Identifiability of a model for discrete frequency distributions with a multidimensional parameter space

Abstract

This paper is concerned with the identifiability of models depending on a multidimensional parameter vector, aimed at fitting a probability distribution to discrete observed data, with a special focus on a recently proposed mixture model. Starting from the necessary and sufficient condition derived by the definition of identifiability, we describe a general method to verify whether a specific model is identifiable or not. This procedure is then applied to investigate the identifiability of a recently proposed mixture model for rating data, Nonlinear CUB, which is an extension of a class of mixture models called CUB (Combination of Uniform and Binomial).\ud Formal proofs and a numerical study show that some sufficient conditions for identifiability of Nonlinear CUB are always satisfied, provided that in the estimation procedure one quantity is fixed at a relatively small value

Efficient qubit phase estimation using adaptive measurements

“…A necessary and sufficient condition for identifiability is that, for any parameters θ 1 , θ 2 ∈ Θ, the set of equations p(i | θ 1 ) = p(i | θ 2 ), i = 1, ..., k admits only one solution in the parametric space Θ [21].…”

Efficient qubit phase estimation using adaptive measurements

“…A sufficient condition for identifiability is that, for any parameters θ 1 , θ 2 ∈ Θ, the equation P (i|θ 1 ) = P (i|θ 2 ) admits only one solution in the parametric space [28] . According to Eq.…”

“…With a modest amount of foresight, it seems fairly natural to expect that if we knew in which interval the parameter 25) and considering θ = 2 and N = 64 probes. Panel (A) shows the likelihood function given by formula (28). Here we have considered g = 1.5 and the number of ones was 32 out of the possible N = 64.…”

“…(25) and considering θ = 2 and N = 64 probes. Panel (A) shows the likelihood function given by formula(28). Here we have considered g = 1.5 and the number of ones was 32 out of the possible N = 64.…”

Ordinal Data Models for No-Opinion Responses in Attitude Survey

“…Extensions and generalizations of this class of models include hierarchical CUB models (Iannario 2012a), CUB models with a shelter effect (Iannario 2012b), generalized CUB models (Iannario and Piccolo 2016c), zero-inflated CUB models (Iannario and Simone 2017), latent class CUB models (Grilli et al 2013), models for rating categories perceived by respondents as unequally spaced (Manisera and Zuccolotto 2014b, 2015a, 2015b, 2017), CUBE models (Iannario 2014, 2015; Piccolo 2015), which allow to capture the overdispersion phenomena, CUB models with varying uncertainty (Gottard, Iannario, and Piccolo 2016), and Combination of Uniform and Preference structures models, replacing the shifted binomial random variable in CUB with classical ordinal response models, as the cumulative and adjacent categories model (Tutz et al 2017). Robustness issues in CUB models are currently being researched using an interesting approach that could also address dk responses when the dk option is not available (Iannario, Monti, and Piccolo 2016).…”