Theory of Gaussian Variational Approximation for a Poisson Mixed Model

Likelihood-based inference for the parameters of generalized linear mixed models is hindered by the presence of intractable integrals. Gaussian variational approximation provides a fast and effective means of approximate inference. We provide some theory for this type of approximation for a simple Poisson mixed model. In particular, we establish consistency at rate m−1/2 + n−1, where m is the number of groups and n is the number of repeated measurements

EPOCHS VI: The Size and Shape Evolution of Galaxies since z ~ 8 with JWST Observations

We present the results of a size and structural analysis of 1395 galaxies at $0.5 \leq z \lesssim 8$ with stellar masses $\log \left(M_* / M_{\odot}\right)$ $>$ 9.5 within the JWST Public CEERS field that overlaps with the HST CANDELS EGS observations. We use GALFIT to fit single S\'ersic models to the rest-frame optical profile of our galaxies, which is a mass-selected sample complete to our redshift and mass limit. Our primary result is that at fixed rest-frame wavelength and stellar mass, galaxies get progressively smaller, evolving as $\sim (1+z)^{-0.71\pm0.19}$ up to $z \sim 8$. We discover that the vast majority of massive galaxies at high redshifts have low S\'ersic indices, thus do not contain steep, concentrated light profiles. Additionally, we explore the evolution of the size-stellar mass relationship, finding a correlation such that more massive systems are larger up to $z \sim 3$. This relationship breaks down at $z > 3$, where we find that galaxies are of similar sizes, regardless of their star formation rates and S\'ersic index, varying little with mass. We show that galaxies are more compact at redder wavelengths, independent of sSFR or stellar mass up to $z \sim 3$. We demonstrate the size evolution of galaxies continues up to $z \sim 8$, showing that the process or causes for this evolution is active at early times. We discuss these results in terms of ideas behind galaxy formation and evolution at early epochs, such as their importance in tracing processes driving size evolution, including minor mergers and AGN activity.Comment: Submitted to MNRA

Analysing decision logs to understand decision-making in serious crime investigations

Objective: To study decision-making by detectives when investigating serious crime through the examination of Decision Logs to explore hypothesis generation and evidence selection. Background: Decision logs are used to record and justify decisions made during serious crime investigations. The complexity of investigative decision-making is well documented, as are the errors associated with miscarriages of justice and inquests. The use of decision logs has not been the subject of an empirical investigation, yet they offer an important window into the nature of investigative decision-making in dynamic, time-critical environments. Method: A sample of decision logs from British police forces was analyzed qualitatively and quantitatively to explore hypothesis generation and evidence selection by police detectives. Results: Analyses revealed diversity in documentation of decisions that did not correlate with case type, and identified significant limitations of the decision log approach to supporting investigative decision-making. Differences emerged between experienced and less experienced officers’ decision log records in exploration of alternative hypotheses, generation of hypotheses, and sources of evidential enquiry opened over phase of investigation. Conclusion: The practical use of decision logs is highly constrained by their format and context of use. Despite this, decision log records suggest that experienced detectives display strategic decision-making to avoid confirmation and satisficing that affect less experienced detectives. Application: Potential applications of this research include both training in case documentation and the development of new decision log media that encourage detectives, irrespective of experience, to generate multiple hypotheses and optimize the timely selection of evidence to test them

The statistical laws of popularity: Universal properties of the box office dynamics of motion pictures

Are there general principles governing the process by which certain products or ideas become popular relative to other (often qualitatively similar) competitors? To investigate this question in detail, we have focused on the popularity of movies as measured by their box-office income. We observe that the log-normal distribution describes well the tail (corresponding to the most successful movies) of the empirical distributions for the total income, the income on the opening week, as well as, the weekly income per theater. This observation suggests that popularity may be the outcome of a linear multiplicative stochastic process. In addition, the distributions of the total income and the opening income show a bimodal form, with the majority of movies either performing very well or very poorly in theaters. We also observe that the gross income per theater for a movie at any point during its lifetime is, on average, inversely proportional to the period that has elapsed after its release. We argue that (i) the log-normal nature of the tail, (ii) the bimodal form of the overall gross income distribution, and (iii) the decay of gross income per theater with time as a power law, constitute the fundamental set of {\em stylized facts} (i.e., empirical "laws") that can be used to explain other observations about movie popularity. We show that, in conjunction with an assumption of a fixed lower cut-off for income per theater below which a movie is withdrawn from a cinema, these laws can be used to derive a Weibull distribution for the survival probability of movies which agrees with empirical data. The connection to extreme-value distributions suggests that popularity can be viewed as a process where a product becomes popular by avoiding failure (i.e., being pulled out from circulation) for many successive time periods. We suggest that these results may apply to popularity in general.Comment: 14 pages, 11 figure

“It’s not just parties, it’s so much more”: Student perceptions of the credibility of Events Management degrees

Purpose: This article explores: 1) student perceptions and understanding of Events Management; 2) how Events Management is positioned by different UK higher education providers through their online marketing; and 3) the perceived value of an Events Management degree among students. Findings: Students demonstrate a lack of knowledge about what Events Management is, what a career in Events Management might entail and, the perceived value of an Events Management degree. This suggests the need to re-position Events Management degrees within a broader applied management base. Course marketing presents a narrow view of Events Management degrees. This does a disservice to Events Management as the narrow vocationally-laden narrative undersells and ‘over-vocationalises’ Events Management degrees. Design/Method/Approach: A mixed-methods approach, combining an online student questionnaire (n=524), semi-structured interviews with current first year Events Management students (n=24) at two UK universities, and website analysis of all Events Management degrees offered in the UK. Practical implications: Better understanding student perceptions will help Universities market Events Management degrees more effectively and will benefit broader efforts to illustrate the value and credibility of it as a degree subject choice and career. More balanced presentation between the practical and non-practical aspects of the courses in University marketing may help reposition Events Management alongside more readily understood vocational subjects. Originality: This is the first study to examine student perceptions over the credibility of Events Management degrees. It also addresses Park and Park’s (2017) observation that reviews of Events Management education and curricula are conspicuously absent from Hospitality and Tourism journals

The effects of climatic fluctuations and extreme events on running water ecosystems

Most research on the effects of environmental change in freshwaters has focused on incremental changes in average conditions, rather than fluctuations or extreme events such as heatwaves, cold snaps, droughts, floods or wildfires, which may have even more profound consequences. Such events are commonly predicted to increase in frequency, intensity and duration with global climate change, with many systems being exposed to conditions with no recent historical precedent. We propose a mechanistic framework for predicting potential impacts of environmental fluctuations on running water ecosystems by scaling up effects of fluctuations from individuals to entire ecosystems. This framework requires integration of four key components: effects of the environment on individual metabolism, metabolic and biomechanical constraints on fluctuating species interactions, assembly dynamics of local food webs and mapping the dynamics of the meta-community onto ecosystem function. We illustrate the framework by developing a mathematical model of environmental fluctuations on dynamically assembling food webs. We highlight (currently limited) empirical evidence for emerging insights and theoretical predictions. For example, widely supported predictions about the effects of environmental fluctuations are: high vulnerability of species with high per capita metabolic demands such as large-bodied ones at the top of food webs; simplification of food web network structure and impaired energetic transfer efficiency; reduced resilience and top-down relative to bottom-up regulation of food web and ecosystem processes. We conclude by identifying key questions and challenges that need to be addressed to develop more accurate and predictive bio-assessments of the effects of fluctuations, and implications of fluctuations for management practices in an increasingly uncertain world