SpatialDE2: Fast and localized variance component analysis of spatial transcriptomics

Spatial transcriptomics is now a mature technology, allowing to assay gene expression changes in the histological context of complex tissues. A canonical analysis workflow starts with the identification of tissue zones that share similar expression profiles, followed by the detection of highly variable or spatially variable genes. Rapid increases in the scale and complexity of spatial transcriptomic datasets demand that these analysis steps are conducted in a consistent and integrated manner, a requirement that is not met by current methods. To address this, we here present SpatialDE2, which unifies the mapping of tissue zones and spatial variable gene detection as integrated software framework, while at the same time advancing current algorithms for both of these steps. Formulated in a Bayesian framework, the model accounts for the Poisson count noise, while simultaneously offering superior computational speed compared to previous methods. We validate SpatialDE2 using simulated data and illustrate its utility in the context of two real-world applications to the spatial transcriptomics profiles of the mouse brain and human endometrium.

Monte Carlo Simulation of the Moments of a Copula-Dependent Risk Process with Weibull Interwaiting Time

The widely used Poisson count process in insurance claims modeling is no longer valid if the claims occurrences exhibit dispersion. In this paper, we consider the aggregate discounted claims of an insurance risk portfolio under Weibull counting process to allow for dispersed datasets. A copula is used to define the dependence structure between the interwaiting time and its subsequent claims amount. We use a Monte Carlo simulation to compute the higher-order moments of the risk portfolio, the premiums and the value-at-risk based on the New Zealand catastrophe historical data. The simulation outcomes under the negative dependence parameter θ, shows the highest value of moments when claims experience exhibit overdispersion. Conversely, the underdispersed scenario yields the highest value of moments when θ is positive. These results lead to higher premiums being charged and more capital requirements to be set aside to cope with unfavorable events borne by the insurers.

KR20 and KR21 for Some Nondichotomous Data (It’s Not Just Cronbach’s Alpha)

This article presents some equivalent forms of the common Kuder–Richardson Formula 21 and 20 estimators for nondichotomous data belonging to certain other exponential families, such as Poisson count data, exponential data, or geometric counts of trials until failure. Using the generalized framework of Foster (2020), an equation for the reliability for a subset of the natural exponential family have quadratic variance function is derived for known population parameters, and both formulas are shown to be different plug-in estimators of this quantity. The equivalent Kuder–Richardson Formulas 20 and 21 are given for six different natural exponential families, and these match earlier derivations in the case of binomial and Poisson data. Simulations show performance exceeding that of Cronbach’s alpha in terms of root mean square error when the formula matching the correct exponential family is used, and a discussion of Jensen’s inequality suggests explanations for peculiarities of the bias and standard error of the simulations across the different exponential families.

Reliability of researcher capacity estimates and count data dispersion: a comparison of Poisson, negative binomial, and Conway-Maxwell-Poisson models

Item-response models from the psychometric literature have been proposed for the estimation of researcher capacity. Canonical items that can be incorporated in such models to reflect researcher performance are count data (e.g., number of publications, number of citations). Count data can be modeled by Rasch’s Poisson counts model that assumes equidispersion (i.e., mean and variance must coincide). However, the mean can be larger as compared to the variance (i.e., underdispersion), or b) smaller as compared to the variance (i.e., overdispersion). Ignoring the presence of overdispersion (underdispersion) can cause standard errors to be liberal (conservative), when the Poisson model is used. Indeed, number of publications or number of citations are known to display overdispersion. Underdispersion, however, is far less acknowledged in the literature. In the current investigation the flexible Conway-Maxwell-Poisson count model is used to examine reliability estimates of capacity in relation to various dispersion patterns. It is shown, that reliability of capacity estimates of inventors drops from .84 (Poisson) to .68 (Conway-Maxwell-Poisson) or .69 (negative binomial). Moreover, with some items displaying overdispersion and some items displaying underdispersion, the dispersion pattern in a reanalysis of Mutz and Daniel’s (2018b) researcher data was found to be more complex as compared to previous results. To conclude, a careful examination of competing models including the Conway-Maxwell-Poisson count model should be undertaken prior to any evaluation and interpretation of capacity reliability. Moreover, this work shows that count data psychometric models are well suited for decisions with a focus on top researchers, because conditional reliability estimates (i.e., reliability depending on the level of capacity) were highest for the best researchers.

KR-20 and KR-21 for some non-dichotomous data (It's not just Cronbach's alpha)

This paper presents some equivalent forms of the common Kuder-Richardson Formula 21 and 20 estimators for non-dichotomous data belonging to certain other exponential families, such as Poisson count data, exponential data, or geometric counts of trials until failure. Using the generalized framework of Foster (2020), an equation for the reliability for a subset of the natural exponential family have quadratic variance function is derived for known population parameters, and both formulas are shown to be different plug-in estimators of this quantity. The equivalent Kuder-Richards formulas 20 and 21 are given for six different natural exponential families, and these match earlier derivations in the case of binomial and Poisson data. Simulations show performance exceeding that of Cronbach's alpha in terms of root mean squared error when the formula matching the correct exponential family is used, and a discussion of Jensen's inequality suggests explanations for peculiarities of the bias and standard error of the simulations across the different exponential families.