We introduce an entropic prior for multinomial parameter estimation problems and solve for its maximum...

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We present a theory, a system and an application for common sense reasoning based on propositional logic, the probability calculus and the concept of maximum entropy. The task of the system Pit (Probability Induction Tool) is to provide decisions under incomplete knowledge, while keeping the necessary additional assumptions as minimal and clear as possible. We therefore enrich the probability calculus by two principles which have their common source in the concept of model-quantification ([8, 17]) and find their dense representation in the well-known principle of Maximum Entropy (MaxEnt [6]). As model-quantification delivers a precise semantics to MaxEnt, the corresponding decisions make sense not only in our current project of medical diagnosis in Lexmed.

In learning problems available information is usually divided into two categories: examples of function values (or training data) and prior information (e.g. a smoothness constraint).

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By rejecting the use of a prior distribution over parameters, orthodox statistics is forced to focus on estimators, functions which guess parameter values, and to invent heuristics for choosing among estimators. Two popular heuristics are unbiasedness and maximum likelihood. Since these heuristics are not consistent with Bayes' rule, they are also not consistent with the axioms of common sense from which Bayes' rule is derived. Hence we expect there to be situations in which they violate common sense and indeed it is not hard to find such situations. This paper reviews a few simple, realistic scenarios where pathologies occur with either the unbiasedness heuristic or the maximum likelihood heuristic. 1 Introduction Many inference problems work like this: we observe some data and want to infer something about the process that generated it. If we have a probability distribution over possible processes, parameterized by `, then there is general agreement that Bayes' rule solves ...

this paper by applying them to a data set obtained by direct optical imaging of rat barrel cortex, before, during, and after whisker stimulation. The images have been pre-processed to estimate optical absorption at the illumination wavelength of 577nm and averaged over 30 trials to reduce the contribution of background vascular processes (in particular a dominant 0.1 Hz vasomotion signal). Each data set contains 12 s of data sampled at 15 Hz. Whisker stimulation began 8 s after image aquisition started and continued for 1 s, image aquisition then continued for a further 3 s. The final data set consists of 180 128 \Theta 96 images. For more details of the experimental procedure, a description of the nonlinear spectral analysis method used to estimate physical parameters from multi-spectral data, and an assessment of the performance of various analysis methods, see [1].

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this paper we follow a more data-driven approach, in which we start with an attribute of interest. Our choice for attribute of interest is based on the observation that most systems that people characterize as complex /living/intelligent have the following property: over different

this paper. Next, we must measure this attribute of interest for many real-world complex systems. That is work in progress. At this point --- and at only at this point --- we must use the data resulting from those measurements to guide our construction of potential models of the common processes underlying complex systems. That is future work. In this paper we consider several potential attributes of interest. These candidate attributes arise from observing that most systems that people intuitively characterize as complex/living/intelligent have the following property: