NBC News Scripts
WBAP-TV (Television station : Fort Worth, Tex.)
1954-12-31
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22 records were found.
Nearest neighbors R-positivity Gibbs measures Geometric ergodicity
Weibull distribution upper truncation parameter maximum likelihood estimator spacings
We study duality relations for zeta and M\"{o}bius matrices and monotone conditions on the kernels. We focus on the cases of family of sets and partitions. The conditions for positivity of the dual kernels are stated in terms of the positive M\"{o}bius cone of functions, which is described in terms of Sylvester formulae. We study duality under coarse-graining and show that an $h-$transform is needed to preserve stochasticity. We give conditions in order that zeta and M\"{o}bius matrices admit coarse-graining, and we prove they are satisfied for sets and partitions. This is a source of relevant examples in genetics on the haploid and multi-allelic Cannings models.
Estimating the number $n$ of unseen species from a $k-$sample displaying only $p\leq k$ distinct sampled species has received attention for long. It requires a model of species abundance together with a sampling model. We start with a discrete model of iid stochastic species abundances, each with Gibbs-Poisson distribution. A $k-$sample drawn from the $n-$species abundances vector is the one obtained while conditioning it on summing to $k$% . We discuss the sampling formulae (species occupancy distributions, frequency of frequencies) in this context. We then develop some aspects of the estimation of $n$ problem from the size $k$ of the sample and the observed value of $P_{n,k}$, the number of distinct sampled species. It is shown that it always makes sense to study these occupancy problems from a Gibbs-Poisson abundance model in the co...
We revisit the multi-allelic mutation-fitness balance problem especially when fitnesses are multiplicative. Using ideas arising from quasi-stationary distributions, we analyze the qualitative differences between the fitness-first and mutation-first models, under various schemes of the mutation pattern. We give some stochastic domination relations between the equilibrium states resulting from these models.
We work out some relations between duality and intertwining in the context of discrete Markov chains, fixing up the background of previous relations first established for birth and death chains and their Siegmund duals. In view of the results, the monotone properties resulting from the Siegmund dual of birth and death chains are revisited in some detail, with emphasis on the non neutral Moran model. We also introduce an ultrametric type dual extending the Siegmund kernel. Finally we discuss the sharp dual, following closely the Diaconis-Fill study.
We reconsider the Dirichlet model for the random division of an interval. This model is parameterized by the number $n>1$ of fragments, together with a set of positive parameters $\left( \theta _{1},...,\theta _{n}\right) $. Its main remarkable properties are recalled, developed and illustrated. Explicit results on the statistical structure of its size-biased permutation are next supplied. This distribution appears in the sorting of items problem under the move-to-front rule. Assuming the parameters satisfy $\sum_{m=1}^{n}\theta _{m}\rightarrow \gamma <\infty $ as $n\uparrow \infty $, it is shown that the Dirichlet distribution has a Dirichlet-Kingman non-degenerate weak limit whose properties are briefly outlined.
Motivated by a problem arising in mining industry, we estimate the energy ${\cal E}(\eta)$ which is needed to reduce a unit mass to fragments of size at most $\eta$ in a fragmentation process, when $\eta\to0$. We assume that the energy used by the instantaneous dislocation of a block of size $s$ into a set of fragments $(s_1,s_2,...)$, is $s^\beta \varphi(s_1/s,s_2/s,..)$, where $\varphi$ is some cost-function and $\beta$ a positive parameter. Roughly, our main result shows that if $\alpha>0$ is the Malthusian parameter of an underlying CMJ branching process (in fact $\alpha=1$ when the fragmentation is mass-conservative), then ${\cal E}(\eta)\sim c \eta^{\beta-\alpha}$ whenever $\beta < \alpha$. We also obtain a limit theorem for the empirical distribution of fragments with size less than $\eta$ which result from the process. In the d...
Solid on solid models Entropic repulsion Pinning surfaces Interface Random walks
Markov chain Stochastic comparison Quasistationary measure
