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In electromechanical actuators Lorentz force law is used to convert electrical energy into rotational or linear mechanical energy. In these conventional electromechanical actuators, rigid wires conducts the electrical current and as such the types of motion generated by these actuators are limited. Recent advances in liquid metal alloys permit designing electrical wires that are stretchable. These flexible wires have been used to fabricate various flexible connections, sensors and antennas. However, there have been very little efforts to use these stretchable liquid metal wires as actuators. Building upon our previous work in this area, we have made a flexible pump which can be used in bio applications. In this design we placed a flexible polymeric substrate filled by liquid metal Galinstan between two permanent magnets. Since the pump should convey the biological cells suspended along the fluid flow, utilizing check valves may increase the risk of clog in the inlet or outlet. Therefore, our design is based on the nozzle/diffuser concept. This new pump can be considered as a peristaltic and valve-less mechanical pumps which utilizes the Lorentz force law as the actuating mechanism.

Real-valued partial differential equations (PDEs) are obtained by substituting the rectangular form of the complex envelope (CE) field and source quantities into the CE versions of Faraday’s and Ampere’s laws, and then separating each resulting complex PDE into real and imaginary parts. These real-valued PDEs result in a CE FDTD scheme that uses only real numbers and operations. As presented here, this CE FDTD scheme alternates at intervals of half a time step between solving for the real and imaginary portions of the CE fields, exactly as the Yee grid alternates spatial components of the fields at half spatial steps. The scheme is demonstrated here for the two-dimensional (2-D) transverse-magnetic case. A split-step method is used in the implicit formation such that only tridiagonal matrices have to be solved. FDTD results are presented for a 2-D cavity with an electric current source.

BayeSys is an MCMC-based program that can be used to perform Bayesian model comparison for problems with atomic models. To sample distributions with more than one parameter, BayeSys uses the Hilbert curve to index the multidimensional parameter space using one very large integer. While the Hilbert curve maintains locality well, computations to translate back and forth between parameter coordinates and Hilbert curve indexes are time-consuming. The Z-order curve is an alternative SFC with faster transformation algorithms. This work presents an efficient bitmask-based algorithm for performing the Z-order curve transformations for an arbitrary number of parameter space dimensions and integer bit-lengths. We compare results for an exponential decay separation problem evaluated using BayeSys with both the Hilbert and Z-order curves. We demonstrate that no appreciable precision penalty is incurred by using the Z-order curve, and there is a significant increase in time efficiency.

Electromechanical actuators exploit the Lorentz force law to convert electrical energy into rotational or linear mechanical energy. In these electromagnetically induced motions, the electrical current flows through wires that are rigid, and consequently, the types of motion generated are limited. Recent advances in preparing liquid metal alloys permit wires that are flexible. Such wires have been used to fabricate various forms of flexible connections, but very little has been done to use liquid metal as an actuator. In this paper, we propose and have tested a new type of motor using liquid metal conductors in which radial (or breathing) modes are activated.

Loudspeaker design requires accurate models of driver voice coil impedance. This paper examines three model classes (standard, Leach, and van Maanen) from the audio literature and compares them using Bayesian model comparison via nested sampling. Data is generated from impedance measurements of two commercial loudspeaker drivers. We conclude that, for most design tasks involving these drivers, the van Maanen model with 3 lossy inductance groups is the most appropriate model.

Based on the observation that design and inference are both generalized inverse problems, we devise a new approach that uses the Bayesian inference framework for the automated design of linear antenna arrays. Compared to the optimization-based techniques that are widely used for automated antenna design, this newly-developed method has a prominent advantage, which is the capability to determine automatically the number of antenna elements required to satisfy design requirements and specifications. Three broadside array design problems, which include the null-controlled pattern, the sector beam pattern, and the Chebyshev pattern, along with an end-fire array design problem, are presented as examples. The obtained results demonstrate the advantages of using the Bayesian inference framework for the design of linear antenna arrays.

The zero-frequency problem of a pair of perfectly-conducting strip electrodes lying on an imperfectly conducting half-space and perturbed by the presence of a nonconductive cylindrical void or tunnel is analyzed. A conformal mapping transforms all of the pertinent boundaries in the potential problem to simple coordinate surfaces in a single cylindrical coordinate frame. Coupled integral equations for the normal electric current density on each strip are numerically solved using the moment method. The effect upon the circuit resistance of various sized subsurface tunnels at arbitrary locations is now easily calculable.

