Calculation Of Posterior Probabilities Research Articles

METHODICAL FEATURES FOR STUDY OF CONCEPT AND PARAMETERS CALCULATION OF THEORETICAL SECRECY IN COMPUTER CRYPTOGRAPHY

The paper presents an original interpretation of the Shannon's ideas related to the concept of privacy with respect to the theoretical symmetric cryptographic transformations in computer cryptography and computation of posterior probabilities of the initial messages and keys. Used representation of symmetric cryptographic transformation as a relation on the set of tuples of the initial messages, keys and cryptograms, which is formed by the Cartesian product of the corresponding sets of finite sequences of 0 and 1. For reasons of practical use and providing a theoretical secrecy defined properties of such relation. The above calculation method can easily be programmed using well-known programming languages. The results help to simplify the process of studying relevant theoretical positions and can be used in the preparation of teaching materials for the presentation of the fundamentals of computer cryptography.

Generalized Continuous Time Bayesian Networks as a modelling and analysis formalism for dependable systems

We discuss the main features of Generalized Continuous Time Bayesian Networks (GCTBN) as a dependability formalism: we resort to two specific case studies adapted from the literature, and we discuss modelling choices, analysis results and advantages with respect to other formalisms. From the modelling point of view, GTCBN allow the introduction of general probabilistic dependencies and conditional dependencies in state transition rates of system components. From the analysis point of view, any task ascribable to a posterior probability computation can be implemented, among which the computation of system unreliability, importance indices, system monitoring, prediction and diagnosis.

Bayesian approach to powder phase identification

Identification of unknown materials using X-ray powder diffraction patterns is a commonly used and well established technique with a number of proved implementations. Generally, qualitative phase analysis of X-ray diffraction data includes ranking of candidate phases on the basis of similarity of their diffraction patterns to the measured one. A standard strategy of such a ranking by algorithmization of manual search criteria may become inconvenient for modification and adaptation for problems that are not supported by our intuition. Here, the problem of providing physically grounded expressions for candidate phase ranking is addressed. The approach is based on calculation of Bayesian posterior probabilities of the phases' presence in the sample. The choice of the expressions for the prior probabilities for deviations of phases' diffraction patterns from database entries determines the degree of physical detailing and may be made according to the specifics of the problem being solved. It is shown that even for simple exponential expressions for prior probabilities the approach identifies the phases for IUCr round robin cases correctly, as well as ensuring sufficient robustness of the results with respect to diffraction peak shifts and intensity variations.

Template-matching for text-dependent speaker verification

In the last decade, i-vector and Joint Factor Analysis (JFA) approaches to speaker modeling have become ubiquitous in the area of automatic speaker recognition. Both of these techniques involve the computation of posterior probabilities, using either Gaussian Mixture Models (GMM) or Deep Neural Networks (DNN), as a prior step to estimating i-vectors or speaker factors. GMMs focus on implicitly modeling phonetic information of acoustic features while DNNs focus on explicitly modeling phonetic/linguistic units. For text-dependent speaker verification, DNN-based systems have considerably outperformed GMM for fixed-phrase tasks. However, both approaches ignore phone sequence information. In this paper, we aim at exploiting this information by using Dynamic Time Warping (DTW) with speaker-informative features. These features are obtained from i-vector models extracted over short speech segments, also called online i-vectors. Probabilistic Linear Discriminant Analysis (PLDA) is further used to project online i-vectors onto a speaker-discriminative subspace. The proposed DTW approach obtained at least 74% relative improvement in equal error rate on the RSR corpus over other state-of-the-art approaches, including i-vector and JFA.

Posterior probability calculation procedure for recognition rate comparison

This paper focuses on the recognition rate comparison for competing recognition algorithms, which is a common problem of many pattern recognition research areas. The paper firstly reviews some traditional recognition rate comparison procedures and discusses their limitations. A new method, the posterior probability calculation (PPC) procedure is then proposed based on Bayesian technique. The paper analyzes the basic principle, process steps and computational complexity of the PPC procedure. In the Bayesian view, the posterior probability represents the credible degree (equal to confidence level) of the comparison results. The posterior probability of correctly selecting or sorting the competing recognition algorithms is derived, and the minimum sample size requirement is also pre-estimated and given out by the form of tables. To further illustrate how to use our method, the PPC procedure is used to prove the rationality of the experiential choice in one application and then to calculate the confidence level with the fixed-size datasets in another application. These applications reveal the superiority of the PPC procedure, and the discussions about the stopping rule further explain the underlying statistical causes. Finally we conclude that the PPC procedure achieves all the expected functions and be superior to the traditional methods.

Evaluation of water quality with application of Bayes' rule and entropy weight method

The quality of water of the river has a significant impact on human population and livestock in basin area. Six water quality indicators are monitored from the gauging stations of Brahmani River to assess the changing trends in the quality of water. The conventional Aggregative Index Evaluation method is applied to know the overall water quality index for its intended use. Further, in this study, Bayes’ rule is applied for comprehensive assessment. The likelihood estimates are obtained from the normal distribution and is pre-owned for posterior probability calculation through Bayes’ rule. Finally, the indicator weights are estimated by Shannon’s entropy weight method. The consequences of analysis specified that the indicator, CODMn, is affecting the quality of water more in Panposh downstream. Biological oxygen demand, TA as CaCO3, NH4–N and Nitrate-N are closely related to domestic pollution and agricultural non-point source pollution. The overall quality of water is improved during dry seasons than during wet seasons due to the dilution of pollutants. Comprehensive evaluation indicates that the water is acceptable for second grade surface source protection zones for centralised drinking water.

