arXiv subjects

Elja Arjas

Publications and source records attributed to Elja Arjas.

7 recordsLinked to original sources

arXiv2026

Thermodynamic Formalism of Stochastic Equilibrium Economics

In economics, construction of perfect models in a way that would be comparable to the standards customary in physical sciences is generally not feasible. In particular, the observed value for an economic equilibrium may deviate significantly from its model-based a priori expected value. Mathematically, the a posteriori observed equilibrium may then represent a large deviation in the sense that it falls outside the region of validity of the Central Limit Theorem. With this as the motivating starting point, we propose a new approach to the theory of stochastic economic equilibrium. Drawing on recent developments in probability theory, we argue for the relevance of the theory of large deviations in stochastic equilibrium economics. Thereby the formalism of stochastic equilibrium economics becomes analogous to that of classical statistical mechanics, as the theory of large deviations forms also the mathematical basis of statistical mechanics. In consequence, thermodynamic concepts such as entropy, partition function and canonical probability can be introduced in a natural way to stochastic equilibrium economics. We focus here on the economic analogs of two fundamental principles, the Second Law of Thermodynamics and the Gibbs Conditioning Principle.

math.PR↗

arXiv2023

Is control of type I error rate needed in Bayesian clinical trial designs?

Practical employment of Bayesian trial designs is still rare. Even if accepted in principle, the regulators have commonly required that such designs be calibrated according to an upper bound for the frequentist type I error rate. This represents an internally inconsistent hybrid methodology, where important advantages from following the Bayesian principles are lost. In particular, all preplanned interim looks have an inflating multiplicity effect on type I error rate. To present an alternative approach, we consider the prototype case of a 2-arm superiority trial with dichotomous outcomes. The design is adaptive, using error control based on sequentially updated posterior probabilities, to conclude efficacy of the experimental treatment or futility of the trial. As gatekeepers for a proposed design, the regulators have the main responsibility in determining the parameters of the control of false positives, whereas the trial sponsors and investigators will have a natural role in specifying the criteria for stopping the trial due to futility. It is suggested that the traditional frequentist operating characteristics in the design, type I and type II error rates, be replaced, respectively, by Bayesian criteria called False Discovery Probability (FDP) and False Futility Probability (FFP), both terms corresponding directly to their probability interpretations. Importantly, the sequential error control during the data analysis based on posterior probabilities will satisfy these numerical criteria automatically, without need of preliminary computations before the trial is started. The method contains the option of applying a decision rule for terminating the trial early if the predicted costs from continuing would exceed the corresponding gains.

stat.ME↗

arXiv2021

Adaptive treatment allocation and selection in multi-arm clinical trials: a Bayesian perspective

Clinical trials are an instrument for making informed decisions based on evidence from well-designed experiments. Here we consider adaptive designs mainly from the perspective of multi-arm Phase II clinical trials, in which one or more experimental treatments are compared to a control. Treatment allocation of individual trial participants is assumed to take place according to a fixed block randomization, albeit with an important twist: The performance of each treatment arm is assessed after every measured outcome, in terms of the posterior distribution of a corresponding model parameter. Different treatments arms are then compared to each other, according to pre-defined criteria and using the joint posterior as the basis for such assessment. If a treatment is found to be sufficiently clearly inferior to the currently best candidate, it can be closed off either temporarily or permanently from further participant accrual. The latter possibility provides a method for adaptive treatment selection, including early stopping of the trial. The main development in the paper is in terms of binary outcomes, but some extensions, notably for handling time-to-event data, are discussed as well. The presentation is to a large extent comparative and expository.

stat.ME↗

arXiv2020

Bayesian non-parametric ordinal regression under a monotonicity constraint

Compared to the nominal scale, the ordinal scale for a categorical outcome variable has the property of making a monotonicity assumption for the covariate effects meaningful. This assumption is encoded in the commonly used proportional odds model, but there it is combined with other parametric assumptions such as linearity and additivity. Herein, the considered models are non-parametric and the only condition imposed is that the effects of the covariates on the outcome categories are stochastically monotone according to the ordinal scale. We are not aware of the existence of other comparable multivariable models that would be suitable for inference purposes. We generalize our previously proposed Bayesian monotonic multivariable regression model to ordinal outcomes, and propose an estimation procedure based on reversible jump Markov chain Monte Carlo. The model is based on a marked point process construction, which allows it to approximate arbitrary monotonic regression function shapes, and has a built-in covariate selection property. We study the performance of the proposed approach through extensive simulation studies, and demonstrate its practical application in two real data examples.

stat.ME↗

arXiv2018

A Bayesian Mallows approach to non-transitive pair comparison data: how human are sounds?

We are interested in learning how listeners perceive sounds as having human origins. An experiment was performed with a series of electronically synthesized sounds, and listeners were asked to compare them in pairs. We propose a Bayesian probabilistic method to learn individual preferences from non-transitive pairwise comparison data, as happens when one (or more) individual preferences in the data contradicts what is implied by the others. We build a Bayesian Mallows model in order to handle non-transitive data, with a latent layer of uncertainty which captures the generation of preference misreporting. We then develop a mixture extension of the Mallows model, able to learn individual preferences in a heterogeneous population. The results of our analysis of the musicology experiment are of interest to electroacoustic composers and sound designers, and to the audio industry in general, whose aim is to understand how computer generated sounds can be produced in order to sound more human.

stat.AP↗

arXiv2017

Probabilistic preference learning with the Mallows rank model

Ranking and comparing items is crucial for collecting information about preferences in many areas, from marketing to politics. The Mallows rank model is among the most successful approaches to analyse rank data, but its computational complexity has limited its use to a particular form based on Kendall distance. We develop new computationally tractable methods for Bayesian inference in Mallows models that work with any right-invariant distance. Our method performs inference on the consensus ranking of the items, also when based on partial rankings, such as top-k items or pairwise comparisons. We prove that items that none of the assessors has ranked do not influence the maximum a posteriori consensus ranking, and can therefore be ignored. When assessors are many or heterogeneous, we propose a mixture model for clustering them in homogeneous subgroups, with cluster-specific consensus rankings. We develop approximate stochastic algorithms that allow a fully probabilistic analysis, leading to coherent quantifications of uncertainties. We make probabilistic predictions on the class membership of assessors based on their ranking of just some items, and predict missing individual preferences, as needed in recommendation systems. We test our approach using several experimental and benchmark datasets.

stat.ME↗

arXiv2014

Modelling and analysis of time in-homogeneous recurrent event processes in a heterogeneous population: A case study of HRTs

In this work we present a method for the statistical analysis of continually monitored data arising in a recurrent diseases problem. The model enables individual level inference in the presence of time transience and population heterogeneity. This is achieved by applying Bayesian hierarchical modelling, where marked point processes are used as descriptions of the individual data, with latent variables providing a means of modelling long range dependence and transience over time. In addition to providing a sound probabilistic formulation of a rather complex data set, the proposed method is also successful in prediction of future outcomes. Computational difficulties arising from the analytic intractability of this Bayesian model were solved by implementing the method into the BUGS software and using standard computational facilities. We illustrate this approach by an analysis of a data set on hormone replacement therapies (HRTs). The data contain, in the form of diaries on bleeding patterns maintained by individual patients, detailed information on how they responded to different HRTs. The proposed model is able to capture the essential features of these treatments as well as provide realistic individual level predictions on the future bleeding patterns.

stat.AP↗