This paper discusses quantitative tools to evaluate the reliability of "decay time estimates" and inter-relationships between multiple decay times for estimates made within a Bayesian framework. Previous works [Xiang and Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001); 113, 2685-2697 (2003)] have applied Bayesian framework to cope with the demanding tasks in estimating multiple decay times from Schroeder decay functions measured in acoustically coupled spaces. A parametric model of Schroeder decay function [Xiang, J. Acoust. Soc. Am. 98, 2112-2121 (1995)] has been used for the Bayesian model-based analysis. The relevance of this work is that architectural acousticians need to know how well determined are the estimated decay times calculated within Bayesian framework using Schroeder decay function data. This paper will first address the estimation of global variance of the residual errors between the Schroeder function data and its model. Moreover, this paper discusses how the "landscape" shape of the posterior probability density function over the decay parameter space influences the individual decay time estimates, their associated variances, and their inter-relationships. This paper uses experimental results from measured room impulse responses in real halls to describe a model-based sampling method for an efficient estimation of decay times, and their individual variances. These parameters along with decay times are relevant decay parameters for evaluation and understanding of acoustically coupled spaces.

This paper applies Bayesian probability theory to determination of the decay times in coupled spaces. A previous paper [N. Xiang and P. M. Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001)] discussed determination of the decay times in coupled spaces from Schroeder's decay functions using Bayesian parameter estimation. To this end, the previous paper described the extension of an existing decay model [N. Xiang, I. Acoust. Soc. Am. 98, 2112-2121 (1995)] to incorporate one or more decay modes for use with Bayesian inference. Bayesian decay time estimation will obtain reasonable results only when it employs an appropriate decay model with the correct number of decay modes. However, in architectural acoustics practice, the number of decay modes may not be known when evaluating Schroeder's decay functions. The present paper continues the endeavor of the previous paper to apply Bayesian probability inference for comparison and selection of an appropriate decay model based upon measured data. Following a summary of Bayesian model comparison and selection, it discusses selection of a decay model in terms of experimentally measured Schroeder's decay functions. The present paper, along with the Bayesian decay time estimation described previously, suggests that Bayesian probability inference presents a suitable approach to the evaluation of decay times in coupled spaces.

Determination of sound decay times in coupled spaces often demands considerable effort. Based on Schroeder's backward integration of room impulse responses, it is often difficult to distinguish different portions of multirate sound energy decay functions. A model-based parameter estimation method, using Bayesian probabilistic inference, proves to be a powerful tool for evaluating decay times. A decay model due to one of the authors [N. Xiang, J. Acoust. Soc. Am. 98, 2112-2121 (1995)] is extended to multirate decay functions. Following a summary of Bayesian model-based parameter estimation, the present paper discusses estimates in terms of both synthesized and measured decay functions. No careful estimation of initial values is required, in contrast to gradient-based approaches. The resulting robust algorithmic estimation of more than one decay time, from experimentally measured decay functions, is clearly superior to the existing nonlinear regression approach.

The complex-envelope representation of bandpass-limited signals is used to formulate a bandpass-limited vector wave equation and a new finite-difference time-domain (FDTD) scheme that solves the bandpass-limited vector wave equation is presented. For narrow-band electromagnetic systems, this new method allows the time step to be several orders of magnitude larger than current FDTD formulations while maintaining an amplification factor equal to one. Example results obtained by this method are presented and compared with analytic solutions.

This paper presents a method for designing intermodal freight rail-to-highway terminals using Bayesian model selection. Each model consists of a unique network of cities and rail terminals. The model parameters are the amount of freight flowing on each individual path in the network. The prior distribution constrains the freight flowing on each path between each pair of origin and destination cities to Gaussian distributions with means corresponding to the estimated freight demand between the cities. The likelihood function favors low total cost in the network and penalizes routing schemes that exceed terminal capacities. Nested sampling is used to compute the Bayesian evidence for each model. The paper describes the generation of, results from, and conclusions drawn from a realistic test case.

This paper examines the problem of assigning a prior pdf for N positive parameters z = {z1,z2,⋯,zN} that are dependent in such a way that their sum is bounded by a known constant. It also derives a set of functions that map N independent and uniformly distributed parameters to the parameters z with the known dependance.

