We study how to sample paths of a random walk up to the first time it crosses a fixed barrier, in the setting where the step sizes are independent and identically distributed with negative mean and have a regularly varying right tail. We introduce a desirable property for a change of measure to be suitable for exact simulation. We study whether the change of measure of Blanchet and Glynn (2008) satisfies this property and show that it does so if and only if the tail index α of the right tail lies in the interval (1, 3/2).

In the aftermath of the global financial crisis, competing measures of the trend in macroeconomic variables such as U.S. real GDP have featured prominently in policy debates. A key question is whether large shocks to macroeconomic variables will have permanent effects—i.e., in econometric terms, do the data contain stochastic trends? Unobserved-components models provide a convenient way to estimate stochastic trends for time series data, with their existence typically motivated by stationarity tests that allow at most a deterministic trend under the null hypothesis. However, given the small sample sizes available for most macroeconomic variables, standard Lagrange multiplier tests of stationarity will perform poorly when the data are highly persistent. To address this problem, we propose the use of a likelihood ratio test of stationarity based directly on the unobserved-components models used in estimation of stochastic trends. We demonstrate that a bootstrap version of this test has far better small-sample properties for empirically relevant data-generating processes than bootstrap versions of the standard Lagrange multiplier tests. An application to U.S. real GDP produces stronger support for the presence of large permanent shocks using the likelihood ratio test than using the standard tests.

Colostral administration practices on dairy farms have significantly improved over the last 15–20 years resulting in prevalence of calves ingesting insufficient colostrum decreasing from 35–40% to 19%. Despite these improvements, the serum immunoglobulin G (IgG) concentration of ≥1000 g/dl and serum total protein (TP) concentrations of ≥5·2 g/dl are considered indicative of adequate transfer of immunity. We hypothesised that the current serum IgG concentrations of ≥1000 mg/dl is too low to indicate adequate transfer of colostral immunity on modern dairies. The objective of this study was to determine the serum IgG and TP concentrations indicating adequate transfer of passive immunity in dairy heifer calves. A cohort study of 1290 heifers from a calf raising facility for 48 dairy farms was performed. Heifers were assigned into strata based on serum IgG and TP concentrations. Mortality events were recorded for the heifers for 4 months. Interval likelihood ratios for mortality were calculated for heifers in each stratum of serum IgG or TP concentrations. Logistic regression to predict probability of mortality events was performed. Estimates of probability of survival were evaluated using survival analysis. Serum strata of ≤1500, 1501–2000 or >2500 were not significant predictors of mortality during the 120 d of rearing. Serum IgG concentration was not a significant predictor of hazard for mortality. In contrast to previous studies, serum IgG and TP concentrations of 2001–2500 mg/dl and 5·8–6·3 g/dl respectively, were considered optimum for indicating adequate passive transfer of colostral immunity in dairy calves based on the likelihood ratios. On dairies with optimum colostral feeding practices, serum IgG and TP concentrations of 2001–2500 mg/dl and 5·8–6·3 g/dl are recommended as endpoints to indicate adequate passive immunity in dairy calves.

Deep vein thrombosis (DVT) with subsequent pulmonary embolus (PE) is frequently fatal if untreated. Athletes may be susceptible to DVT following minor blunt trauma to the popliteal fossa. We report an adult male hockey player with no “classic” risk factors for DVT who presented with a DVT and bilateral PE following minor popliteal blunt trauma. This case report illustrates the utility of likelihood ratios when interpreting the results of diagnostic tests such as Doppler ultrasonography.

Objective: To compare the accuracy of the Rowland Universal Dementia Assessment Scale (RUDAS) and the Folstein Mini-mental State Examination (MMSE) for diagnosis of dementia in a multicultural cohort of elderly persons.

Methods: A total of 129 community-dwelling persons were selected at random from a database of referrals to an aged-care team. Subjects were stratified according to language background and cognitive diagnosis, and matched for age and gender. The RUDAS and the MMSE were administered to each subject in random order. Within several days, a geriatrician assessed each subject for dementia (DSM-IV criteria) and disease severity (Clinical Dementia Rating Scale). All assessments were carried out independent and blind. The geriatrician also administered the Modified Barthel Index and the Lawton Instrumental Activities of Daily Living Scale, and screened all participants for non-cognitive disorders that might affect instrument scores.

Results: The area under the receiver operating characteristic curve (AUC) for the RUDAS [0.92, 95% confidence interval (95%CI) 0.85–0.96] was similar to the AUC for the MMSE (0.91, 95%CI 0.84–0.95). At the published cut-points (RUDAS < 23/30, MMSE < 25/30), the positive and negative likelihood ratios for the RUDAS were 19.4 and 0.2, and for the MMSE 2.1 and 0.14, respectively. The MMSE, but not the RUDAS, scores were influenced by preferred language (p = 0.015), total years of education (p = 0.016) and gender (p = 0.044).

Conclusions: The RUDAS is at least as accurate as the MMSE, and does not appear to be influenced by language, education or gender. The high positive likelihood ratio for the RUDAS makes it particularly useful for ruling-in disease.

Emergency physicians use diagnostic tests extensively, and the ability to order and interpret test results appropriately is a critical skill. An understanding of sensitivity, specificity, predictive values and likelihood ratios, as well as an awareness of the importance of pre-test probability, is essential. The purpose of this article is to explain, in a straightforward and clinically applicable manner, the core concepts related to diagnostic testing.

The problem of discriminating between two Markov chains is considered. It is assumed that the common state space of the chains is finite and all the finite dimensional distributions are mutually absolutely continuous. The Bayes risk is expressed through large deviation probabilities for sums of random variables defined on an auxiliary Markov chain. The proofs are based on a large deviation theorem recently established by Z. Szewczak.

We study convergence in total variation of non-stationary Markov chains in continuous time and apply the results to the image analysis problem of object recognition. The input is a grey-scale or binary image and the desired output is a graphical pattern in continuous space, such as a list of geometric objects or a line drawing. The natural prior models are Markov point processes found in stochastic geometry. We construct well-defined spatial birth-and-death processes that converge weakly to the posterior distribution. A simulated annealing algorithm involving a sequence of spatial birth-and-death processes is developed and shown to converge in total variation to a uniform distribution on the set of posterior mode solutions. The method is demonstrated on a tame example.

Approximate and asymptotic distributional results are obtained for the likelihood ratio test of the hypothesis that a time series is composed from s sinusoidal components, at unknown frequencies, with additive Gaussian white noise, against the hypothesis that there are an additional r sinusoidal components at unknown frequencies. The work extends that of Fisher (1929), and contains a number of simulations illustrating the results.

Let a Poisson process be observed whose output rate is one of two levels given by the state of an unseen Markov process. If one of the levels is 0, a simple formula is given for the best guess of the state at any instant based on the stream of past Poisson events. In other cases bounds are given for the likelihood ratio of the state probabilities given the event stream.