Efficient Bayesian inference for COM-Poisson regression models

Chanialidis, Charalampos; Evers, Ludger; Neocleous, Tereza; Nobile, Agostino

doi:10.1007/s11222-017-9750-x

Cited by 35 publications

(55 citation statements)

References 15 publications

(18 reference statements)

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“…Notably, much work has been done on fitting data with the COM-Poisson distribution using likelihood, Bayesian, and other techniques [22,25]. While the COM-Poisson distribution has many appealing properties, one problem with it for the application of modeling ionization statistics is that the distribution parameters λ and ν do not correspond to the mean, variance, or Fano factor, or indeed to anything with physical meaning.…”

Section: The Com-poisson Distributionmentioning

confidence: 99%

Novel approach to assess the impact of the Fano factor on the sensitivity of low-mass dark matter experiments

Durnford¹,

Arnaud²,

Gerbier³

2018

Phys. Rev. D

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As first suggested by U. Fano in the 1940s, the statistical fluctuation of the number of pairs produced in an ionizing interaction is known to be sub-Poissonian. The dispersion is reduced by the so-called "Fano factor," which empirically encapsulates the correlations in the process of ionization. In modeling the energy response of an ionization measurement device, the effect of the Fano factor is commonly folded into the overall energy resolution. While such an approximate treatment is appropriate when a significant number of ionization pairs are expected to be produced, the Fano factor needs to be accounted for directly at the level of pair creation when only a few are expected. To do so, one needs a discrete probability distribution of the number of pairs created N with independent control of both the expectation µ and Fano factor F . Although no distribution P (N |µ, F ) with this convenient form exists, we propose the use of the COM-Poisson distribution together with strategies for utilizing it to effectively fulfill this need. We then use this distribution to assess the impact that the Fano factor may have on the sensitivity of low-mass WIMP search experiments.

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Section: The Com-poisson Distributionmentioning

confidence: 99%

Novel approach to assess the impact of the Fano factor on the sensitivity of low-mass dark matter experiments

Durnford¹,

Arnaud²,

Gerbier³

2018

Phys. Rev. D

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show abstract

“…We base our models on Poisson distributions, as they are widely-applied to modelling the trial-to-trial distribution of the number of spikes generated by a neuron ( Dayan and Abbott, 2005 ; Macke et al, 2011a ). We will also generalize our Poisson models with Conway-Maxwell (CoM) Poisson distributions, because they can capture the broad range of Fano factors (FF; the variance divided by the mean) observed in cortex, in contrast with Poisson distributions for which the FF is always 1 ( Sur et al, 2015 ; Stevenson, 2016 ; Chanialidis et al, 2018 ).…”

Section: Resultsmentioning

confidence: 99%

Modelling the neural code in large populations of correlated neurons

Sokoloski

Aschner

Coen-Cagli

2020

Preprint

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The activity of a neural population encodes information about the stimulus that caused it, and decoding population activity reveals how neural circuits process that information. Correlations between neurons strongly impact both encoding and decoding, yet we still lack models that simultaneously capture stimulus encoding by large populations of correlated neurons and allow for accurate decoding of stimulus information, thus limiting our quantitative understanding of the neural code. To address this, we propose a class of models of large-scale population activity based on the theory of exponential family distributions. We apply our models to macaque primary visual cortex (V1) recordings, and show they capture a wide range of response statistics, facilitate accurate Bayesian decoding, and provide interpretable representations of fundamental properties of the neural code. Ultimately, our framework could allow researchers to quantitatively validate predictions of theories of neural coding against both large-scale response recordings and cognitive performance.

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“…However, such extensions of the RPCM can already be estimated (e.g., Muth en, Muth en, & Asparouhov, 2017;Wedel, B€ ockenholt, & Kamakura, 2003). Finally, Bayesian estimation for a mode reparametrization of the CMP distribution is available (Chanialidis, Evers, Neocleous, & Nobile, 2018;Guikema & Goffelt, 2008). Under certain conditions the mode in this regression model is pretty close to the mean of the distribution, and approximate formulas to calculate the mean from estimated model parameters exist, but the direct interpretation of the estimated parameters is clearly less straightforward as compared to the mean parametrization (Huang, 2017).…”

Section: Discussionmentioning

confidence: 99%

Revisiting dispersion in count data item response theory models: The Conway–Maxwell–Poisson counts model

Forthmann

Gühne

Doebler

2019

Brit J Math & Statis

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Count data naturally arise in several areas of cognitive ability testing, such as processing speed, memory, verbal fluency, and divergent thinking. Contemporary count data item response theory models, however, are not flexible enough, especially to account for overand underdispersion at the same time. For example, the Rasch Poisson counts model (RPCM) assumes equidispersion (conditional mean and variance coincide) which is often violated in empirical data. This work introduces the Conway-Maxwell-Poisson counts model (CMPCM) that can handle underdispersion (variance lower than the mean), equidispersion, and overdispersion (variance larger than the mean) in general and specifically at the item level. A simulation study revealed satisfactory parameter recovery at moderate sample sizes and mostly unbiased standard errors for the proposed estimation approach. In addition, plausible empirical reliability estimates resulted, while those based on the RPCM were biased downwards (underdispersion) and biased upwards (overdispersion) when the simulation model deviated from equidispersion. Finally, verbal fluency data were analysed and the CMPCM with item-specific dispersion parameters fitted the data best. Dispersion parameter estimates indicated underdispersion for three out of four items. Overall, these findings indicate the feasibility and importance of the suggested flexible count data modelling approach.

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Efficient Bayesian inference for COM-Poisson regression models

Cited by 35 publications

References 15 publications

Novel approach to assess the impact of the Fano factor on the sensitivity of low-mass dark matter experiments

Novel approach to assess the impact of the Fano factor on the sensitivity of low-mass dark matter experiments

Modelling the neural code in large populations of correlated neurons

Revisiting dispersion in count data item response theory models: The Conway–Maxwell–Poisson counts model

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