One of the important advantages of nested sampling as an MCMC technique is its ability to draw representative samples from multimodal distributions and distributions with other degeneracies. This coverage is accomplished by maintaining a number of so-called live samples within a likelihood constraint. In usual practice, at each step, only the sample with the least likelihood is discarded from this set of live samples and replaced. In [1], Skilling shows that for a given number of live samples, discarding only one sample yields the highest precision in estimation of the log-evidence. However, if we increase the number of live samples, more samples can be discarded at once while still maintaining the same precision. For computer code running only serially, this modification would considerably increase the wall clock time necessary to reach convergence. However, if we use a computer with parallel processing capabilities, and we write our code to take advantage of this parallelism to replace multiple samples ...

Spectrum estimation is a problem common to many fields of physics, science, and engineering, and it has thus received a great deal of attention from the Bayesian data analysis community. In room acoustics, the modal or frequency response of a room is important for diagnosing and remedying acoustical defects. The physics of a sound field in a room dictates a model comprised of exponentially decaying sinusoids. Continuing in the tradition of the seminal work of Bretthorst and Jaynes, this work contributes an approach to analyzing the modal responses of rooms with a time-domain model. Room acoustic spectra are constructed of damped sinusoids, and the modelbased approach allows estimation of the number of sinusoids in the signal as well as their frequencies, amplitudes, damping constants, and phase delays. The frequency-amplitude spectrum may be most useful for characterizing a room, but in some settings the damping constants are of primary interest. This is the case for measuring the absorptive properties of materials, for example. A further challenge of the room acoustic spectrum problem is that modal density increases quadratically with frequency. At a point called the Schroeder frequency, adjacent modes overlap enough that the spectrum - particularly when estimated with the discrete Fourier transform - can be treated as a continuum. The time-domain, model-based approach can resolve overlapping modes and in some cases be used to estimate the Schroeder frequency. The proposed approach addresses the issue of filtering and preprocessing in order for the sampling to accurately identify all present room modes with their quadratically increasing density.

Stuttering is generally considered to be a speech disorder that affects ∼1% of the global population. Various forms of speech feedback have been shown to reduce overt stuttered speaking, and in particular, second speech signal through speech feedback has drastically reduced utterances of stuttered speech in adults with persistent stuttering. This study reports data for increased overt fluency of speech in an adult stuttering population, whereby the vocalization of the speaker is captured by a microphone or an accelerometer, signal processed, and returned as mechanical tactile speech feedback to the speaker's skin. A repeated measures analysis of variance was used to show that both the microphone and the accelerometer speaking conditions were significantly more fluent than a control (no feedback) condition, with the microphone-driven tactile feedback reducing instances of stuttering by 71% and the accelerometer-driven tactile feedback reducing instances of stuttering by 80%. It is apparent that self-generated tactile feedback can be used to enhance fluency significantly in those who stutter.

The paper presents an efficient procedure to calculate the electromagnetic field scattered by an inhomogeneous object consisting of N+1 linear isotropic homogeneous regions. The procedure is based on surface integral equation (SIE) formulations and the method of moments. The method of moments (MM) is used to reduce the integral equations for each homogeneous dielectric region into individual matrices. These matrices are each solved for the equivalent electric current in terms of the equivalent magnetic current. A simple algebraic procedure is used to combine these solutions and to solve for the magnetic current on the outer dielectric surfaces of the scatterer. With the magnetic current determined, the electric current on the outer surface of the scatterer is calculated. Because the matrix corresponding to each dielectric region is solved separately, the authors call this procedure the region-by-region method. The procedure is simple and efficient. It requires less computer storage and less execution time than the conventional MM approach, in which all the unknown currents are solved for simultaneously. To illustrate the use of the procedure, the bistatic and monostatic radar cross sections (RCS) of several objects are computed. The computed results are verified by comparison with results obtained numerically using the conventional numerical procedure as well as via the series solution for circular cylindrical structures. The possibility of nonunique solutions has also been investigated. >

Due to recent developments in concert hall design, there is an increasing interest in the analysis of sound energy decays consisting of multiple exponential decay rates. It has been considered challenging to estimate parameters associated with double-rate (slope) decay characteristics, and even more challenging when the coupled-volume systems contain more than two decay processes. To meet the need of characterizing energy decays of multiple decay processes, this work investigates coupled-volume systems using acoustic scale-models of three coupled rooms. Two Bayesian formulations are compared using the experimentally measured sound energy decay data. A fully parameterized Bayesian formulation has been found to be capable of characterization of multiple-slope decays beyond the single-slope and double-slope energy decays. Within the Bayesian framework using this fully parameterized formulation, an in-depth analysis of likelihood distributions over multiple-dimensional decay parameter space motivates the use of Bayesian information criterion, an efficient approach to solving Bayesian model selection problems that are suitable for estimating the number of exponential decays. The analysis methods are then applied to a geometric-acoustics simulation of a conceptual concert hall. Sound energy decays more complicated than single-slope and double-slope nature, such as triple-slope decays have been identified and characterized.

