Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response

A fundamental issue when predicting structural response by using mathematical models is how to treat both modeling and excitation uncertainty. A general framework for this is presented which uses probability as a multi-valued conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The fundamental probability models that represent the structure’s uncertain behavior are specified by the choice of a stochastic system model class: a set of input-output probability models for the structure and a prior probability distribution over this set that quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic structural model by stochastic embedding utilizing Jaynes’ Principle of Maximum Information Entropy. Robust predictive analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if structural response data is available, by its posterior probability from Bayes’ Theorem for the model class. Additional robustness to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates weighted by the prior or posterior probability of the model class, the latter being computed from Bayes’ Theorem. This higherlevel application of Bayes’ Theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more complex model classes that extract more information from the data. Robust predictive analyses involve integrals over highdimensional spaces that usually must be evaluated numerically. Published applications have used Laplace's method of asymptotic approximation or Markov Chain Monte Carlo algorithms

Maximum entropy, fluctuations and priors

The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to be ruled out. Two applications are given. The first is to the theory of thermodynamic fluctuations. The formulation is exact, covariant under changes of coordinates, and allows fluctuations of both the extensive and the conjugate intensive variables. The second application is to the construction of an objective prior for Bayesian inference. The prior obtained by following the ME method to its inevitable conclusion turns out to be a special case of what are currently known under the name of entropic priors.Comment: presented at MaxEnt 2000, the 20th International Workshop on Bayesian Inference and Maximum Entropy Methods (July 8-13, Gif-sur-Yvette, France)

Quantum Probabilities as Behavioral Probabilities

We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.Comment: Latex file, 32 page

Lightweight Probabilistic Deep Networks

Even though probabilistic treatments of neural networks have a long history, they have not found widespread use in practice. Sampling approaches are often too slow already for simple networks. The size of the inputs and the depth of typical CNN architectures in computer vision only compound this problem. Uncertainty in neural networks has thus been largely ignored in practice, despite the fact that it may provide important information about the reliability of predictions and the inner workings of the network. In this paper, we introduce two lightweight approaches to making supervised learning with probabilistic deep networks practical: First, we suggest probabilistic output layers for classification and regression that require only minimal changes to existing networks. Second, we employ assumed density filtering and show that activation uncertainties can be propagated in a practical fashion through the entire network, again with minor changes. Both probabilistic networks retain the predictive power of the deterministic counterpart, but yield uncertainties that correlate well with the empirical error induced by their predictions. Moreover, the robustness to adversarial examples is significantly increased.Comment: To appear at CVPR 201

Statistical mechanics of error exponents for error-correcting codes

Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general, thermodynamic, formalism that we illustrate with maximum-likelihood decoding of low-density parity-check (LDPC) codes on the binary erasure channel (BEC) and the binary symmetric channel (BSC). In this formalism, we apply the cavity method for large deviations to derive expressions for both the average and typical error exponents, which differ by the procedure used to select the codes from specified ensembles. When decreasing the noise intensity, we find that two phase transitions take place, at two different levels: a glass to ferromagnetic transition in the space of codewords, and a paramagnetic to glass transition in the space of codes.Comment: 32 pages, 13 figure

Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

Automating Contract Negotiation

The automation of contract negotiation requires intelligent agents that can assimilate and use real-time information flows wisely. Electronic markets are information-rich with access to the Internet and the World Wide Web. A new breed o