Tree-like patterns are ubiquitous in nature. Botanical trees, river networks, and blood systems are the most well-known examples of complex hierarchical systems met in observations. Interestingly, many of such systems exhibit statistical self-similarity. There are two main types of self-similarity: Horton self-similarity and Tokunaga self-similarity. Although there is an increased...
Many geophysical phenomena exhibit complicated dynamics that, due to a variety of factors, diverge quickly from physical models. The arrival of new observations allows researchers to combine the model estimate with measurements in a statistical process called data assimilation to produce a revised estimate of the phenomenon. This assimilation of...
Markov Chain Monte Carlo methods may be used to determine normalizations and moments of distributions. However, these methods may perform poorly when starting from distributions that have little overlap with the target. We develop a homotopy based iterative process of incremental importance sampling to normalize distributions when observations can only...