The authors discuss the aspects of the radar target/identification problem which have made progress slow and difficult. They summarize their research program and discuss the mathematical foundations for solving the problem. To simplify the discussion, only aircraft-type targets are considered, and clutter is ignored. Target-library problems, are examined in some detail, including the proposed use of scattering-center models to mitigate problems and related electromagnetic-modeling considerations. >

It has been previously shown that one can use the ME methodology (Caticha Giffin 2006) to reproduce a mean field solution for a simple fluid (Tseng 2004). One could easily use the case of a simple ferromagnetic material as well. The drawback to the mean field approach is that one must assume that all atoms must all act the same. The problem becomes more tractable when the agents are only allowed to interact with their nearest neighbors and can be in only two possible states. The easiest case being an Ising model. The purpose of this paper is to illustrate the use of the ME method as an approximation tool. The paper show a simple case to compare with the traditional mean field approach. Then we show two examples that lie outside of traditional methodologies. These cases explore a ferromagnetic material with defects. The main result is that regardless of the case, the ME method provides good approximations for each case which would not otherwise be possible or at least well justified., Presented at the 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Oxford, MS, July 5-10, 2009. 10 pages, 0 figures

A systematic procedure for modeling electromagnetic scattering problems involving bodies with electrically thin features is discussed. The scattering bodies are represented using standard surface integral equation formulations and solutions are obtained via the method of moments (MOM). It is demonstrated that accurate evaluation of the moment matrix elements is critical for obtaining accurate solutions for scatterers having thin features. It is also shown (by numerical example) that some of the various surface integral formulations remain valid and can be used to obtain accurate scattering results for arbitrarily thin dielectric and conducting features. The use of the systematic approach for such problems is illustrated by incorporating the procedures into a two-dimensional (MOM) program. Sample results illustrating the technique's utility and validity are provided. >

Some criticisms that have been raised against the Cox approach to probability theory are addressed. Should we use a single real number to measure a degree of rational belief? Can beliefs be compared? Are the Cox axioms obvious? Are there counterexamples to Cox? Rather than justifying Cox's choice of axioms we follow a different path and derive the sum and product rules of probability theory as the unique (up to regraduations) consistent representations of the Boolean AND and OR operations., Presented at MaxEnt 2009, the 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 5-10, 2009, Oxford, Mississippi, USA.) In version 2 one mistake and a few typos have been corrected

In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and nested sampling from a unified perspective., Comment: 12 pages, 4 figures, submitted to the proceedings of MaxEnt 2009, July 05-10, 2009, to be published by the American Institute of Physics

The entropy of a distribution with finite support is widely used in all applications involving random variables. A natural equivalent for random processes is the entropy rate. For ergodic pure‐jump finite‐state Markov processes, this rate is an explicit function of the stationary distribution and the infinitesimal generator.The case of two‐state Markov processes is of particular interest. We estimate the entropy rate of such processes by plug‐in, from estimators of the stationary distribution and the infinitesimal generator.Three situations of observation are discussed, several independant trajectories are observed, one long trajectory is observed, or the process is observed at discrete times. The asymptotic behavior of the plug‐in estimators is established.

A long‐standing debate over the interpretation of quantum mechanics has centered on the meaning of Schroedinger’s wave function Ψ for an electron. Broadly speaking, there are two major opposing schools. On the one side, the Copenhagen school (led by Bohr, Heisenberg and Pauli) holds that Ψ provides a complete description of a single electron state; hence the probability interpretation of ΨΨ* expresses an irreducible uncertainty in electron behavior that is intrinsic in nature. On the other side, the realist school (led by Einstein, de Broglie, Bohm and Jaynes) holds that Ψ represents a statistical ensemble of possible electron states; hence it is an incomplete description of a single electron state. I contend that the debaters have overlooked crucial facts about the electron revealed by Dirac theory. In particular, analysis of electron zitterbewegung (first noticed by Schroedinger) opens a window to particle substructure in quantum mechanics that explains the physical significance of the complex phase factor in Ψ. This led to a testable model for particle substructure with surprising support by recent experimental evidence. If the explanation is upheld by further research, it will resolve the debate in favor of the realist school. I give details. The perils of research on the foundations of quantum mechanics have been foreseen by Lewis Carroll in The Hunting of the Snark!

