Likelihood Functions for State Space Models with Diffuse Initial Conditions

State space models with nonstationary processes and fixed regression effects require a state vector with diffuse initial conditions. Different likelihood functions can be adopted for the estimation of parameters in time series models with diffuse initial conditions. In this paper we consider profile, diffuse and marginal likelihood functions. The marginal likelihood is defined as the likelihood function of a transformation of the data vector. The transformation is not unique. The diffuse likelihood is a marginal likelihood for a specific data transformation that may depend on parameters. Therefore, the diffuse likelihood can not be used generally for parameter estimation. Our newly proposed marginal likelihood function is based on an orthonormal transformation that does not depend on parameters. Likelihood functions for state space models are evaluated using the Kalman filter. The diffuse Kalman filter is specifically designed for computing the diffuse likelihood function. We show that a modification of the diffuse Kalman filter is needed for the evaluation of our proposed marginal likelihood function. Diffuse and marginal likelihood functions have better small sample properties compared to the profile likelihood function for the estimation of parameters in linear time series models. The results in our paper confirm the earlier findings and show that the diffuse likelihood function is not appropriate for a range of state space model specifications

Differences in insect resistance between tomato species endemic to the Galapagos Islands

Background The Galapagos Islands constitute a highly diverse ecosystem and a unique source of variation in the form of endemic species. There are two endemic tomato species, Solanum galapagense and S. cheesmaniae and two introduced tomato species, S. pimpinellifolium and S. lycopersicum. Morphologically the two endemic tomato species of the Galapagos Islands are clearly distinct, but molecular marker analysis shows no clear separation. Tomatoes on the Galapagos are affected by both native and exotic herbivores. Bemisia tabaci is one of the most important introduced insects species that feeds on a wide range of plants. In this article, we address the question whether the differentiation between S. galapagense and S. cheesmaniae may be related to differences in susceptibility towards phloem-feeders and used B. tabaci as a model to evaluate this. Results We have characterized 12 accessions of S. galapagense, 22 of S. cheesmaniae, and one of S. lycopersicum as reference for whitefly resistance using no-choice experiments. Whitefly resistance was found in S. galapagense only and was associated with the presence of relatively high levels of acyl sugars and the presence of glandular trichomes of type I and IV. Genetic fingerprinting using 3316 SNP markers did not show a clear differentiation between the two endemic species. Acyl sugar accumulation as well as the climatic and geographical conditions at the collection sites of the accessions did not follow the morphological species boundaries

VIM-positive Pseudomonas aeruginosa in a large tertiary care hospital: Matched case-control studies and a network analysis

Background: Emergence of multidrug-resistant Pseudomonas aeruginosa is of global concern. We aimed to identify epidemiological relationships, the most common way of transmission, and risk factors for presence of Verona Integron-encoded Metallo-β-lactamase (VIM)-positive P. aeruginosa (VIM-PA). Methods: We conducted a network analysis and matched case-control studies (1:2:2). Controls were hospital-based and matched with cases for ward, day of admission (control group 1 and 2) and time between admission and the identification of VIM-PA (control group 1). The network was visualized using Cytoscape, an