Stationary probability of the identity for the TASEP on a ring

Consider the following Markov chain on permutations of length $n$. At each time step we choose a random position. If the letter at that position is smaller than the letter immediately to the left (cyclically) then these letters swap positions. Otherwise nothing happens, corresponding to a loop in the Markov chain. This is the circular TASEP. We compute the average proportion of time the chain spends at the identity permutation (and, in greater generality, at sorted words). This answers a conjecture by Thomas Lam.Comment: 6 page

The effect of screening on treatment cost: The case of colorectal cancer

This paper presents a medical cost function developed for a screening programme. The medical cost function is a function of advancement both directly and indirectly through survival. We discuss how the medical cost function is affected by screening through a shift in the distribution of cancers according to advancement. We show that screening reduces the treatment cost for cancers diagnosed at the screening, even though the medical cost function not unambiguously increases with stage of advancement. This is the first step in a cost-effectiveness analysis, and even though the results are favourable to the introduction of screening for colorectal cancer as a preventive health measure, total screening costs and health benefits must be evaluated to arrive at a recommendation.treatment cost; stage of advancement; screening; probabilistic sensitivity analysis; bootstrap method

Pecuniary compensation increases the participation rate in screening for colorectal cancer

Typically, the participation rate is below 100 per cent. In this paper pecuniary compensation is used to increase the participation rate. In a postal questionnaire to 5,000 people invited to screening for colorectal cancer, those not participating were asked "would you participate if you were given NOK X in compensation?" The results show that compensation increases participation and that the participation probability systematically varies with travel expenses, income, age, county, native country, marital status, use of health care services, genetic predisposition, expected benefit from the screening, subjective health status, and education. The estimated costs per additional screening are increasingparticipation; willingness-to pay; compensation; costs; binary probit

Optical bistability in one dimensional doped photonic crystals with spontaneously generated coherence

We investigate optical bistability in a multilayer one-dimensional photonic crystal where the central layer is doped with $\Lambda$-type three level atoms. We take into account the influence of spontaneously generated coherence when the lower atomic levels are sufficiently close to each other, in which case Kerr-type nonlinear response of the atoms is enhanced. We calculate the propagation of a probe beam in the defect mode window using numerical nonlinear transfer matrix method. We find that Rabi frequency of a control field acting on the defect layer and the detuning of the probe field from the atomic resonance can be used to control the size and contrast of the hysteresis loop and the threshold of the optical bistability. In particular we find that, at the optimal spontaneously generated coherence, three orders of magnitude lower threshold can be achieved relative to the case without the coherence.Comment: 9 pages, 7 figure

Multivariate Estimation of Poisson Parameters

This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under this loss function, a class of minimax estimators that uniformly dominate the maximum likelihood estimator is derived. Crucially, these methods have the property that for estimating a given component parameter, the full data vector is utilised. Estimators in this class can be fine-tuned to limit shrinkage away from the maximum likelihood estimator, thereby avoiding implausible estimates of the sum of the parameters. Further light is shed on this new class of estimators by showing that it can be derived by Bayesian and empirical Bayesian methods. In particular, we exhibit a generalisation of the Clevenson-Zidek estimator, and prove its admissibility. Moreover, a class of prior distributions for which the Bayes estimators uniformly dominate the maximum likelihood estimator under the new loss function is derived. A section is included involving weighted loss functions, notably also leading to a procedure improving uniformly on the maximum likelihood method in an infinite-dimensional setup. Importantly, some of our methods lead to constructions of new multivariate models for both rate parameters and count observations. Finally, estimators that shrink the usual estimators towards a data based point in the parameter space are derived and compared