It is known that all autonomous Markovian processes can be represented as a limit from a Poisson process. We obtain this result by explicitly solving the Chapman‐Kolmogorov equation under some assumptions. The demonstration shed some light on the different possibilities allowed within the Markov property. It also can be regarded as the general solution to the gain‐loss master equation.

Graphical representations of the independence relations in joint probability functions—commonly known as Bayesian networks—have played an essential role in knowledge representation and decision support. In this paper, we present a graphical representation of the independence relations in multiattribute utility functions, which we call bidirectional utility diagrams. These diagrams apply to more general functional forms that relax both the grounding conditions and n‐increasing conditions of joint cumulative probability functions. We also provide an expansion theorem for multiattribute utility functions and show how special cases of this expansion lead to some of the well‐known formulations of utility independence that occur in the literature.

In the probability literature, a martingale is often referred to as a fair game. A risk neutral decision maker would be indifferent to engaging in a martingale investment for any number of stages or not engaging into it at all if its expected value is equal to his current wealth. But a risk‐averse decision maker would not accept a martingale pay‐off in exchange for its expected value since his certain equivalent for uncertain deals is less than their mean. Therefore the traditional martingale sequences that are widely studied in probability and finance are not rational investments for risk averse decision makers. A risk seeking decision maker, on the other hand would welcome a martingale investment, since the certain equivalent is larger than the mean. We introduce a class of stochastic processes whose expected utility is constant and equal to the utility of the current wealth. We refer to such processes as risk‐adjusted martingales. We show how to construct such processes for any continuous and strictly ...

In biomedical studies, detecting the changes in a response distribution under different testing conditions is one of the important issues. For example, increase in dose level may lead to increase or decrease in the gene expression level. To address this issue, we propose a nonparametric Bayesian test for testing the difference in location when samples are collected under two different conditions. We apply Dirichlet process priors to estimate the probabilities, which imply constraint on cumulative distribution functions of occurrence evaluated at cut‐off value that partitions the expression range of that gene into two intervals. The proposed test can be easily extended for multiple samples comparisons in gene expression analysis.

The family of Tsallis entropies was introduced by Tsallis in 1988. The Shannon entropy belongs to this family as the limit case q→1. The canonical distributions in Rn that maximize this entropy under a covariance constraint are easily derived as Student‐t (q 1) multivariate distributions. A nice geometrical result about these Student‐r distributions is that they are marginal of uniform distributions on a sphere of larger dimension d with the relationship p = n+2+2q−1. As q→1, we recover the famous Poincare’s observation according to which a Gaussian vector can be viewed as the projection of a vector uniformly distributed on the infinite dimensional sphere. A related property in the case q

Originally the maximum entropy method for exponent deconvolution was restricted to the positive exponent’s amplitudes by the entropy S(f, m) definition. It limits application of the method, since many experimental kinetics show both the rise and the decay, which manifest themselves as positive and negative amplitudes in the exponent spectrum. The generalization of entropy formulation for non‐negative distribution (S. F. Gull and J. Skilling) overcomes this limitation. The drawback of the approach was, that m lost the meaning of the prior distribution, since that maximum of generalized S(f, m) is independent on m and achieved at f ≡ 0. It is significant problem when there are apriori information about possible spectrum behaviour. In the present work some assumptions of the entropy generalization was relaxed and alternative entropy formulation, with non‐uniform prior was used for analysis of simulated and experimental data. The new approach was applied to spectra analysis of the absorption kinetics of the bacteriorhodopsin (bR—light driven proton pump from archea Halobacterium salinarium) photocycle. It was shown that the process of the intermediate M formation is non‐exponential in the wild type bR. The non‐exponential process could be interpreted as result of the protein conformational changes during proton transfer from the Shiff‐base of bR.

