary statistics, such as Ripley's $K$-function, when testing for complete spatial randomness; and they provide new tools such as the compensator of the $K$-function for testing other fitted models. The results also support localization methods such as the scan statistic and smoothed residual plots. Software for computing the diagnostics is provided.Comment: Published in at http://dx.doi.org/10.1214/11-STS367 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Determinantal point process models on the sphere

We consider determinantal point processes on the $d$-dimensional unit sphere $\mathbb S^d$. These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified by a so-called kernel which we assume is a complex covariance function defined on $\mathbb S^d\times\mathbb S^d$. We review the appealing properties of such processes, including their specific moment properties, density expressions and simulation procedures. Particularly, we characterize and construct isotropic DPPs models on $\mathbb{S}^d$, where it becomes essential to specify the eigenvalues and eigenfunctions in a spectral representation for the kernel, and we figure out how repulsive isotropic DPPs can be. Moreover, we discuss the shortcomings of adapting existing models for isotropic covariance functions and consider strategies for developing new models, including a useful spectral approach

Tingkat Cemaran Aflatoksin B pada Jagung di Kabupaten Kupang, Nusa Tenggara Timur

Penelitian ini bertujuan untuk mengetahui tingkat cemaran aflatoksin B pada jagung di tingkat petani di beberapa sentra produksi jagung di Kabupaten Kupang. Sebanyak 75 sampel diambil dari 4 kecamatan dan dilakukan pengujian tingkat cemaran aflatoksin B menggunakan metode ELISA. Hasil uji kandungan aflatoksin terhadap sampel menunjukkanbahwa 71 sampel (95%) dengan cemaran aflatoksin 15 ppb. Cemaran aflatoksin tertinggi pada sampel sebesar 42,3 ppb

Does Corporate Performance Improve After Mergers?

We examine the post-acquisition operating performance of merged firms using a sample of the 50 largest mergers between U.S. public industrial firms completed in the period 1979 to 1983. The results indicate that merged firms have significant improvement in asset productivity relative to their industries after the merger, leading to higher post-merger operating cash flow returns. Sample firms maintain their capital expenditure and R&D rates relative to their industries after the merger, indicating that merged firms do not reduce their long-term investments. There is a strong positive relation between postmerger increases in operating cash flows and abnormal stock returns at merger announcements, indicating that expectations of economic improvements underlie the equity revaluations of the merging firms.

Effect of "motivational interviewing" on quality of care measures in screen detected type 2 diabetes patients: A one-year follow-up of an RCT, ADDITION Denmark

OBJECTIVE: “Motivational interviewing” (MI) has shown to be broadly applicable in the management of behavioural problems and diseases. Only a few studies have evaluated the effect of MI on type 2 diabetes treatment and none has explored the effect of MI on target-driven intensive treatment. METHODS: Patients were cluster-randomized by GPs, who were randomized to training in MI or not. Both groups received training in target-driven intensive treatment of type 2 diabetes. The intervention consisted of a 1½-day residential course in MI with half-day follow-up twice during the first year. Blood samples, case record forms, national registry files, and validated questionnaires from patients were obtained. RESULTS: After one year significantly improved metabolic status measured by HbA1c (p < 0.01) was achieved in both groups. There was no difference between groups. Medication adherence was close to 100% within both treatment groups. GPs in the intervention group did not use more than an average of 1.7 out of three possible MI consultations. CONCLUSION: The study found no effect of MI on metabolic status or on adherence of medication in people with screen detected type 2 diabetes. However, there was a significantly improved metabolic status and excellent medication adherence after one year within both study groups. An explanation may be that GPs in the control group may have taken up core elements of MI, and that GPs trained in MI used less than two out of three planned MI consultations. The five-year follow-up of this study will reveal whether MI has an effect over a longer period