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The β-model of random graphs is an exponential family model with the degree sequence as a sufficient statistic. In this paper, we contribute three key results. First, we characterize conditions that lead to a quadratic time algorithm to check for the existence of MLE of the β-model, and show that the MLE never exists for the degree partition β-model. Second, motivated by privacy problems with network data, we derive a differentially private estimator of the parameters of β-model, and show it is consistent and asymptotically normally distributed—it achieves the same rate of convergence as the nonprivate estimator. We present an efficient algorithm for the private estimator that can be used to release synthetic graphs. Our techniques can also be used to release degree distributions and degree partitions accurately and privately, and to perform inference from noisy degrees arising from contexts other than privacy. We evaluate the proposed estimator on real graphs and compare it with a current algorithm for releasing degree distributions and find that it does significantly better. Finally, our paper addresses shortcomings of current approaches to a fundamental problem of how to perform valid statistical inference from data released by privacy mechanisms, and lays a foundational groundwork on how to achieve optimal and private statistical inference in a principled manner by modeling the privacy mechanism; these principles should be applicable to a class of models beyond the β-model.

In this paper, we study sharp thresholds for detecting sparse signals in β-models for potentially sparse random graphs. The results demonstrate interesting interplay between graph sparsity, signal sparsity and signal strength. In regimes of moderately dense signals, irrespective of graph sparsity, the detection thresholds mirror corresponding results in independent Gaussian sequence problems. For sparser signals, extreme graph sparsity implies that all tests are asymptotically powerless, irrespective of the signal strength. On the other hand, sharp detection thresholds are obtained, up to matching constants, on denser graphs. The phase transitions mentioned above are sharp. As a crucial ingredient, we study a version of the higher criticism test which is provably sharp up to optimal constants in the regime of sparse signals. The theoretical results are further verified by numerical simulations.

We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the β-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based on the polytope of degree sequences, for the existence of the maximum likelihood estimator (MLE) of the model parameters. We characterize in a combinatorial fashion sample points leading to a nonexistent MLE, and nonestimability of the probability parameters under a nonexistent MLE. We formulate conditions that guarantee that the MLE exists with probability tending to one as the number of nodes increases.

We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts. We then characterize all possible Markov structures for finitely exchangeable random graphs, thereby identifying a new class of Markov network models corresponding to bidirected Kneser graphs. In particular, we demonstrate that the fundamental property of dissociatedness corresponds to a Markov property for exchangeable networks described by bidirected line graphs. Finally we study those exchangeable models that are also summarized in the sense that the probability of a network depends only on the degree distribution, and we identify a class of models that is dual to the Markov graphs of Frank and Strauss. Particular emphasis is placed on studying consistency properties of network models under the process of forming subnetworks and we show that the only consistent systems of Markov properties correspond to the empty graph, the bidirected line graph of the complete graph and the complete graph.

PurposeThis paper aims to identify the key drivers of occupancy rates in peer-to-peer accommodation.Design/methodology/approachThe applied methodology fits the specific characteristics of this market segment: the peculiar distribution of the occupancy rate (a ratio characterised by a large share of zeros) requires the adoption of a mixed discrete-continuous model; the insidious issue of price endogeneity is dealt with a control function approach; the econometric specification takes into account the monopolistic competition, the relevant market regime in the hospitality industry. The model is tested on Airbnb listings in the Balearic Islands (Spain).FindingsThe occupancy rate of peer-to-peer properties in the Balearic Islands strongly depends on their geographical location and online reputation. There is a qualitative difference between two groups: listings with positive occupancy rates, which demand tends to be inelastic, and listings with zero occupancy. The authors found that the price is a not a statistically significant determinant of the latter group membership.Originality/valueThis paper applies a zero-inflated beta model, never used in previous analyses of occupancy rates, to provide a benchmark for future studies. This procedure allows the estimation of unbiased marginal effects. It, thus, offers important technical and managerial implications, as a wrong understanding of how occupancy depends on price would deliver ineffective managerial decisions. This paper highlights the importance of methodological choices, as coefficients are highly sensitive to misspecifications of the model.

The accurate assessment and management of Blue Mackerel (Scomber australasicus) and Chub Mackerel (Scomber japonicus) resources in the high seas of the Northwest Pacific are constrained by the persistent issue of data misreporting in catch records, which arises from their high morphological similarity. This study integrates fishery logbooks and field sampling data from Chinese purse seine fleets (2014–2023), along with key oceanographic factors—six of which were finally selected after correlation analysis. We introduce, for the first time, a Zero-One Inflated Beta Model (ZOIBM) to analyze the spatiotemporal distribution of the relative abundance of these two mackerel species. Furthermore, a Generalized Additive Model (GAM) was employed to reveal the environmental mechanisms driving their niche differentiation. The results show that the ZOIBM demonstrates excellent performance (R2 = 0.63, RMSE = 0.305), effectively quantifying the proportional composition of the two species in mixed catches. Spatially, high-abundance areas of Blue Mackerel were concentrated within 35–44° N, 145–160° E, with its proportion decreasing at higher latitudes. In contrast, Chub Mackerel exhibited an opposite latitudinal pattern, with its high-abundance areas covering a broader latitudinal range (35–47.5° N). The analysis of environmental drivers indicated that SST was the most critical factor for differentiation, while Chla and VO further amplified the divergence in resource utilization strategies between the species. From 2014 to 2023, the distribution centroids of both mackerel species showed significant northward and eastward shifts, and their spatial overlap has been continuously increasing. This research provides a methodological reference for the fine-scale assessment of co-occurring fish resources and offers a scientific basis for the sustainable management of the North Pacific mackerel fishery.