The problem of estimation in binary response data has receivied a great number of alternative statistical solutions. Generalized linear models allow for a wide range of statistical models for regression data. The most used model is the logistic regression, see Hosmer et al. [6]. However, as Chen et al. [5] mentions, when the probability of a given binary response approaches 0 at a different rate than it approaches 1, symmetric linkages are inappropriate. A class of models based on Weibull distribution indexed by three parameters is introduced here. Maximum likelihood methods are employed to estimate the parameters. The objective of the present paper is to show a solution for the estimation problem under the Weibull model. An example showing the quality of the model is illustrated by comparing it with the alternative probit and logit models.

Tumor hypoxia is a state of oxygen deprivation in tumors. It has been associated with aggressive tumor phenotypes and with increased resistance to conventional cancer therapies. In this study, we report on the application of Bayesian sequential analysis in estimating the most probable value of tumor hypoxia quantification based on immunohistochemical assays of a biomarker.The ‘gold standard’ of tumor hypoxia assessment is a direct measurement of pO2 in vivo by the Eppendorf polarographic electrode, which is an invasive technique restricted to accessible sites and living tissues. An attractive alternative is immunohistochemical staining to detect proteins expressed by cells during hypoxia. Carbonic anhydrase IX (CAIX) is an enzyme expressed on the cell membrane during hypoxia to balance the immediate extracellular microenvironment. CAIX is widely regarded as a surrogate marker of chronic hypoxia in various cancers.The study was conducted with two different experimental procedures. The first data set was a ...

Data analysis suffers the curses of dimensionality and ill‐conditioning. These are often connected, incomplete data being an extreme form of ill‐conditioning. The conjugate gradient algorithm models the parameter‐to‐data transform to yield a convergent approximation that can largely compensate for ill‐conditioning. Long seen as restricted to optimisation, conjugate gradient can in fact be used to focus MCMC exploration, with potential gains in power.

In comparison with the foundations of probability calculus, the inescapable and controversial issue of how to assign probabilities has only recently become a matter of formal study. The introduction of information as a technical concept was a milestone, but the most promising entropic assignment methods still face unsolved difficulties, manifesting the incompleteness of plausible inference theory. In this paper we examine the situation faced by risk analysts in the critical field of extreme events modelling, where the former difficulties are especially visible, due to scarcity of observational data, the large impact of these phenomena and the obligation to assume professional responsibilities. To respond to the claim for a sound framework to deal with extremes, we propose a metafoundational approach to inference, based on a canon of extramathematical requirements. We highlight their strong moral content, and show how this emphasis in morality, far from being new, is connected with the historic origins of plausible inference. Special attention is paid to the contributions of Caramuel, a contemporary of Pascal, unfortunately ignored in the usual mathematical accounts of probability.

Modern data mining and bioinformatics have presented an important playground for statistical learning techniques, where the number of input variables is possibly much larger than the sample size of the training data. In supervised learning, logistic regression or probit regression can be used to model a binary output and form perceptron classification rules based on Bayesian inference. In these cases , there is a lot of interest in searching for sparse model in High Dimensional regression(/classification) setup. we first discuss two common challenges for analyzing high dimensional data. The first one is the curse of dimensionality. The complexity of many existing algorithms scale exponentially with the dimensionality of the space and by virtue of that algorithms soon become computationally intractable and therefore inapplicable in many real applications. secondly, multicollinearities among the predictors which severely slowdown the algorithm. In order to make Bayesian analysis operational in high dimensio...

Ensembles provide a powerful method for improving the performance of automated classifiers by constructing piecewise models that combine individual component classifier hypotheses. Together, the combined output of the component classifiers is more capable of fitting the type of complex decision boundaries in data sets where class boundaries overlap and class exemplars are disperse in feature space. A key ingredient to ensemble classifier induction is error diversity among component classifiers. Work in the ensemble literature suggests that ensemble construction should consider diversity even at some expense to individual classifier performance. To make such tradeoffs, a component classifier inducer requires knowledge of the choices made by its peers in the ensemble. In this work, we present a method called MaxEnt‐DiSCO that trains component classifiers collectively using entropy as a measure of error diversity. Using the maximum entropy framework, we share information on instance selection among component...

