Groups, information theory, and Einstein's likelihood principle

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.

A maximum likelihood framework for protein design

Affiliation: Claudia Kleinman, Nicolas Rodrigue & Hervé Philippe : Département de biochimie, Faculté de médecine, Université de Montréal

A SURVEY OF THE LIKELIHOOD APPROACH TO BIOEQUIVALENCE TRIALS

Bioequivalence trials are abbreviated clinical trials whereby a generic drug or new formulation is evaluated to determine if it is "equivalent" to a corresponding previously approved brand-name drug or formulation. In this manuscript, we survey the process of testing bioequivalence and advocate the likelihood paradigm for representing the resulting data as evidence. We emphasize the unique conflicts between hypothesis testing and confidence intervals in this area - which we believe are indicative of the existence of the systemic defects in the frequentist approach - that the likelihood paradigm avoids. We suggest the direct use of profile likelihoods for evaluating bioequivalence and examine the main properties of profile likelihoods and estimated likelihoods under simulation. This simulation study shows that profile likelihoods are a reasonable alternative to the (unknown) true likelihood for a range of parameters commensurate with bioequivalence research. Our study also shows that the standard methods in the current practice of bioequivalence trials offers only weak evidence from the evidential point of view.

Statistical Models for Co-occurrence Data

Modeling and predicting co-occurrences of events is a fundamental problem of unsupervised learning. In this contribution we develop a statistical framework for analyzing co-occurrence data in a general setting where elementary observations are joint occurrences of pairs of abstract objects from two finite sets. The main challenge for statistical models in this context is to overcome the inherent data sparseness and to estimate the probabilities for pairs which were rarely observed or even unobserved in a given sample set. Moreover, it is often of considerable interest to extract grouping structure or to find a hierarchical data organization. A novel family of mixture models is proposed which explain the observed data by a finite number of shared aspects or clusters. This provides a common framework for statistical inference and structure discovery and also includes several recently proposed models as special cases. Adopting the maximum likelihood principle, EM algorithms are derived to fit the model parameters. We develop improved versions of EM which largely avoid overfitting problems and overcome the inherent locality of EM--based optimization. Among the broad variety of possible applications, e.g., in information retrieval, natural language processing, data mining, and computer vision, we have chosen document retrieval, the statistical analysis of noun/adjective co-occurrence and the unsupervised segmentation of textured images to test and evaluate the proposed algorithms.

Aggregation functions based on penalties

This article studies a large class of averaging aggregation functions based on minimizing a distance from the vector of inputs, or equivalently, minimizing a penalty imposed for deviations of individual inputs from the aggregated value. We provide a systematization of various types of penalty based aggregation functions, and show how many special cases arise as the result. We show how new aggregation functions can be constructed either analytically or numerically and provide many examples. We establish connection with the maximum likelihood principle, and present tools for averaging experimental noisy data with distinct noise distributions.

Statistical Information: A Bayesian Perspective

We explore the meaning of information about quantities of interest. Our approach is divided in two scenarios: the analysis of observations and the planning of an experiment. First, we review the Sufficiency, Conditionality and Likelihood principles and how they relate to trivial experiments. Next, we review Blackwell Sufficiency and show that sampling without replacement is Blackwell Sufficient for sampling with replacement. Finally, we unify the two scenarios presenting an extension of the relationship between Blackwell Equivalence and the Likelihood Principle.

Modeling the survival of T-cell lymphocytes using compound branching processes

Radiotherapy has been a method of choice in cancer treatment for a number of years. Mathematical modeling is an important tool in studying the survival behavior of any cell as well as its radiosensitivity. One particular cell under investigation is the normal T-cell, the radiosensitivity of which may be indicative to the patient's tolerance to radiation doses.^ The model derived is a compound branching process with a random initial population of T-cells that is assumed to have compound distribution. T-cells in any generation are assumed to double or die at random lengths of time. This population is assumed to undergo a random number of generations within a period of time. The model is then used to obtain an estimate for the survival probability of T-cells for the data under investigation. This estimate is derived iteratively by applying the likelihood principle. Further assessment of the validity of the model is performed by simulating a number of subjects under this model.^ This study shows that there is a great deal of variation in T-cells survival from one individual to another. These variations can be observed under normal conditions as well as under radiotherapy. The findings are in agreement with a recent study and show that genetic diversity plays a role in determining the survival of T-cells. ^

Longitudinal categorical data analysis: A continuous -time Markov chain approach

In this dissertation, we propose a continuous-time Markov chain model to examine the longitudinal data that have three categories in the outcome variable. The advantage of this model is that it permits a different number of measurements for each subject and the duration between two consecutive time points of measurements can be irregular. Using the maximum likelihood principle, we can estimate the transition probability between two time points. By using the information provided by the independent variables, this model can also estimate the transition probability for each subject. The Monte Carlo simulation method will be used to investigate the goodness of model fitting compared with that obtained from other models. A public health example will be used to demonstrate the application of this method. ^

Quantum mechanics versus equivalence principle

We consider the scattering of a photon by a weak gravitational field, treated as an external field, up to second order of the perturbation expansion. The resulting cross section is energy dependent which indicates a violation of Galileo's equivalence principle (universality of free fall) and, consequently, of the classical equivalence principle. The deflection angle theta for a photon passing by the sun is evaluated afterward and the likelihood of detecting Delta theta/theta(E) theta-theta(E)/theta(E) (where theta(E) is the value predicted by Einstein's geometrical theory for the light bending) in the foreseeable future, is discussed.

The optimization principle in phylogenetic analysis tends to give incorrect topologies when the number of nucleotides or amino acids used is small

In the maximum parsimony (MP) and minimum evolution (ME) methods of phylogenetic inference, evolutionary trees are constructed by searching for the topology that shows the minimum number of mutational changes required (M) and the smallest sum of branch lengths (S), respectively, whereas in the maximum likelihood (ML) method the topology showing the highest maximum likelihood (A) of observing a given data set is chosen. However, the theoretical basis of the optimization principle remains unclear. We therefore examined the relationships of M, S, and A for the MP, ME, and ML trees with those for the true tree by using computer simulation. The results show that M and S are generally greater for the true tree than for the MP and ME trees when the number of nucleotides examined (n) is relatively small, whereas A is generally lower for the true tree than for the ML tree. This finding indicates that the optimization principle tends to give incorrect topologies when n is small. To deal with this disturbing property of the optimization principle, we suggest that more attention should be given to testing the statistical reliability of an estimated tree rather than to finding the optimal tree with excessive efforts. When a reliability test is conducted, simplified MP, ME, and ML algorithms such as the neighbor-joining method generally give conclusions about phylogenetic inference very similar to those obtained by the more extensive tree search algorithms.

Likelihood-maximising frameworks for enhanced in-car speech recognition

Speech recognition in car environments has been identified as a valuable means for reducing driver distraction when operating non-critical in-car systems. Likelihood-maximising (LIMA) frameworks optimise speech enhancement algorithms based on recognised state sequences rather than traditional signal-level criteria such as maximising signal-to-noise ratio. Previously presented LIMA frameworks require calibration utterances to generate optimised enhancement parameters which are used for all subsequent utterances. Sub-optimal recognition performance occurs in noise conditions which are significantly different from that present during the calibration session - a serious problem in rapidly changing noise environments. We propose a dialog-based design which allows regular optimisation iterations in order to track the changing noise conditions. Experiments using Mel-filterbank spectral subtraction are performed to determine the optimisation requirements for vehicular environments and show that minimal optimisation assists real-time operation with improved speech recognition accuracy. It is also shown that the proposed design is able to provide improved recognition performance over frameworks incorporating a calibration session.