Optimal scaling of Metropolis algorithms: Heading toward general target distributions

The authors provide an overview of optimal scaling results for the Metropolis algorithm with Gaussian proposal distribution. They address in more depth the case of high‐dimensional target distributions formed of independent, but not identically distributed components. They attempt to give an intuitive explanation as to why the well‐known optimal acceptance rate of 0.234 is not always suitable. They show how to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimes necessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple example.     

Refined Inference on Long Memory in Realized Volatility

There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et al., 2001; Martens et al., 2004). The present article provides some illustrative analysis of how long memory may arise from the accumulative process underlying realized volatility. The article also uses results in Lieberman and Phillips (2004, 2005) to refine statistical inference about d by higher order theory. Standard asymptotic theory has an O(n^-1/2) error rate for error rejection probabilities, and the theory used here refines the approximation to an error rate of o(n^-1/2). The new formula is independent of unknown parameters, is simple to calculate and user-friendly. The method is applied to test whether the reported long memory parameter estimates of Andersen et al. (2001) and Martens et al. (2004) differ significantly from the lower boundary (d = 0.5) of nonstationary long memory, and generally confirms earlier findings.     

Bayesian inference for a discretely observed stochastic kinetic model

The ability to infer parameters of gene regulatory networks is emerging as a key problem in systems biology. The biochemical data are intrinsically stochastic and tend to be observed by means of discrete-time sampling systems, which are often limited in their completeness. In this paper we explore how to make Bayesian inference for the kinetic rate constants of regulatory networks, using the stochastic kinetic Lotka-Volterra system as a model. This simple model describes behaviour typical of many biochemical networks which exhibit auto-regulatory behaviour. Various MCMC algorithms are described and their performance evaluated in several data-poor scenarios. An algorithm based on an approximating process is shown to be particularly efficient.     

A new mixture model for capture heterogeneity

Summary.  We propose a mixture of binomial and beta–binomial distributions for estimating the size of closed populations. The new mixture model is applied to several real capture–recapture data sets and is shown to provide a convenient, objective framework for model selection. The new model is compared with three alternative models in a simulation study, and the results shed light on the general performance of models in this area. The new model provides a robust flexible analysis, which automatically deals with small capture probabilities.     

A semi-parametric approach to robust parameter design

Parameter design or robust parameter design (RPD) is an engineering methodology intended as a cost-effective approach for improving the quality of products and processes. The goal of parameter design is to choose the levels of the control variables that optimize a defined quality characteristic. An essential component of RPD involves the assumption of well estimated models for the process mean and variance. Traditionally, the modeling of the mean and variance has been done parametrically. It is often the case, particularly when modeling the variance, that nonparametric techniques are more appropriate due to the nature of the curvature in the underlying function. Most response surface experiments involve sparse data. In sparse data situations with unusual curvature in the underlying function, nonparametric techniques often result in estimates with problematic variation whereas their parametric counterparts may result in estimates with problematic bias. We propose the use of semi-parametric modeling within the robust design setting, combining parametric and nonparametric functions to improve the quality of both mean and variance model estimation. The proposed method will be illustrated with an example and simulations.     

D-efficient window experimental designs

In the paper we present a new method of calculating sampling intervals, so-called windows, allowing an experimenter some flexibility in timing the sample collection, while a minimum required design efficiency for parameter estimation is assured. The method is based on the Equivalence Theorem for D-optimality what makes the length of each window related to the parameter sensitivities. An example of calculating the windows in a pharmacokinetic study is presented. Some other methods of calculating efficient sampling windows are briefly discussed.     

Correlates of infant pointing frequency in the first year

This study examines the emergence of concurrent correlates of infant pointing frequency with the aim of contributing to its ontogenetic theories. We measured monthly from 8 to 12 months infants' (N = 56) index-finger pointing frequency along with several candidate correlates: (1) family socioeconomic status (SES), (2) mothers' pointing production, and (3) infants' point following to targets in front of and behind them. Results revealed that (1) infants increased their pointing frequency across age, but high-SES infants had a steeper increase, and a higher pointing frequency than low-SES infants from 10 months onward, (2) maternal pointing frequency was not associated with infant pointing frequency at any age, (3) infants' point following abilities to targets behind their visual fields was positively associated with their pointing frequency at 12 months, after pointing had already emerged around 10 months. Findings suggest that family SES impacts infants' pointing development more generally, not just through maternal pointing. The association between pointing and following points to targets behind, but not in front, suggests that a higher level of referential understanding emerges after, and perhaps through the production of pointing.     

Caseworkers as a source of hope leading to perceptions of academic success for transitional age foster youth

Research among adolescent samples has consistently demonstrated that a hopeful mindset is associated with resilience and global well-being. Further, research suggests that hope is influenced from an early age from connections with supportive caregivers. However, because older youth in the child welfare system may lack supportive caregivers, alternative sources of hope may be needed. To test a theory that supportive child welfare caseworkers can serve as external sources of hope, we conducted a cross-sectional study of youth in the child welfare system from a single state (N = 149). Using surveys with established scales to measure the variables of interest, the study tested a structural equation model of (1) youth's external hope in their caseworker as a driver of (2) internal hope in themselves leading to (3) more positive perceptions of academic success. Perceptions of academic success were chosen as the final consequence of the model because academic success has been linked to many other variables of well-being across the lifespan. The results indicate that the proposed structural model fits the data well (χ² = 327.9, df = 150; P < 0.001; root-mean-square error of approximation [RMSEA] = 0.09 [90% confidence interval – CI: 0.076, 0.103]; comparative fit index [CFI]: 0.920; standardized root-mean-square residual [SRMR]: 0.05). The results indicate that youths' hope in themselves had origins in external hope in the caseworker. Moreover, the final consequence was an increase in perceptions of academic success. Such results have implications by revealing how case management services can positively influence foster youths' hope and thereby influence their academic success.