The Spatial Sensitivity Function (SSF) is used to quantify a detector’s sensitivity to a spatially‐distributed input signal. By weighting the incoming signal with the SSF and integrating, the overall scalar response of the detector can be estimated. This project focuses on estimating the SSF of a light intensity sensor consisting of a photodiode. This light sensor has been used previously in the Knuth Cyberphysics Laboratory on a robotic arm that performs its own experiments to locate a white circle in a dark field (Knuth et al., 2007). To use the light sensor to learn about its surroundings, the robot’s inference software must be able to model and predict the light sensor’s response to a hypothesized stimulus. Previous models of the light sensor treated it as a point sensor and ignored its spatial characteristics. Here we propose a parametric approach where the SSF is described by a mixture of Gaussians (MOG). By performing controlled calibration experiments with known stimulus inputs, we used nested sampling to estimate the SSF of the light sensor using an MOG model with the number of Gaussians ranging from one to five. By comparing the evidence computed for each MOG model, we found that one Gaussian is sufficient to describe the SSF to the accuracy we require. Future work will involve incorporating this more accurate SSF into the Bayesian machine learning software for the robotic system and studying how this detailed information about the properties of the light sensor will improve robot’s ability to learn.

Bayesian methods since the time of Laplace have been understood by their practitioners as closely aligned to the scientific method. Indeed a recent Champion of Bayesian methods, E. T. Jaynes, titled his textbook on the subject Probability Theory: the Logic of Science. Many philosophers of science including Karl Popper and Donald Campbell have interpreted the evolution of Science as a Darwinian process consisting of a ‘copy with selective retention’ algorithm abstracted from Darwin’s theory of Natural Selection. Arguments are presented for an isomorphism between Bayesian Methods and Darwinian processes. Universal Darwinism, as the term has been developed by Richard Dawkins, Daniel Dennett and Susan Blackmore, is the collection of scientific theories which explain the creation and evolution of their subject matter as due to the Operation of Darwinian processes. These subject matters span the fields of atomic physics, chemistry, biology and the social sciences. The principle of Maximum Entropy states that Systems will evolve to states of highest entropy subject to the constraints of scientific law. This principle may be inverted to provide illumination as to the nature of scientific law. Our best cosmological theories suggest the universe contained much less complexity during the period shortly after the Big Bang than it does at present. The scientific subject matter of atomic physics, chemistry, biology and the social sciences has been created since that time. An explanation is proposed for the existence of this subject matter as due to the evolution of constraints in the form of adaptations imposed on Maximum Entropy. It is argued these adaptations were discovered and instantiated through the Operations of a succession of Darwinian processes.

Physics is real. Measurement produces real numbers. Yet quantum mechanics uses complex arithmetic, in which −1 is necessary but mysteriously relates to nothing else. By applying the same sort of symmetry arguments that Cox [1, 2] used to justify probability calculus, we are now able to explain this puzzle.The dual device/object nature of observation requires us to describe the world in terms of pairs of real numbers about which we never have full knowledge. These pairs combine according to complex arithmetic, using Feynman’s rules.

In research situations usually approached by Decision Theory, it is only considered one researcher who collects a sample and makes a decision based on it. It can be shown that randomization of the sample does not improve the utility of the obtained results. Nevertheless, we present situations in which this approach is not satisfactory. First, we present a case in which randomization can be an important tool in order to achieve agreement between people with different opinions. Next, we present another situation in which there are two agents: the researcher—a person who collects the sample; and the decision‐maker—a person who makes decisions based on the sample collected. We show that problems emerge when the decision‐maker allows the researcher to arbitrarily choose a sample. We also show that the decision‐maker maximizes his expected utility requiring that the sample is collected randomly.

We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured, weakening the usual Bayesian "Occam's Razor". This is illustrated with a simple example involving what Jaynes called a "sure thing" hypothesis. Jaynes' resolution of the situation involved introducing a large number of alternative "sure thing" hypotheses that were possible before we observed the data. However, in more complex situations, it may not be possible to explicitly enumerate large numbers of alternatives. The entropic priors formalism produces the desired result without modifying the hypothesis space or requiring explicit enumeration of alternatives; all that is required is a good model for the prior predictive distribution for the data. This idea is illustrated with a simple rigged-lottery example, and we outline how this idea may help to resolve a recent debate amongst cosmologists: is dark energy a cosmological constant, or has it evolved with time in some way? And how shall we decide, when the data are in?, Comment: Presented at MaxEnt 2009, the 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 5-10, 2009, Oxford, Mississippi, USA)