Formalising the multidimensional nature of social networks

Individuals interact with conspecifics in a number of behavioural contexts or dimensions. Here, we formalise this by considering a social network between n individuals interacting in b behavioural dimensions as a nxnxb multidimensional object. In addition, we propose that the topology of this object is driven by individual needs to reduce uncertainty about the outcomes of interactions in one or more dimension. The proposal grounds social network dynamics and evolution in individual selection processes and allows us to define the uncertainty of the social network as the joint entropy of its constituent interaction networks. In support of these propositions we use simulations and natural 'knock-outs' in a free-ranging baboon troop to show (i) that such an object can display a small-world state and (ii) that, as predicted, changes in interactions after social perturbations lead to a more certain social network, in which the outcomes of interactions are easier for members to predict. This new formalisation of social networks provides a framework within which to predict network dynamics and evolution under the assumption that it is driven by individuals seeking to reduce the uncertainty of their social environment.Comment: 16 pages, 4 figure

Book Reviews

Book review

Isotonic Distributional Regression

Distributional regression estimates the probability distribution of a response variable conditional on covariates. The estimated conditional distribution comprehensively summarizes the available information on the response variable, and allows to derive all statistical quantities of interest, such as the conditional mean, threshold exceedance probabilities, or quantiles. This thesis develops isotonic distributional regression, a method for estimating conditional distributions under the assumption of a monotone relationship between covariates and a response variable. The response variable is univariate and real-valued, and the covariates lie in a partially ordered set. The monotone relationship is formulated in terms of stochastic order constraints, that is, the response variable increases in a stochastic sense as the covariates increase in the partial order. This assumption alone yields a shape-constrained non-parametric estimator, which does not involve any tuning parameters. The estimation of distributions under stochastic order restrictions has already been studied for various stochastic orders, but so far only with totally ordered covariates. Apart from considering more general partially ordered covariates, the first main contribution of this thesis lies in a shift of focus from estimation to prediction. Distributional regression is the backbone of probabilistic forecasting, which aims at quantifying the uncertainty about a future quantity of interest comprehensively in the form of probability distributions. When analyzed with respect to predominant criteria for probabilistic forecast quality, isotonic distributional regression is shown to have desirable properties. In addition, this thesis develops an efficient algorithm for the computation of isotonic distributional regression, and proposes an estimator under a weaker, previously not thoroughly studied stochastic order constraint. A main application of isotonic distributional regression is the uncertainty quantification for point forecasts. Such point forecasts sometimes stem from external sources, like physical models or expert surveys, but often they are generated with statistical models. The second contribution of this thesis is the extension of isotonic distributional regression to allow covariates that are point predictions from a regression model, which may be trained on the same data to which isotonic distributional regression is to be applied. This combination yields a so-called distributional index model. Asymptotic consistency is proved under suitable assumptions, and real data applications demonstrate the usefulness of the method. Isotonic distributional regression provides a benchmark in forecasting problems, as it allows to quantify the merits of a specific, tailored model for the application at hand over a generic method which only relies on monotonicity. In such comparisons it is vital to assess the significance of forecast superiority or of forecast misspecification. The third contribution of this thesis is the development of new, safe methods for forecast evaluation, which require no or minimal assumptions on the data generating processes

Antagonistic regulation of parvalbumin expression and mitochondrial calcium handling capacity in renal epithelial cells

