A table of short-period Tausworthe generators for Markov chain quasi-Monte Carlo

Estimating the number of zero-one multi-way tables via sequential importance sampling

In 2005, Chen et al introduced a sequential importance sampling (SIS) procedure to analyze zero-one two-way tables with given fixed marginal sums (row and column sums) via the conditional Poisson (CP) distribution. They showed that compared with Monte Carlo Markov chain (MCMC)-based approaches, their importance sampling method is more efficient in terms of running time and also provides an easy and accurate estimate of the total number of contingency tables with fixed marginal sums. In this paper we extend their result to zero-one multi-way ($d$-way, $d \geq 2$) contingency tables under the no…

State-Dependent Kernel Selection for Conditional Sampling of Graphs

This paper introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and sampling conditional on vertex strengths in weighted graphs. The algorithms can sample conditional on the presence or absence of an arbitrary number of edges. The resulting conditional distributions provide the basis for exact tests. Existing samplers based on MCMC or sequential importance sampling are generally not scalable; their efficiency degrades in sparse graphs. MCMC methods usually require explicit computation of a Markov basis to navigate the complex state …

Minimal Markov basis for tests of main effect models for $2^{p-1}$ fractional factorial designs of resolution $p$

We consider conditional exact tests of factor effects in designed experiments for discrete response variables. Similarly to the analysis of contingency tables, Markov chain Monte Carlo methods can be used for performing exact tests, especially when large-sample approximations of the null distributions are poor and the enumeration of the conditional sample space is infeasible. To construct a connected Markov chain over the appropriate sample space, a common approach is to compute a Markov basis. Theoretically, a Markov basis can be characterized as a generator of a well-specified toric ideal in…

谁会害怕沃伦纽斯分布？

Who's Afraid of the Wallenius Distribution?

本文探讨沃伦纽斯非中心超几何分布在固定边际列联表分析中的应用，提出似然与贝叶斯推断方法，通过实例验证，简化2×2表分析并解决多组表数值挑战，还构建球面行走Metropolis算法。

Dynamic Markov Bases

We present a computational approach for generating Markov bases for multi-way contingency tables whose cells counts might be constrained by fixed marginals and by lower and upper bounds. Our framework includes tables with structural zeros as a particular case. In- stead of computing the entire Markov basis in an initial step, our framework finds sets of local moves that connect each table in the reference set with a set of neighbor tables. We construct a Markov chain on the reference set of tables that requires only a set of local moves at each iteration. The union of these sets of local moves…

Recursive Monte Carlo and Variational Inference with Auxiliary Variables

A key design constraint when implementing Monte Carlo and variational inference algorithms is that it must be possible to cheaply and exactly evaluate the marginal densities of proposal distributions and variational families. This takes many interesting proposals off the table, such as those based on involved simulations or stochastic optimization. This paper broadens the design space, by presenting a framework for applying Monte Carlo and variational inference algorithms when proposal densities cannot be exactly evaluated. Our framework, recursive auxiliary-variable inference (RAVI), instead …

Exact tests to compare contingency tables under quasi-independence and quasi-symmetry

In this work we define log-linear models to compare several square contingency tables under the quasi-independence or the quasi-symmetry model, and the relevant Markov bases are theoretically characterized. Through Markov bases, an exact test to evaluate if two or more tables fit a common model is introduced. Two real-data examples illustrate the use of these models in different fields of applications.

稀疏列联表统计显著性检验中的SAT抽样

SAT-sampling for statistical significance testing in sparse contingency tables

本文提出基于SAT的列联表条件检验抽样方法，将纤维编码为布尔电路，并结合混合MCMC方案，在稀疏及结构零场景下提供可靠的条件p值，优于传统马尔可夫基方法。

A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting

This paper explores and develops alternative statistical representations and estimation approaches for dynamic mortality models. The framework we adopt is to reinterpret popular mortality models such as the Lee-Carter class of models in a general state-space modelling methodology, which allows modelling, estimation and forecasting of mortality under a unified framework. Furthermore, we propose an alternative class of model identification constraints which is more suited to statistical inference in filtering and parameter estimation settings based on maximization of the marginalized likelihood …