This is an up-to-date introduction to, and overview of, marginal likelihood computation for model selection and hypothesis testing. Computing normalizing constants of probability
models (or ratio of constants) is a fundamental issue in many applications in statistics, applied mathematics, signal processing and machine learning. This article provides a comprehensive study of the state-of-the-art of the topic. We highlight limitations, benets, connections and differences among the dierent techniques. Problems and possible solutions with the use of improper priors are also described. Some of the most relevant methodologies are compared through theoretical comparisons and numerical experiments.
Authors: Giordano Colò
Comments: 32 Pages.
Finding anomalies when dealing with a great amount of data creates
issues related to the heterogeneity of different values and to the
difficulty of modelling trend data during time. In this paper we combine
the classical methods of time series analysis with deep learning
techniques, with the aim to improve the forecast when facing time
series with long-term dependencies. Starting with forecasting methods
and comparing the expected values with the observed ones, we
will find anomalies in time series. We apply this model to a bank
cybersecurity case to find anomalous behavior related to branches applications
Authors: Robert A. Herrmann
Comments: 10 Pages.
In this paper, we show how nonstandard consequence operators, ultralogics, can generate the general informational content displayed by probability models. In particular, a model that states a specific probability that an event will occur and those models that use a specific distribution to predict that an event will occur. These results have many diverse applications and even apply to the collapse of the wave function.