Parvalbumin (PV) is a cytosolic Ca²⁺-binding protein acting as a slow-onset Ca²⁺ buffer modulating the shape of Ca²⁺ transients in fast-twitch muscles and a subpopulation of neurons. PV is also expressed in non-excitable cells including distal convoluted tubule (DCT) cells of the kidney, where it might act as an intracellular Ca²⁺ shuttle facilitating transcellular Ca²⁺ resorption. In excitable cells, upregulation of mitochondria in “PV-ergic” cells in PV-/- mice appears to be a general hallmark, evidenced in fast-twitch muscles and cerebellar Purkinje cells. Using Gene Chip Arrays and qRT-PCR, we identified differentially expressed genes in the DCT of PV-/- mice. With a focus on genes implicated in mitochondrial Ca²⁺ transport and membrane potential, uncoupling protein 2 (Ucp2), mitocalcin (Efhd1), mitochondrial calcium uptake 1 (Micu1), mitochondrial calcium uniporter (Mcu), mitochondrial calcium uniporter regulator 1 (Mcur1), cytochrome c oxidase subunit 1 (COX1), and ATP synthase subunit β (Atp5b) were found to be up-upregulated. At the protein level, COX1 was increased by 31 ± 7%, while ATP-synthase subunit β was unchanged. This suggested that these mitochondria were better suited to uphold the electrochemical potential across the mitochondrial membrane, necessary for mitochondrial Ca²⁺ uptake. Ectopic expression of PV in PV-negative Madin-Darby canine kidney (MDCK) cells decreased COX1 and concomitantly mitochondrial volume, while ATP synthase subunit β levels remained unaffected. Suppression of PV by shRNA in PV-expressing MDCK cells led subsequently to an increase in COX1 expression. The collapsing of the mitochondrial membrane potential by the uncoupler CCCP occurred at lower concentrations in PV-expressing MDCK cells than in control cells. In support, a reduction of the relative mitochondrial mass was observed in PV-expressing MDCK cells. Deregulation of the cytoplasmic Ca²⁺ buffer PV in kidney cells was counterbalanced in vivo and in vitro by adjusting the relative mitochondrial volume and modifying the mitochondrial protein composition conceivably to increase their Ca²⁺-buffering/sequestration capacity

Some new inequalities for beta distributions

This note provides some new tail inequalities and exponential inequalities of Hoeffding and Bernstein type for beta distributions

A Rank-Based Sequential Test of Independence

We consider the problem of independence testing for two univariate random variables in a sequential setting. By leveraging recent developments on safe, anytime-valid inference, we propose a test with time-uniform type-I error control and derive explicit bounds on the finite sample performance of the test and the expected stopping time. We demonstrate the empirical performance of the procedure in comparison to existing sequential and non-sequential independence tests. Furthermore, since the proposed test is distribution free under the null hypothesis, we empirically simulate the gap due to Ville's inequality, the supermartingale analogue of Markov's inequality, that is commonly applied to control type I error in anytime-valid inference, and apply this to construct a truncated sequential test

Why Machiavellianism Matters in Childhood: The Relationship Between Children's Machiavellian Traits and Their Peer Interactions in a Natural Setting

The current study investigated the association between Machiavellianism and children’s peer interactions in the playground using observational methods. Primary school children (N = 34; 17 female), aged 9 to 11 years, completed the Kiddie Mach scale and were observed in natural play during 39 recesses (average observed time = 11.70 hours) over a full school year. Correlations for boys revealed that Machiavellianism was related to more time engaging in direct and indirect aggression, being accepted into other peer groups, and accepting peers into their own social group. Correlations revealed that for girls, Machiavellianism was associated with lower levels of indirect aggression, less time being accepted into other groups and less time accepting and rejecting other children into their own group. This preliminary pilot study indicates that Machiavellianism is associated with children’s observed social behaviour and aims to promote future observational research in this area

Valid sequential inference on probability forecast performance

Probability forecasts for binary events play a central role in many applications. Their quality is commonly assessed with proper scoring rules, which assign forecasts a numerical score such that a correct forecast achieves a minimal expected score. In this paper, we construct e-values for testing the statistical significance of score differences of competing forecasts in sequential settings. E-values have been proposed as an alternative to p-values for hypothesis testing, and they can easily be transformed into conservative p-values by taking the multiplicative inverse. The e-values proposed in this article are valid in finite samples without any assumptions on the data generating processes. They also allow optional stopping, so a forecast user may decide to interrupt evaluation taking into account the available data at any time and still draw statistically valid inference, which is generally not true for classical p-value based tests. In a case study on postprocessing of precipitation forecasts, state-of-the-art forecasts dominance tests and e-values lead to the same conclusions