We consider conditions under which parametric estimates of the intensity of a spatial-temporal point process are consistent. Although the actual point process being estimated may not be Poisson, an estimate involving maximizing a function that corresponds exactly to the log-likelihood if the process is Poisson is consistent under certain simple conditions. A second estimate based on weighted least squares is also shown to be consistent under quite similar assumptions. The conditions for consistency are simple and easily verified, and examples are provided to illustrate the extent to which consistent estimation may be achieved. An important special case is when the point processes being etimated are in fact Poisson, though other important examples are explored as well.

# Your search: "author:Frederic Schoenberg"

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Methods of examining the fit of multi-dimensional point process models using residual analysis are proposed. One method involves rescaled residuals, obtained by transforming points along one coordinate to form a homogeneous Poisson process inside a random irregular boundary. Both vertical and horizontal forms of this rescaling are discussed. We also present a different method of residual analysis, involving thinning the point process according to the conditional intensity to form a homogeneous Poisson process on the original, untransformed space. These methods for assessing goodness-of-fit are applied to point process models for the space-time-magnitude distribution of earthquake occurrences, using in particular the multi-dimensional versio of Ogata's epidemic-type aftershock sequence (ETAS) model and a 30-year catalog of 580 earthquakes occurring in Bear Valley, California, as an example. The thinned residuals suggest that the fit of the model may be significantly improved by using an anisotropic spatial distance function in the estimation of the spatially varying background rate. Using rescaled residuals, it is shown that the temporal-magnitude distribution of aftershock activity is not separable, and that in particular, in contrast to the ETAS model, the triggering density of earthquakes appears to depend on the magnitude of the secondary events. The residual analysis highlights that the fit of the space-time ETAS model may be substantially improved by allowing the parameters governing the triggering density to vary for earthquakes of different magnitudes. Such modifications are important since the ETAS model is widely used seismology for hazard analysis.

For models used to describe multi-dimensional marked point processes with covariates, the high number of parameters typically involved and the high dimensionality of the process can make model evaluation, construction, and estimation using maximum likelihood quite difficult. Conditions are explored here under which parameters governing one set of coordinates or covariates affecting a multi-dimensional marked point process may be estimated separately. The resulting estimates are, under the given conditions, similar to maximum likelihood estimates.

Simple point processes are often characterized by their associated compensators or conditional intensities. For non-simple point processes, however, the conditional intensity and compensator do not uniquely determine the distribution of the process. Various ways of characterizing non-simple multivariate point processes are discussed here, some important classes of separable non-simple processes are investigated, and methods of simplification involving thinning, rescaling, and changing the mark space are presented.

Content creators on YouTube face two related issues. First, after publishing a video, theywould like an accurate prediction of its future views. Second, prior to publishing a video, they would like recommendations on setting key video attributes in order to achieve a desired growth pattern in the video’s views. This thesis addresses the first issue by fitting time series models to video views across a diverse selection of YouTube videos. On average, the fitted models can use the first two days of a video’s lifetime to predict the following 24 hours with a 5% absolute percent error. This thesis addresses the second issue by using a probabilistic classifier to identify video attributes likely to produce favorable view growth patterns. The duration, number of characters in the title, and dominant color of the thumbnail are identified as the best indicators of the video view growth pattern.

For models used to describe multi-dimensional marked point processes with covariates, the high number of parameters typically involved and the high dimensionality of the process can make model evaluation, construction, and estimation using maximum likelihood quite difficult. Conditions are explored here under which parameters governing one set of coordinates or covariates affecting a multi-dimensional marked point process may be estimated separately. The resulting estimates are, under the given conditions, similar to maximum likelihood estimates.

e consider conditions under which parametric estimates of the intensity of a spatial-temporal point process are consistent. Although the actual point process being estimated may not be Poisson, an estimate involving maximizing a function that corresponds exactly to the log-likelihood if the process is Poisson is consistent under certain simple conditions. A second estimate based on weighted least squares is also shown to be consistent under quite similar assumptions. The conditions for consistency are simple and easily verified, and examples are provided to illustrate the extent to which consistent estimation may be achieved. An important special case is when the point processes being etimated are in fact Poisson, though other important examples are explored as well.

Self-harm is a subset of mental health that is considered a severe condition requiringimmediate attention. This research aims to predict individuals’ risk of self-harm using their social media history. This dataset and broader task were originally developed by the eRisk lab at the Conference and Labs of the Evaluation Forum (CLEF). By analyzing the text corpus, it is possible to identify writing patterns that are highly correlated with self-harm. Various methods rooted in Natural Language Processing (NLP) are explored to this end, including sentiment analysis, random forest classification, and deep learning classification using BERT. The results show that adequate classification is attainable with these methods, but the potential to incorporate additional processing steps and model features to increase predictiveness is also discussed.

This study uses Poisson regression techniques to analyse the location of biotechnology companies throughout the USA. Three hypotheses are considered: that firms locate in population centres in order to attract workers, that they locate near colleges and universities where potential workers are likely to be better educated, and that they locate in close proximity to research-oriented universities and institutes because high-technology firms frequently spin-off from these research centres. We find that clusters do tend to be located near population centres colleges and universities but the influence of research-based universities is particularly striking. This highlights a powerful policy instrument for regions hoping to promote high-tech industrial clusters: the creation and maintenance of a first-rate research-oriented university. While these ideas have been suggested in the past, our approach to defining, measuring, and analysing these variables provides new insights into their significance, and also suggests avenues for future research.