The restricted EM algorithm under inequality restrictions on the parameters

AbstractOne of the most powerful algorithms for maximum likelihood estimation for many incomplete-data problems is the EM algorithm. The restricted EM algorithm for maximum likelihood estimation under linear restrictions on the parameters has been handled by Kim and Taylor (J. Amer. Statist. Assoc. 430 (1995) 708–716). This paper proposes an EM algorithm for maximum likelihood estimation under inequality restrictions A0β⩾0, where β is the parameter vector in a linear model W=Xβ+ε and ε is an error variable distributed normally with mean zero and a known or unknown variance matrix Σ>0. Some convergence properties of the EM sequence are discussed. Furthermore, we consider the consistency of the restricted EM estimator and a related testing problem

Quantum correlation and classical correlation dynamics in the spin-boson model

We study the quantum correlation and classical correlation dynamics in a spin-boson model. For two different forms of spectral density, we obtain analytical results and show that the evolutions of both correlations depend closely on the form of the initial state. At the end of evolution, all correlations initially stored in the spin system transfer to reservoirs. It is found that for a large family of initial states, quantum correlation remains equal to the classical correlation during the course of evolution. In addition, there is no increase in the correlations during the course of evolution.Comment: 10 pages, 5 figure

(E)-1-Ferrocenyl-3-(2-fur­yl)prop-2-en-1-one

The title compound, [Fe(C5H5)(C12H9O2)], exhibits an E configuration. In the ferrocene unit, the two cyclo­penta­dienyl rings are almost parallel [dihedral angle = 0.76 (12)°] and the C atoms are in an eclipsed conformation. An intra­molecular C—H⋯O hydrogen bond generates an S(5) ring. In the crystal, the mol­ecules are linking into zigzag chains via two C—H⋯O hydrogen-bonding inter­actions along the c axis and neighbouring chains are stabilized by electrostatic inter­action forces

Colorectal cancer screening with fecal occult blood test: A 22-year cohort study.

The aim of the present study was to investigate the efficacy of colorectal cancer (CRC) screening with a three-tier fecal occult blood test (FOBT) in the Chinese population. The study was performed between 1987 and 2008 at the Beijing Military General Hospital, in a cohort of army service males and females aged >50 years. Between 1987 and 2005, a three-tier screening program, comprising guaiac-based FOBTs (gFOBTs), followed by immunochemical FOBTs for positive guaiac test samples and then colonoscopy for positive immunochemical test subjects, was performed annually. The cohort was followed up until 2008. The cohort included 5,104 subjects, of which, 3,863 subjects participated in screening (screening group) and 1,241 did not (non-screening group). The two groups did not differ in age, gender or other major risk factors for colon cancer. Overall, 36 CRCs occurred in the screening group and 21 in the non-screening group. Compared with the non-screening group, the relative risk for the incidence and mortality of CRC was 0.51 [95% confidence interval (CI), 0.30-0.87] and 0.36 (95% CI, 0.18-0.71), respectively, in the screening group. The general sensitivity of this three-tier FOBT was 80.6% (95% CI, 65.3-91.1). Thus, annual screening using the three-tier FOBT program may reduce the CRC incidence and mortality rate