Empirical models of crop–weed competition are integral components of bioeconomic models, which depend on predictions of the impact of weeds on crop yields to make cost-effective weed management recommendations. Selection of the best empirical model for a specific crop–weed system is not straightforward, however. We used information–theoretic criteria to identify the model that best describes barley yield based on data from barley–wild oat competition experiments conducted at three locations in Montana over 2 yr. Each experiment consisted of a complete addition series arranged as a randomized complete block design with three replications. Barley was planted at 0, 0.5, 1, and 2 times the locally recommended seeding rate. Wild oat was planted at target infestation densities of 0, 10, 40, 160, and 400 plants m−2. Twenty-five candidate yield models were used to describe the data from each location and year using maximum likelihood estimation. Based on Akaike's Information Criterion (AIC), a second-order small-sample version of AIC (AICc), and the Bayesian Information Criterion (BIC), most data sets supported yield models with crop density (Dc), weed density (Dw), and the relative time of emergence of the two species (T) as variables, indicating that all variables affected barley yield in most locations. AIC, AICc, and BIC selected identical best models for all but one data set. In contrast, the Information Complexity criterion, ICOMP, generally selected simpler best models with fewer parameters. For data pooled over years and locations, AIC, AICc, and BIC strongly supported a single best model with variables Dc, Dw, T, and a functional form specifying both intraspecific and interspecific competition. ICOMP selected a simpler model with Dc and Dw only, and a functional form specifying interspecific, but no intraspecific, competition. The information–theoretic approach offers a rigorous, objective method for choosing crop yield and yield loss equations for bioeconomic models.

This paper presents a new order selection technique of matrix memory polynomial technique that models the nonlinearities of single-branch and multi-branch transmitters. The new criteria take into account the complexity of the model in addition to its mean-square error in the selection criteria. The quasi-convexity of the proposed criteria was proven in this work. By using this proposed Akaike information criterion (AIC) and Bayesian information criterion (BIC) criteria, the model order selection was cast as a cost minimization problem. To minimize the criteria, modified gradient descent and simulated annealing algorithms were utilized which resulted in a considerable reduction in the number of search iterations. The performances of the criteria were shown by comparing the normalized mean square error (NMSE) of a higher-order model and the optimum model. It has been shown that the NMSE difference is <0.5 dB, but the complexity is much smaller.

Background: The study of mental disorders in the elderly presents substantial challenges due to population heterogeneity, coexistence of different mental disorders, and diagnostic uncertainty. While reliable tools have been developed to collect relevant data, new approaches to study design and analysis are needed. We focus on a new analytic approach.

Methods: Our framework is based on latent class analysis and hidden Markov chains. From repeated measurements of a multivariate disease index, we extract the notion of underlying state of a patient at a time point. The course of the disorder is then a sequence of transitions among states. States and transitions are not observable; however, the probability of being in a state at a time point, and the transition probabilities from one state to another over time can be estimated.

Results: Data from 444 patients with and without diagnosis of delirium and dementia were available from a previous study. The Delirium Index was measured at diagnosis, and at 2 and 6 months from diagnosis. Four latent classes were identified: fairly healthy, moderately ill, clearly sick, and very sick. Dementia and delirium could not be separated on the basis of these data alone. Indeed, as the probability of delirium increased, so did the probability of decline of mental functions. Eight most probable courses were identified, including good and poor stable courses, and courses exhibiting various patterns of improvement.

Conclusion: Latent class analysis and hidden Markov chains offer a promising tool for studying mental disorders in the elderly. Its use may show its full potential as new data become available.

A diverse small mammal fauna inhabits the tropical savannas of Kakadu National Park in northern Australia. A detailed long-term capture–mark–recapture study was conducted to estimate body growth parameters in relation to intrinsic and extrinsic factors that may influence them. Three non-linear growth increment functions were compared to determine which one best represented the general growth patterns of nine small mammal species at Kapalga. The von Bertalanffy growth increment function provided the best fit to a pooled species dataset. Hierarchical mixed-effects models were then used to examine variation in body size asymptote and growth and account for non-independence of observations. Model selection was based on the Kullback–Leibler information theoretic approach. As expected, the body size growth constant was correlated to body mass at Kapalga, and body size sexual dimorphism was evident in most species. Difference in body growth constant was only evident in Isoodon macrourus, where females showed accelerated growth. Three of the four marsupial species exhibited either temporal (annual) and spatial (catchment level) variation in body size asymptote, whereas rodent species showed none. There was no clear influence of other extrinsic factors such as fire treatment, rainfall or habitat on body size asymptote or growth rate constant. Our results suggest that body growth is largely controlled by intrinsic factors for each species such as gender in small mammal species at Kapalga. Change in body size and growth caused by human-induced changes to the landscape from factors such as altered fire regimes is unlikely to be substantial for tropical small mammals in northern Australia.

The paper reviews the formulation of the linked stress release model for large scale seismicity together with aspects of its application. Using data from Taiwan for illustrative purposes, models can be selected and verified using tools that include Akaike's information criterion (AIC), numerical analysis, residual point processes and Monte Carlo simulation.

The Akaike information criterion, AIC, for autoregressive model selection is derived by adopting −2T times the expected predictive density of a future observation of an independent process as a loss function, where T is the length of the observed time series. The conditions under which AIC provides an asymptotically unbiased estimator of the corresponding risk function are derived. When the unbiasedness property fails, the use of AIC is justified heuristically. However, a method for estimating the risk function, which is applicable for all fitted orders, is given. A derivation of the generalized information criterion, AICα, is also given; the loss function used being obtained by a modification of the Kullback-Leibler information measure. Results paralleling those for AIC are also obtained for the AICα criterion.

This paper presents a review of recent results for the identification of ARMA processes according to the principles introduced by Akaike, i.e. assuming that the true orders exist and proposing criteria such as AIC and BIC. The development both of these methods and of consistency theory has been led by E. J. Hannan.

This paper is in three parts. The first deals with the algebraic and topological structure of spaces of rational transfer function linear systems—ARMAX systems, as they have been called. This structure theory is dominated by the concept of a space of systems of order, or McMillan degree, n, because of the fact that this space, M(n), can be realised as a kind of high-dimensional algebraic surface of dimension n(2s + m) where s and m are the numbers of outputs and inputs. In principle, therefore, the fitting of a rational transfer model to data can be considered as the problem of determining n and then the appropriate element of M(n). However, the fact that M(n) appears to need a large number of coordinate neighbourhoods to cover it complicates the task. The problems associated with this program, as well as theory necessary for the analysis of algorithms to carry out aspects of the program, are also discussed in this first part of the paper, Sections 1 and 2.

The second part, Sections 3 and 4, deals with algorithms to carry out the fitting of a model and exhibits these algorithms through simulations and the analysis of real data.

The third part of the paper discusses the asymptotic properties of the algorithm. These properties depend on uniform rates of convergence being established for covariances up to some lag increasing indefinitely with the length of record, T. The necessary limit theorems and the analysis of the algorithms are given in Section 5. Many of these results are of interest independent of the algorithms being studied.

The asymptotic behavior of the maximum likelihood estimators of Markov models or autoregressive models are given when the true distribution is not a member of the assumed parametric family. The derivation of Akaike's Information Criterion is reviewed for this case.