digital marketing analysts

Abstract: Many real systems can be represented as growing networks where new nodes and links gradually emerge. The Barabási-Albert model for growing networks, and many models inspired by it, are based on the idea that nodes compete for links. However, the strength and the very presence of this competition have not been tested. We propose a robust statistical approach to quantify how strongly nodes compete for links, and apply it to data from various real systems---commenting on online news and cinema attendance data. We find a range of possible behaviors, from the perfectly elastic case, where new entrants shape network growth in a way that leaves the rest of the system unaffected, to an intermediate case where new entrants measurably affect the rest. Perfect competition is never observed. These findings have direct implications for complex systems modeling and e-commerce applications.

Abstract: We develop a statistically explicit sentiment index for Google Play user reviews and establish the mathematical results supporting its construction. Normalized star ratings and text-sentiment scores are treated as noisy measures of latent review valence and fused by covariance-aware inverse-variance weighting. Review-level estimates are aggregated with bounded helpfulness and recency weights, then shrunk toward a population mean using estimated precision rather than an arbitrary review-count threshold. App-level rating histograms provide a distributional diagnostic for samples returned under different API sort orders; because star ratings are discrete, classical continuous Kolmogorov-Smirnov critical values are not used. A local-level state-space model and the Kalman filter provide a denoised temporal trend. Full proofs cover the BLUE and Gaussian maximum-likelihood result, Gaussian-conjugate shrinkage, the Glivenko-Cantelli and Donsker theorems, count transformations via the delta method, and exact Gaussian Kalman filtering. A worked three-review example shows how textual complaints can materially reduce an apparently perfect star-only score.

Abstract: Large language models (LLMs) are increasingly used for product recommendation, but evaluating their recommendations presents challenges that differ from conventional information retrieval and recommender systems. LLMs can generate recommendations without an explicit candidate set, and repeated responses to the same query can produce different brands and rankings. We introduce a framework for evaluating open-ended LLM brand recommendations that defines the competitive set independently of model outputs and estimates recommendation prevalence and prominence through repeated sampling. We operationalize these constructs using Brand Recommendation Probability (BRP@$k$) and Mean Reciprocal Rank (MRR@$k$), and apply the framework to six LLMs across five product categories. Category-only queries reveal substantial omission of established brands and limited evidence that recommendation prominence follows conventional brand popularity. Instead, prominence is associated with broader marketplace-visibility signals, particularly search interest and online brand conversation. Needs-based queries show that contextualizing users' goals and constraints changes which brands are retrieved, while diagnostic positioning probes demonstrate that brands omitted from ordinary recommendations can remain conditionally retrievable when distinctive cues are supplied. These findings highlight the need to evaluate LLM recommendation as a stochastic retrieval-and-ranking process rather than from individual generated lists. We provide open-source software and data to support reproducible evaluation of LLM-generated brand recommendations.