In this article we propose a novel MCMC method based on deterministic transformations T : X ×D → X where X is the state-space and D is some set which may or may not be a subset of X . We refer to our new methodology as Transformation-based Markov chain Monte Carlo (TMCMC). One of the remarkable advantages of our proposal is that even if the underlying target distribution is very high-dimensional, deterministic transformation of a one-dimensional random variable is sufficient to generate an appropriate Markov chain that is guaranteed to converge to the high-dimensional target distribution. Apart from clearly leading to massive computational savings, this idea of deterministically transforming a single random variable very generally leads to excellent acceptance rates, even though all the random variables associated with the high-dimensional target distribution are updated in a single block. Since it is well-known that joint updating of many random variables using Metropolis-Hastings (MH) algorithm generally leads to poor acceptance rates, TMCMC, in this regard, seems to provide a significant advance. We validate our proposal theoretically, establishing the convergence properties. Furthermore, we show that TMCMC can be very effectively adopted for simulating from doubly intractable distributions.We show that TMCMC includes hybrid Monte Carlo (HMC) as a special case. We also contrast TMCMC with the generalized Gibbs and Metropolis methods of Liu and Yu (1999), Liu and Sabatti (2000) and Kou et al. (2005), pointing out that even though the latter also use transformations, their goal is to seek improvement of the standard Gibbs and Metropolis Hastings algorithms by adding a transformation-based step, while TMCMC is an altogether new and general methodology for simulating from intractable, particularly, high-dimensional distributions.TMCMC is compared with MH using the well-known Challenger data, demonstrating the effectiveness of of the former in the case of highly correlated variables. Moreover, we apply our methodology to a challenging posterior simulation problem associated with the geostatistical model of Diggle * Corresponding et al. (1998), updating 160 unknown parameters jointly, using a deterministic transformation of a one-dimensional random variable. Remarkable computational savings as well as good convergence properties and acceptance rates are the results.

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We consider sparse spatial mixed linear models, particularly those described by Besag and Higdon, and develop an h-likelihood method for their statistical inference.The method proposed allows for singular precision matrices, as it produces estimates that coincide with those from the residual maximum likelihood based on appropriate differencing of the data and has a novel approach to estimating precision parameters by a gamma linear model. Furthermore, we generalize the h-likelihood method to include continuum spatial variations by making explicit use of scaling limit connections between Gaussian intrinsic Markov random fields on regular arrays and the de Wijs process. Keeping various applications of spatial mixed linear models in mind, we devise a novel sparse conjugate gradient algorithm that allows us to achieve fast matrix-free statistical computations. We provide two applications. The first is an extensive analysis of an agricultural variety trial that brings forward various new aspects of nearest neighbour adjustment such as effects on statistical analyses to changes of scale and use of implicit continuum spatial formulation. The second application concerns an analysis of a large cotton field which gives a focus to matrix-free computations. The paper closes with some further considerations, such as applications to irregularly spaced data, use of the parametric bootstrap and some generalizations to the Gaussian Matérn mixed effect models.

Prion diseases are transmissible spongiform encephalopathies (TSEs) characterized by fatal, progressive neurologic diseases with prolonged incubation periods and an accumulation of infectious misfolded prion proteins. Antemortem diagnosis is often difficult due to a long asymptomatic incubation period, differences in the pathogenesis of different prions, and the presence of very low levels of infectious prion in easily accessible samples. Chronic wasting disease (CWD) is a TSE affecting both wild and captive populations of cervids, including mule deer, white-tailed deer, elk, moose, muntjac, and most recently, wild reindeer. This study represents a well-controlled evaluation of a newly developed real-time quaking-induced conversion (RT-QuIC) assay as a potential CWD diagnostic screening test using rectal biopsy sections from a depopulated elk herd. We evaluated 69 blinded samples of recto-anal mucosa-associated lymphoid tissue (RAMALT) obtained from USDA Veterinary Services. The results were later un-blinded and statistically compared to immunohistochemical (IHC) results from the USDA National Veterinary Services Laboratories (NVSL) for RAMALT, obex, and medial retropharyngeal lymph node (MRPLN). Comparison of RAMALT RT-QuIC assay results with the IHC results of RAMALT revealed 92% relative sensitivity (95% confidence limits: 61.52-99.8%) and 95% relative specificity (95% confidence limits: 85.13-99%). Collectively, our results show a potential utility of the RT-QuIC assay to advance the development of a rapid, sensitive, and specific prion diagnostic assay for CWD prions.

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Most farrowing facilities in the United States use stalls and heat lamps to improve sow and piglet productivity. This study investigated these factors by comparing production outcomes for three different farrowing stall layouts (traditional, expanded creep area, expanded sow area) and use of one or two heat lamps. Data were collected on 427 sows and their litters over one year. Results showed no statistical differences due to experimental treatment for any of the production metrics recorded, excluding percent stillborn. Parity one sows had fewer piglets born alive (p < 0.001), lower percent mortality (p = 0.001) and over-lay (p = 0.003), and a greater number of piglets weaned (p < 0.001) with lower average daily weight gain (ADG) (p < 0.001) and more uniform litters (p = 0.001) as compared to higher parity sows. Farrowing turn, associated with group/seasonal changes, had a significant impact on most of the production metrics measured. Number of piglets born influenced the percent stillborn (p < 0.001). Adjusted litter size had a significant impact on percent mortality (p < 0.001), percent over-lay (p < 0.001), and number of piglets weaned (p < 0.001). As the number of piglets weaned per litter increased, both piglet ADG and litter uniformity decreased (p < 0.001). This information can be used to guide producers in farrowing facility design.

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