Philosophy of Modeling: Neglected Pages of History

The work done in the philosophy of modeling by Vaihinger (1876), Craik (1943), Rosenblueth and Wiener (1945), Apostel (1960), Minsky (1965), Klaus (1966) and Stachowiak (1973) is still almost completely neglected in the mainstream literature. However, this work seems to contain original ideas worth to be discussed. For example, the idea that diverse functions of models can be better structured as follows: in fact, models perform only a single function – they are replacing their target systems, but for different purposes. Another example: the idea that all of cognition is cognition in models or by means of models. Even perception, reflexes and instincts (animal and human) can be best analyzed as modeling. The paper presents an analysis of the above-mentioned work

Explanation and Understanding in a Model-Based Model of Cognition

This article is an experiment. Consider a minimalist model of cognition (models, means of model-building and history of their evolution). In this model, explanation could be defined as a means allowing to advance: production of models and means of model-building (thus, yielding 1st class understanding), exploration and use of them (2nd class), and/or teaching (3rd class). At minimum, 3rd class understanding is necessary for an explanation to be respected

Spline histogram method for reconstruction of probability density function of clusters of galaxies

We describe the spline histogram algorithm which is useful for visualization of the probability density function setting up a statistical hypothesis for a test. The spline histogram is constructed from discrete data measurements using tensioned cubic spline interpolation of the cumulative distribution function which is then differentiated and smoothed using the Savitzky-Golay filter. The optimal width of the filter is determined by minimization of the Integrated Square Error function. The current distribution of the TCSplin algorithm written in f77 with IDL and Gnuplot visualization scripts is available from http://www.virac.lv/en/soft.htmlComment: 8 pages, 3 figures, to be published in "Galaxies and Chaos: Theory and Observations", eds. N.Voglis, G.Contoupoulos, conference proceedings (CD version), uses Springer Verlag svmult.cls style file

Mixture of bivariate Poisson regression models with an application to insurance

In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.Zero-inflation, Overdispersion, EM algorithm, Automobile insurance, A priori ratemaking.

Treating missing values in INAR(1) models

Time series models for count data have found increased interest in recent days. The existing literature refers to the case of data that have been fully observed. In the present paper, methods for estimating the parameters of the first-order integer-valued autoregressive model in the presence of missing data are proposed. The first method maximizes a conditional likelihood constructed via the observed data based on the k-step-ahead conditional distributions to account for the gaps in the data. The second approach is based on an iterative scheme where missing values are imputed in order to update the estimated parameters. The first method is useful when the predictive distributions have simple forms. We derive in full details this approach when the innovations are assumed to follow a finite mixture of Poisson distributions. The second method is applicable when there are not closed form expressions for the conditional likelihood or they are hard to derive. Simulation results and comparisons of the methods are reported. The proposed methods are applied to a data set concerning syndromic surveillance during the Athens 2004 Olympic Games.Imputation; Markov Chain EM algorithm; mixed Poisson; discrete valued time series