Considerate Approaches to Achieving Sufficiency for ABC model selection

For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations from a model, but cannot evaluate the likelihood directly. When summary statistics of real and simulated data are compared --- rather than the data directly --- information is lost, unless the summary statistics are sufficient. Here we employ an information-theoretical framework that can be used to construct (approximately) sufficient statistics by combining different statistics until the loss of information is minimized. Such sufficient sets of statistics are constructed for both parameter estimation and model selection problems. We apply our approach to a range of illustrative and real-world model selection problems

On the accuracy of phase-type approximations of heavy-tailed risk models

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin probability. The goals of this paper are to investigate the number of phases required so that we can achieve a pre-specified accuracy for the ruin probability and to provide error bounds. Also, in the special case of a completely monotone claim size distribution we develop an algorithm to estimate the ruin probability by approximating the excess claim size distribution with a hyperexponential one. Finally, we compare our approximation with the heavy traffic and heavy tail approximations.Comment: 24 pages, 13 figures, 8 tables, 38 reference

Information retrieval in multimedia databases using relevance feedback algorithms. Applying logistic regression to relevance feedback in image retrieval systems

This master tesis deals with the problem of image retrieval from large image databases. A particularly interesting problem is the retrieval of all images which are similar to one in the user's mind, taking into account his/her feedback which is expressed as positive or negative preferences for the images that the system progressively shows during the search. Here, a novel algorithm is presented for the incorporation of user preferences in an image retrieval system based exclusively on the visual content of the image, which is stored as a vector of low-level features. The algorithm considers the probability of an image belonging to the set of those sought by the user, and models the logit of this probability as the output of a linear model whose inputs are the low level image features. The image database is ranked by the output of the model and shown to the user, who selects a few positive and negative samples, repeating the process in an iterative way until he/she is satisfied. The problem of the small sample size with respect to the number of features is solved by adjusting several partial linear models and combining their relevance probabilities by means of an ordered weighted averaged (OWA) operator. Experiments were made with 40 users and they exhibited good performance in finding a target image (4 iterations on average) in a database of about 4700 imagesZuccarello, PD. (2007). Information retrieval in multimedia databases using relevance feedback algorithms. Applying logistic regression to relevance feedback in image retrieval systems. http://hdl.handle.net/10251/12196Archivo delegad