Driving Markov chain Monte Carlo with a dependent random stream

Markov chain Monte Carlo is a widely-used technique for generating a dependent sequence of samples from complex distributions. Conventionally, these methods require a source of independent random variates. Most implementations use pseudo-random numbers instead because generating true independent variates with a physical system is not straightforward. In this paper we show how to modify some commonly used Markov chains to use a dependent stream of random numbers in place of independent uniform variates. The resulting Markov chains have the correct invariant distribution without requiring detailed knowledge of the stream's dependencies or even its marginal distribution. As a side-effect, sometimes far fewer random numbers are required to obtain accurate results.Comment: 16 pages, 4 figure

Ice formation on a smooth or rough cold surface due to the impact of a supercooled water droplet

Ice accretion is considered in the impact of a supercooled water droplet on a smooth or rough solid surface, the roughness accounting for earlier icing. In this theoretical investigation the emphasis and novelty lie in the full nonlinear interplay of the droplet motion and the growth of the ice surface being addressed for relatively small times, over a realistic range of Reynolds numbers, Froude numbers, Weber numbers, Stefan numbers and capillary underheating parameters. The Prandtl number and the kinetic under-heating parameter are taken to be order unity. The ice accretion brings inner layers into play forcibly, affecting the outer flow. (The work includes viscous effects in an isothermal impact without phase change, as a special case, and the differences between impact with and without freezing.) There are four main findings. First, the icing dynamically can accelerate or decelerate the spreading of the droplet whereas roughness on its own tends to decelerate spreading. The interaction between the two and the implications for successive freezings are found to be subtle. Second, a focus on the dominant physical effects reveals a multi-structure within which restricted regions of turbulence are implied. The third main finding is an essentially parabolic shape for a single droplet freezing under certain conditions. Fourth is a connection with a body of experimental and engineering work and with practical findings to the extent that the explicit predictions here for ice-accretion rates are found to agree with the experimental range.

The major transcriptional regulatory protein of herpes simplex virus type 1 includes a protease resistant DNA binding domain

Herpes simplex virus type 1 expresses five immediateearly (IE) polypeptides. In the absence of functional Vmw175 (the product of IE gene 3) activation of transcription of later classes of viral genes and repression of IE gene expression does not occur. The recognition of specific DNA sequences by Vmw175 requires, as determined by sensitivity to mutation, a part of the protein highly conserved in the corresponding proteins of related herpes viruses. However, mutations in other parts of the protein can also disrupt specific DNA binding. This paper shows that the DNA binding domain of Vmw175 can be liberated as a functional unit by digestion with proteinase K. Analysis of mutant Vmw175 proteinsshowed that the proteinase K resistant domain has an amino terminus between amino acid residues 229 and 292, while its carboxy terminus is between residues 495 and 518. Mutations outside this region which affect DNA binding by the intact protein do not eliminate binding of the proteinase K resistant domain. This implies that direct DNA binding by Vmw175 involves a linear subsection of the polypeptide, and that mutations in other parts of the polypeptide which affect DNA binding of the whole protein do so by indirect means

A nonparametric HMM for genetic imputation and coalescent inference

Genetic sequence data are well described by hidden Markov models (HMMs) in which latent states correspond to clusters of similar mutation patterns. Theory from statistical genetics suggests that these HMMs are nonhomogeneous (their transition probabilities vary along the chromosome) and have large support for self transitions. We develop a new nonparametric model of genetic sequence data, based on the hierarchical Dirichlet process, which supports these self transitions and nonhomogeneity. Our model provides a parameterization of the genetic process that is more parsimonious than other more general nonparametric models which have previously been applied to population genetics. We provide truncation-free MCMC inference for our model using a new auxiliary sampling scheme for Bayesian nonparametric HMMs. In a series of experiments on male X chromosome data from the Thousand Genomes Project and also on data simulated from a population bottleneck we show the benefits of our model over the popular finite model fastPHASE, which can itself be seen as a parametric truncation of our model. We find that the number of HMM states found by our model is correlated with the time to the most recent common ancestor in population bottlenecks. This work demonstrates the flexibility of Bayesian nonparametrics applied to large and complex genetic data