This article introduces exponentiated transmuted-inverted beta (ET-IB) distribution, supported by a continuous positive real line, as a synthetic aperture radar (SAR) imagery descriptor. It is an extension of the inverted beta distribution, an important texture model for SAR imagery. The considered distribution extension approach increases the flexibility of the baseline distribution, and is a new probabilistic model useful in SAR image applications. Besides introducing the new model, the maximum likelihood method is discussed for parameter estimation. Numerical experiments are performed to validate the use of the ET-IB distribution as a SAR amplitude image descriptor. Finally, three measured SAR images referring to forest, ocean, and urban regions are considered, and the performance of the proposed distribution is compared to distributions usually considered in this field. The proposed distribution outperforms the competitor models for modeling SAR images in terms of some selected goodness-of-fit measures. The results show that the ET-IB distribution is suitable as a SAR descriptor and can be used to develop image-processing tools in remote sensing applications.

Stem blight and dieback rank among the most relevant diseases affecting blueberry production worldwide. In Northern Italy, Neofusicoccum parvum, Diaporthe rudis, Cadophora luteo-olivacea and Peroneutypa scoparia have been reported to cause stem blight and dieback in blueberry. Considering that the incidence and severity of these diseases are on the rise in Northern Italy, two of the main aims of the present study were a—to compare the in vitro growth rate of the four fungi at different temperatures and b—to assess the aggressiveness of the same fungi on four commercial blueberry cultivars. Neofusicoccum parvum had the fastest growth rate and was the most aggressive pathogen. A possible effect of temperature on host colonization by N. parvum and disease expression was postulated and tested as a third aim. In planta trials were performed to model and predict the influence of temperature on the severity of blueberry stem blight and dieback caused by N. parvum. Increasing temperatures boosted the aggressiveness of the pathogen, causing higher disease severity and host mortality. Our findings suggest that temperature plays a relevant role in the severity of blueberry stem blight and dieback caused by N. parvum. Given the predictions of a warmer climate, this disease may become increasingly more significant and should be actively managed.

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area-level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an estimation error. Thus, it is desirable to consider the uncertain prior distribution, which is expressed as the mixture of a one-point distribution and a proper prior distribution. In this paper, we develop an empirical Bayes approach for estimating area-level means, using the uncertain prior distribution in the context of a natural exponential family, which we call the empirical uncertain Bayes (EUB) method. The regression model considered in this paper includes the Poisson-gamma and the binomial-beta, and the normal-normal (Fay–Herriot) model, which are typically used in small area estimation. We obtain the estimators of hyperparameters based on the marginal likelihood by using a well-known expectation-maximization algorithm and propose the EUB estimators of area means. For risk evaluation of the EUB estimator, we derive a second-order unbiased estimator of a conditional mean squared error by using some techniques of numerical calculation. Through simulation studies and real data applications, we evaluate a performance of the EUB estimator and compare it with the usual empirical Bayes estimator.

Faced with decaying networks, poor revenue collections, and substantial sunk costs and operating losses, over the last two decades, many developing countries have embarked on electricity sector reforms. This analysis examines factors driving the lack of household access to electricity in sub-Saharan Africa, including poor basic infrastructure, inadequate incentives in public service policies, geophysical barriers, and constraints in institutional environment. Based on cross-region panel datasets from Demographic and Health Surveys of 31 African countries between 2003 and 2018, a general-to-specific model selection procedure is applied to parametric regressions, with special attention to border discontinuities between power trading agreements and related border region effects. The chosen specifications are replicated in beta-function generalised linear models and kernel regressions, which specifically account for upper and lower bounds in the dependent variable. The econometric results turn out to be fairly robust to different estimation methods and data panels and suggest that sector restructuring and regional power integration initiatives have contributed to reducing the percentage shares of households without electricity access. However, remoteness from agglomeration economies of major urban centres and lack of substantive improvements in the grid and off-grid networks between neighbouring power trading pools have left many regions lagging behind, particularly in Central Africa. Programmes of poverty alleviation, including electricity services, should be more carefully targeted by strengthening local infrastructure development, access to modern energy, and cross-border integration within and between African regional power pools.