arXiv subjects

Tamás Rudas

Publications and source records attributed to Tamás Rudas.

8 recordsLinked to original sources

arXiv2026

On the analysis of sequential designs without a specified number of observations

The paper focuses on sequential experiments whose outcomes, success or failure, can be expressed using a binomial distribution, and in which whether or not a further experiment is made depends on the prior outcomes. Examples include subsequent medical interventions until a target response is achieved. The maximum likelihood estimate of the treatment success probability is the ratio of the number of observed successes and the total number of times the treatment was administered. Despite a prespecified initial sample size, the total number of conducted interventions cannot be determined in advance, and the estimated total number of successes may not be equal to the one observed, so the estimated variance of success probability is not that of a binomial distribution. These results generalize to designs with a tree structure consisting of groups of the experiments with group-specific outcome distributions. The multiplicative models entailed are studied using the tools from algebraic statistics and the theory of relational models. The estimates of success probabilities and their covariance are derived and shown to depend on the structural properties of the relevant exponential family.

stat.ME↗

arXiv2021

The presence of occupational structure in online texts based on word embedding NLP models

Research on social stratification is closely linked to analysing the prestige associated with different occupations. This research focuses on the positions of occupations in the semantic space represented by large amounts of textual data. The results are compared to standard results in social stratification to see whether the classical results are reproduced and if additional insights can be gained into the social positions of occupations. The paper gives an affirmative answer to both questions. The results show fundamental similarity of the occupational structure obtained from text analysis to the structure described by prestige and social distance scales. While our research reinforces many theories and empirical findings of the traditional body of literature on social stratification and, in particular, occupational hierarchy, it pointed to the importance of a factor not discussed in the main line of stratification literature so far: the power and organizational aspect.

cs.CL↗

arXiv2020

Reducing Variance with Sample Allocation Based on Expected Response Rates

Several techniques exist to assess and reduce nonresponse bias, including propensity models, calibration methods, or post-stratification. These approaches can only be applied after the data collection, and assume reliable information regarding unit nonresponse patterns for the entire population. In this paper, we demonstrate that sample allocation taking into account the expected response rates (ERR) have advantages in this context. The performance of ERR allocation is assessed by comparing the variances of estimates obtained those arising from a classical allocation proportional to size (PS) and then applying post-stratification. The main theoretical tool is asymptotic calculations using the delta-method, and these are complemented with extensive simulations. The main finding is that the ERR allocation leads to lower variances than the PS allocation, when the response rates are correctly specified, and also under a wide range of conditions when the response rates can not be correctly specified in advance.

stat.ME↗

arXiv2020

Hierarchical Aitchison-Silvey models for incomplete binary sample spaces

Multivariate sample spaces may be incomplete Cartesian products, when certain combinations of the categories of the variables are not possible. Traditional log-linear models, which generalize independence and conditional independence, do not apply in such cases, as they may associate positive probabilities with the non-existing cells. To describe the association structure in incomplete sample spaces, this paper develops a class of hierarchical multiplicative models which are defined by setting certain non-homogeneous generalized odds ratios equal to one and are named after Aitchison and Silvey who were among the first to consider such ratios. These models are curved exponential families that do not contain an overall effect and, from an algebraic perspective, are non-homogeneous toric ideals. The relationship of this model class with log-linear models and quasi log-linear models is studied in detail in terms of both statistics and algebraic geometry. The existence of maximum likelihood estimates and their properties, as well as the relevant algorithms are also discussed.

stat.ME↗

arXiv2019

Testing the fit of relational models

Relational models generalize log-linear models to arbitrary discrete sample spaces by specifying effects associated with any subsets of their cells. A relational model may include an overall effect, pertaining to every cell after a reparameterization, and in this case, the properties of the maximum likelihood estimates (MLEs) are analogous to those computed under traditional log-linear models, and the goodness-of-fit tests are also the same. If an overall effect is not present in any reparameterization, the properties of the MLEs are considerably different, and the Poisson and multinomial MLEs are not equivalent. In the Poisson case, if the overall effect is not present, the observed total is not always preserved by the MLE, and thus, the likelihood ratio statistic is not identical with twice the Kullback-Leibler divergence. However, as demonstrated, its general form may be obtained from the Bregman divergence. The asymptotic equivalence of the Pearson chi-squared and likelihood ratio statistics holds, but the generality considered here requires extended proofs.

stat.ME↗

arXiv2017

On the role of the overall effect in exponential families

Exponential families of discrete probability distributions when the normalizing constant (or overall effect) is added or removed are compared in this paper. The latter setup, in which the exponential family is curved, is particularly relevant when the sample space is an incomplete Cartesian product or when it is very large, so that the computational burden is significant. The lack or presence of the overall effect has a fundamental impact on the properties of the exponential family. When the overall effect is added, the family becomes the smallest regular exponential family containing the curved one. The procedure is related to the homogenization of an inhomogeneous variety discussed in algebraic geometry, of which a statistical interpretation is given as an augmentation of the sample space. The changes in the kernel basis representation when the overall effect is included or removed are derived. The geometry of maximum likelihood estimates, also allowing zero observed frequencies, is described with and without the overall effect, and various algorithms are compared. The importance of the results is illustrated by an example from cell biology, showing that routinely including the overall effect leads to estimates which are not in the model intended by the researchers.

stat.ME↗

arXiv2015

On the closure of relational models

Relational models for contingency tables are generalizations of log-linear models, allowing effects associated with arbitrary subsets of cells in a possibly incomplete table, and not necessarily containing the overall effect. In this generality, the MLEs under Poisson and multinomial sampling are not always identical. This paper deals with the theory of maximum likelihood estimation in the case when there are observed zeros in the data. A unique MLE to such data is shown to always exist in the set of pointwise limits of sequences of distributions in the original model. This set is equal to the closure of the original model with respect to the Bregman information divergence. The same variant of iterative scaling may be used to compute the MLE in the original model and in its closure.

stat.ME↗

arXiv2011

Relational models for contingency tables

The paper considers general multiplicative models for complete and incomplete contingency tables that generalize log-linear and several other models and are entirely coordinate free. Sufficient conditions of the existence of maximum likelihood estimates under these models are given, and it is shown that the usual equivalence between multinomial and Poisson likelihoods holds if and only if an overall effect is present in the model. If such an effect is not assumed, the model becomes a curved exponential family and a related mixed parameterization is given that relies on non-homogeneous odds ratios. Several examples are presented to illustrate the properties and use of such models.

stat.ME↗