Upcoming volume is Volume 45, Number 2.
It will include the following papers:
|
Asymptotic Behaviour of a BIPF Algorithm with an Improper Target | |
| Claudio Asci and Mauro Piccioni | |
| Abstract: The BIPF algorithm is a Markovian algorithm with the purpose of simulating certain probability distributions supported by contingency tables belonging to hierarchical log-linear models. The updating steps of the algorithm depend only on the required expected marginal tables over the maximal terms of the hierarchical model. Usually these tables are marginals of a positive joint table, in which case it is well known that the algorithm is a blocking Gibbs Sampler. But the algorithm makes sense even when these marginals do not come from a joint table. In this case the target distribution of the algorithm is necessarily improper. In this paper we investigate the simplest non trivial case, i.e. the 2x2x2 hierarchical interaction. Our result is that the algorithm is asymptotically attracted by a limit cycle in law. | |
| Pages: 169-188 | |
|
Hierarchical Models, Marginal Polytopes, and Linear Codes | |
| Thomas Kahle, Walter Wenzel and and Nihat Ay | |
| Abstract: In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. (Via the sufficient statistics, each hierarchical model is mapped to a convex polytope, the marginal polytope. We realize the marginal polytopes as 0/1-polytopes and show that their vertices form a linear code.) The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them. | |
| Pages: 189-208 | |
|
Two Operations of Merging and Splitting Components in a Chain Graph | |
| Milan Studený, Alberto Roverato and Šárka Štěpánová | |
| Abstract: In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example of the use of this operation, we derive some important invariants of LWF Markov equivalence of chain graphs. Last, we recall analogous basic results on the operation of legal merging components. This operation is related to the so-called strong equivalence of chain graphs, which includes both classic LWF equivalence and alternative AMP (Andersson, Madigan and Perlman) Markov equivalence. | |
| Pages: 209-250 | |
|
Markov Bases of Conditional Independence Models for Permutations | |
| Villő Csiszár | |
| Abstract: The L-decomposable and the bi-decomposable models are two families of distributions on the set S_n of all permutations of the first n positive integers. Both of these models are characterized by collections of conditional independence relations. We first compute a Markov basis for the L-decomposable model, then give partial results about the Markov basis of the bi-decomposable model. Using these Markov bases, we show that not all bi-decomposable distributions can be approximated arbitrarily well by strictly positive bi-decomposable distributions. | |
| Pages: 251-262 | |
|
Checking Proportional Rates in the Two-sample Transformation Model | |
| David Kraus | |
| Abstract: Transformation models for two samples of censored data are considered. Main examples are the proportional hazards and proportional odds model. The key assumption of these models is that the ratio of transformation rates (e.g., hazard rates or odds rates) is constant in time. A method of verification of this proportionality assumption is developed. The proposed procedure is based on the idea of Neyman's smooth test and its data-driven version. The method is suitable for detecting monotonic as well as nonmonotonic ratios of rates. | |
| Pages: 263-280 | |
|
Conditions for Bimodality and Multimodality of a Mixture of Two Unimodal Densities | |
| Šárka Došlá | |
| Abstract: Conditions for bimodality of mixtures of two unimodal distributions are investigated in some special cases. Based on general characterizations, explicit criteria for the parameters are derived for mixtures of two Cauchy, logistic, Student, gamma, log-normal, Gumbel and other distributions. | |
| Pages: 281-294 | |
|
On Testing of General Random Closed Set Model Hypothesis | |
| Tomáš Mrkvička | |
| Abstract: A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set Ξ, subset of Rd, with values in the extended convex ring is introduced. The method is based on the summary statistics -- normalized intrinsic volumes densities of the ε-parallel sets to Ξ. The estimated summary statistics are compared with theirs envelopes produced from simulations of the model given by the tested hypothesis. The p-level of the test is then computed via approximation of the summary statistics by multinormal distribution which mean and the correlation matrix is computed via given simulations. A new estimator of the intrinsic volumes densities from [MR06] is used, which is especially suitable for estimation of the intrinsic volumes densities of ε-parallel sets. The power of this test is estimated for planar Boolean model hypothesis and two different alternatives and the resulted powers are compared to the powers of known Boolean model tests. The method is applied on the real data set of a heather incidence. | |
| Pages: 295-310 | |
|
Optimal Sequential Multiple Hypothesis Tests | |
| Andrey Novikov | |
| Abstract: This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized. | |
| Pages: 311-332 | |
|
Stability Estimating in Optimal Sequential Hypotheses Testing | |
| Evgueni Gordienko, Andrey Novikov and Elena Zaitseva | |
| Abstract: We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations $X_1,X_2,\dots$ when testing two simple hypotheses about their common density $f$: $f=f_0$ versus $f=f_1$. As a functional to be minimized, it is used a weighted sum of the average (under $f_0$) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by $X_1,X_2,\dots$ with the density $f_0$. For $\tau_*$ being the corresponding optimal stopping time we consider a situation when this rule is applied for testing between $f_0$ and an alternative $\tilde f_1$, where $\tilde f_1$ is some approximation to $f_1$. An inequality is obtained which gives an upper bound for the expected cost excess, when $\tau_*$ is used instead of the rule $\tilde\tau_*$ optimal for the pair $(f_0,\tilde f_1)$. The inequality found also estimates the difference between the minimal expected costs for optimal tests corresponding to the pairs $(f_0,f_1)$ and $(f_0,\tilde f_1)$. | |
| Pages: 333-346 | |