Harris recurrence of Metropolis-within-Gibbs and trans-dimensional Markov chains

A $\phi$-irreducible and aperiodic Markov chain with stationary probability distribution will converge to its stationary distribution from almost all starting points. The property of Harris recurrence allows us to replace ``almost all'' by ``all,'' which is potentially important when running Markov chain Monte Carlo algorithms. Full-dimensional Metropolis--Hastings algorithms are known to be Harris recurrent. In this paper, we consider conditions under which Metropolis-within-Gibbs and trans-dimensional Markov chains are or are not Harris recurrent. We present a simple but natural two-dimensional counter-example showing how Harris recurrence can fail, and also a variety of positive results which guarantee Harris recurrence. We also present some open problems. We close with a discussion of the practical implications for MCMC algorithms.Comment: Published at http://dx.doi.org/10.1214/105051606000000510 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Minimising MCMC variance via diffusion limits, with an application to simulated tempering

We derive new results comparing the asymptotic variance of diffusions by writing them as appropriate limits of discrete-time birth-death chains which themselves satisfy Peskun orderings. We then apply our results to simulated tempering algorithms to establish which choice of inverse temperatures minimises the asymptotic variance of all functionals and thus leads to the most efficient MCMC algorithm.Comment: Published in at http://dx.doi.org/10.1214/12-AAP918 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Standardization of guidelines for patient photograph deidentification

IMPORTANCE: This work was performed to advance patient care by protecting patient anonymity. OBJECTIVES: This study aimed to analyze the current practices used in patient facial photograph deidentification and set forth standardized guidelines for improving patient autonomy that are congruent with medical ethics and Health Insurance Portability and Accountability Act. DESIGN: The anonymization guidelines of 13 respected journals were reviewed for adequacy in accordance to facial recognition literature. Simple statistics were used to compare the usage of the most common concealment techniques in 8 medical journals which may publish the most facial photographs. SETTING: Not applicable. PARTICIPANTS: Not applicable. MAIN OUTCOME MEASURES: Facial photo deidentification guidelines of 13 journals were ascertained. Number and percentage of patient photographs lacking adequate anonymization in 8 journals were determined. RESULTS: Facial image anonymization guidelines varied across journals. When anonymization was attempted, 87% of the images were inadequately concealed. The most common technique used was masking the eyes alone with a black box. CONCLUSIONS: Most journals evaluated lack specific instructions for properly de-identifying facial photographs. The guidelines introduced here stress that both eyebrows and eyes must be concealed to ensure patient privacy. Examples of proper and inadequate photo anonymization techniques are provided. RELEVANCE: Improving patient care by ensuring greater patient anonymity

Adaptive Gibbs samplers and related MCMC methods

We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run by learning as they go in an attempt to optimize the algorithm. We present a cautionary example of how even a simple-seeming adaptive Gibbs sampler may fail to converge. We then present various positive results guaranteeing convergence of adaptive Gibbs samplers under certain conditions.Comment: Published in at http://dx.doi.org/10.1214/11-AAP806 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: substantial text overlap with arXiv:1001.279

Weight-Preserving Simulated Tempering

Simulated tempering is popular method of allowing MCMC algorithms to move between modes of a multimodal target density {\pi}. One problem with simulated tempering for multimodal targets is that the weights of the various modes change for different inverse-temperature values, sometimes dramatically so. In this paper, we provide a fix to overcome this problem, by adjusting the mode weights to be preserved (i.e., constant) over different inverse-temperature settings. We then apply simulated tempering algorithms to multimodal targets using our mode weight correction. We present simulations in which our weight-preserving algorithm mixes between modes much more successfully than traditional tempering algorithms. We also prove a diffusion limit for an version of our algorithm, which shows that under appropriate assumptions, our algorithm mixes in time O(d [log d]^2)

Residual Stress Effects on Fatigue Life via the Stress Intensity Parameter, K

Residual stresses are known to have a significant effect on fatigue crack propagation and thus fatigue life. These effects have generally been quantified through an empirical approach, lending little help in the quantitative prediction of such effects. The weight function method has been used as a quantitative predictor, but its use neglects residual stress redistribution, treating the residual stress as a constant during crack growth. At least three different behaviors contribute to the redistribution of residual stress. First, the residual stress behind the crack tip is reduced to a negligible level as soon as the crack tip passes. Second, the residual stress tends to redistribute away from the crack tip with crack growth, and third, crack growth results in an overall relaxation of residual stress. An alternative method for predicting the effect of a residual stress distribution on fatigue crack growth is herein developed. The stress intensity factor due to residual stress, Kres, is characterized as the change in crack driving force due to the presence of the residual stress. This crack driving force, being the derivative of a potential, is found through superposition of an applied stress and a residual stress, and subsequent manipulation of finite element strain energy and nodal displacement results. Finite element modeling is carried out using a spatial distribution of non-uniform thermal expansion coefficients and a unit temperature load to simulate the desired residual stress. Crack growth is then achieved through use of a node release algorithm which sequentially removes nodal displacement constraint. The complete stress distribution, nodal displacements and internal strain energy are captured for each increment of crack growth, and from this information, knowledge of the stress intensity factor as a function of crack length is derived. Results of the Kres calculations are used in a fatigue crack growth model to predict fatigue lives. The fatigue life model involves step by step analysis of crack growth increment based on knowledge of stress intensity factors resulting from applied and residual stress. The qualitative effects of residual stress predicted by this model agree with documented empirical results which show that compressive residual stress increases fatigue life, while tensile residual stress decreases fatigue life. Two solutions for Kres are possible, depending on the choice of loadcontrol or displacement-control modeling. Use of displacement-control, or fixed displacement loading, minimizes redistribution of residual stress and, under net tensile loading, tends to lead to more conservative fatigue life predictions. Load-control modeling, not having the same displacement constraint, allows more relaxation of the residual stress and tends to provide the more non-conservative life estimates. Three residual stress patterns, two due to welding and one to shot peening, are also investigated. Kres solutions for each residual stress are developed, and fatigue life predictions made. Regression analyses on the parameters defining the residual stress patterns indicate that, within the range specified for these parameters, the residual stress half-width plays a significant role in fatigue life, while the initial stress amplitude may be of less importance. The conclusions reached in this research are as follows: The effect of residual stress on fatigue life can be quantified by the energy methods detailed herein. Weight function methods for predicting fatigue lives fail to account for residual stress redistribution, which can have a significant effect. Knowledge of Kres allows subsequent predictions of fatigue life via a simple superposition of applied and residual stress intensity factors, and enables further investigation of relevant residual stress parameters and their effects. The ability to analytically vary residual stress parameters and quantify their effects on fatigue life could prove to be a significant design aid. Based on these conclusions, it is recommended that further development of the energy methods, as presented here, be pursued

Current Development: How One Faith-Based Organization Uses Satellite Technology to Bridge the Digital Divide

From its founding in 1830, the Church of Jesus Christ of Latter-day Saints has endeavored to fulfill the divine command to Go ye into all the world, and preach the gospel to every creature. Proclaiming the gospel of Jesus Christ throughout the world remains a daunting challenge even in modern times. How does a religious organization preach its doctrine to people of all nations, race, cultures, etc? How does it support its growing membership and provide the necessary training for new members and new leaders? How does it assure that its teachings remain consistent around the world? How does it help people in far off locations feel included in the organization as a whole