Modelling Preference Data with the Wallenius Distribution

Grazian, Clara; Leisen, Fabrizio; Liseo, Brunero

doi:10.1111/rssa.12415

Cited by 2 publications

(6 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…from mutually-exclusive categories (Grazian et al, 2018). But this model's exact likelihood contains a computationally-costly integral for each person (Grazian et al, 2018). In this study, we will show that the QIL, as a surrogate to the Wallenius model likelihood, can provide tractable and accurate posterior inferences for the model's choice weight parameters.…”

Section: (Multivariate Non-iid Data)mentioning

confidence: 88%

“…The Bayesian approach to the multivariate Wallenius (noncentral hypergeometric) distribution (Wallenius, 1963;Chesson, 1976) is useful for the analysis of individual choice data, where each person chooses (without replacement) any number of objects from a total set of objects (resp.) from mutually-exclusive categories (Grazian et al, 2018). But this model's exact likelihood contains a computationally-costly integral for each person (Grazian et al, 2018).…”

Section: (Multivariate Non-iid Data)mentioning

confidence: 99%

“…This is done by specifying this QIL to depend on means and variances of the category counts given the Wallenius model parameters. The original Bayesian Wallenius model (Grazian et al, 2018) assumes that the choice parameters are the same for all persons, implying that the choice data observations are iid over persons. The current study introduces a new hierarchical Bayesian Wallenius model which can handle noniid choice data by allowing for the choice weight parameters to vary across persons.…”

Section: (Multivariate Non-iid Data)mentioning

confidence: 99%

“…. , θ c ) ⊺ which are identifiable by the constraints 0 ≤ θ j ≤ 1 and c j=1 θ j = 1 (Grazian et al, 2018), and κ i,j = c j=1 θ j (m j − y i,j ) (Wallenius, 1963;Chesson, 1976). The Wallenius likelihood (3.8) is computationally costly to evaluate when the sample size n is large, due to its n intractable integral terms.…”

Section: Hierarchical Wallenius Model For Multivariate Non-iid Datamentioning

confidence: 99%

“…The Wallenius likelihood (3.8) is computationally costly to evaluate when the sample size n is large, due to its n intractable integral terms. For posterior distribution inference of the Bayesian Wallenius iid model, previous research addressed this problem using an ABC method (Grazian et al, 2018).…”

Section: Hierarchical Wallenius Model For Multivariate Non-iid Datamentioning

confidence: 99%

See 4 more Smart Citations

Bayes Calculations from Quantile Implied Likelihood

Karabatsos,

Leisen

2018

Preprint

Self Cite

View full text Add to dashboard Cite

In statistical practice, a realistic Bayesian model for a given data set can be defined by a likelihood function that is analytically or computationally intractable, due to large data sample size, high parameter dimensionality, or complex likelihood functional form. This in turn poses challenges to the computation and inference of the posterior distribution of the model parameters. For such a model, a tractable likelihood function is introduced which approximates the exact likelihood through its quantile function. It is defined by an asymptotic chi-square confidence distribution for a pivotal quantity, which is generated by the asymptotic normal distribution of the sample quantiles given model parameters. This Quantile Implied Likelihood (QIL) gives rise to an approximate posterior distribution which can be estimated by using penalized log-likelihood maximization or any suitable Monte Carlo algorithm. The QIL approach to Bayesian Computation is illustrated through the Bayesian analysis of simulated and real data sets having sample sizes that reach the millions. The analyses involve various models for univariate or multivariate iid or non-iid data, with low or high parameter dimensionality, many of which are defined by intractable likelihoods. The probability models include the Student's t, g-and-h, and g-and-k distributions; the Bayesian logit regression model with many covariates; exponential random graph model, a doubly-intractable model for networks; the multivariate skew normal model, for robust inference of the inverse-covariance matrix when it is large relative to the sample size; and the Wallenius distribution model.

show abstract

Section: (Multivariate Non-iid Data)mentioning

confidence: 88%

Section: (Multivariate Non-iid Data)mentioning

confidence: 99%

Section: (Multivariate Non-iid Data)mentioning

confidence: 99%

Section: Hierarchical Wallenius Model For Multivariate Non-iid Datamentioning

confidence: 99%

Section: Hierarchical Wallenius Model For Multivariate Non-iid Datamentioning

confidence: 99%

See 3 more Smart Citations

Bayes Calculations from Quantile Implied Likelihood

Karabatsos,

Leisen

2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Fisher's Noncentral Hypergeometric Distribution for Population Size Estimation

Ballerini¹,

Liseo²

2022

Preprint

View full text Add to dashboard Cite

We introduce a method to make inference on the subgroups' sizes of a heterogeneous population using survey data, even in the presence of a single list. To this aim, we use Fisher's noncentral hypergeometric distribution, which allows us to account for the possibility that capture heterogeneity is related to key survey variables. We propose a Bayesian approach for estimating the population sizes posterior distributions, exploiting both extra-experimental information, e.g., coming from administrative data, and the computational efficiency of MCMC and ABC methods. The motivating case study deals with the size estimation of the population of Italian youngsters who are not employed one year after graduating by gender and degree program. We account for the possibility that surveys' response rates differ according to individuals' employment status, implying a not-at-random missing data scenario. We find that employed persons are generally more inclined to answer the questionnaire; this behavior might imply the overestimation of the employment rate.

show abstract

Modelling Preference Data with the Wallenius Distribution

Cited by 2 publications

References 29 publications

Bayes Calculations from Quantile Implied Likelihood

Bayes Calculations from Quantile Implied Likelihood

Fisher's Noncentral Hypergeometric Distribution for Population Size Estimation

Contact Info

Product

Resources

About