In applications such as environmental monitoring and disease surveillance, spatial data are often collected sequentially over time, forming spatio-temporal data streams. Effectively monitoring these streams in real time is critical for detecting anomalies in the underlying spatio-temporal processes. Due to the complex nature of spatio-temporal data—including intricate correlation structures, evolving mean patterns, and nonstandard distributions—this remains a challenging research problem. In this talk, we will present several recent methodologies developed by our research team, using spatio-temporal local linear kernel smoothing, exponentially weighted spatial LASSO, and other advanced data smoothing techniques. We will also showcase applications of these methods in analyzing real infectious disease datasets.

Much recent research has focused on directional data, i.e., data on the unit sphere. The angular halfspace depth is a tool for nonparametric analysis of directional data. This depth was proposed as early as 1987, but its widespread use has been hampered by significant computational problems. We present an efficient algorithm for the exact computation of the angular halfspace depth in arbitrary dimensions, which does not require the data to be in general position. The algorithm is based on a two-step projection scheme. In the first step, the data are repeatedly projected onto a lower-dimensional sphere. Then, the data are projected from this low-dimensional sphere onto a linear space in which the usual halfspace depth is computed with respect to a signed measure. Compared to known algorithms, this new algorithm is significantly faster. However, the main advantage of the proposed algorithm is that it is able to compute the depth of all data points in a sample (with respect to that sample) with the same time complexity as the depth of a single point. Another important advantage of our algorithm is its good parallelizability.

Empirical research has access to ever larger data sets as technological advances make it easier and less costly to collect large amounts of data. However, the amount of available data often exceeds the capabilities of the methods ultimately used to answer the research question, meaning that either not all of the data can be used or techniques such as shrinkage or dimensionality reduction have to be used. In the latter case, assuming a latent factor structure in the data is common. One of the most widely used methods for factor extraction is solving a principal component estimation problem for which efficient implementations exist. Although mixed data types may be considered via generalized linear models driven by latent factors, PCA is not available for those. To enable the use of such data, we propose a maximum likelihood-based iterative alternating least squares procedure capable of accommodating mixed data types, and we empirically demonstrate its practical applicability.