Annealing-based model-free expectation maximisation for multi-colour flow cytometry data clustering

This paper proposes an optimised model-free expectation maximisation method for automated clustering of high-dimensional datasets. The method is based on a recursive binary division strategy that successively divides an original dataset into distinct clusters. Each binary division is carried out using a model-free expectation maximisation scheme that exploits the posterior probability computation capability of the quasi-supervised learning algorithm subjected to a line-search optimisation over the reference set size parameter analogous to a simulated annealing approach. The divisions are continued until a division cost exceeds an adaptively determined limit. Experiment results on synthetic as well as real multi-colour flow cytometry datasets showed that the proposed method can accurately capture the prominent clusters without requiring any prior knowledge on the number of clusters or their distribution models.

Learn-as-you-go acceleration of cosmological parameter estimates

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitly describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of ΛCDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of 6.5 for Metropolis-Hastings and 3.5 for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly.

PWE-097 Pharmacological treatments for primary sclerosing cholangitis: a network meta-analysis

Introduction The optimal pharmaceutical treatment of primary sclerosing cholangitis (PSC) remains controversial. We performed a systematic review and network meta-analysis of different pharmacological interventions for the treatment of patients with PSC. Method We included randomised controlled trials (RCTs) of various pharmacological interventions compared with each other or with placebo in patients with PSC. We conducted network meta-analyses following the National Institute for Health and Care Excellence Decision Support Unit guidance to compare multiple interventions simultaneously for each of the primary (mortality, adverse events, health-related quality of life (HRQoL)) and secondary outcomes (decompensated cirrhosis, liver transplantation, malignancies) and only included trials in which participants could receive any of the interventions being assessed (transitivity assumption). We conducted a Bayesian network meta-analysis and calculated the odds ratios (OR), rate ratios, or hazard ratios with 95% credible intervals or Bayesian confidence intervals (CrI) for assessing the effect of treatment. We used three different non-informative priors and ensured that the results converged prior to calculation of posterior probabilities for Bayesian network meta-analysis. Results We included 22 RCTs on different treatment regimens for PSC, comprising of 1111 patients. There was no statistically significant difference in the mortality at 1-year, 5-years or at maximal follow-up between any of the treatments and placebo. There was no statistically significant difference in the proportion of patients with any adverse event, serious adverse events, liver decompensation, liver transplant, any malignancy, cholangiocarcinoma, or colorectal cancer at maximal follow-up or in the HRQoL between any of the treatments and placebo. Penicillamine was associated with higher number of total adverse events compared to placebo (rate ratio 1.93; 95% CrI 1.07 to 3.49) and to low-dose ursodeoxycholic acid (rate ratio 2.38; 95% CrI 1.02 to 5.56). There was no statistically significant difference in the total number of serious adverse events between any of the treatments and placebo. Conclusion None of the current therapies for primary sclerosing cholangitis are effective. Disclosure of interest K. Gurusamy: None Declared, F. Saffioti: None Declared, C. Toon: None Declared, B. Davidson: None Declared, E. Tsochatzis: None Declared, D. Thorburn Grant/Research Support from: Boston Scientific to fund a clinical research fellow.

A Recurrent Probabilistic Neural Network with Dimensionality Reduction Based on Time-series Discriminant Component Analysis.

This paper proposes a probabilistic neural network (NN) developed on the basis of time-series discriminant component analysis (TSDCA) that can be used to classify high-dimensional time-series patterns. TSDCA involves the compression of high-dimensional time series into a lower dimensional space using a set of orthogonal transformations and the calculation of posterior probabilities based on a continuous-density hidden Markov model with a Gaussian mixture model expressed in the reduced-dimensional space. The analysis can be incorporated into an NN, which is named a time-series discriminant component network (TSDCN), so that parameters of dimensionality reduction and classification can be obtained simultaneously as network coefficients according to a backpropagation through time-based learning algorithm with the Lagrange multiplier method. The TSDCN is considered to enable high-accuracy classification of high-dimensional time-series patterns and to reduce the computation time taken for network training. The validity of the TSDCN is demonstrated for high-dimensional artificial data and electroencephalogram signals in the experiments conducted during the study.

Applying Generalized Continuous Time Bayesian Networks to a reliability case study

We discuss the main features of Generalized Continuous Time Bayesian Networks (GCTBN) as a reliability formalism: we resort to a specific case study taken from the literature, and we discuss modeling choices, analysis results and advantages with respect to other formalisms. From the modeling point of view, GTCBN can represent dependencies involving system components, together with the possibility of a continuous time evaluation of the model. From the analysis point of view, any task ascribable to a posterior probability computation can be implemented, such as the computation of system unreliability, importance (sensitivity) indices, system state prediction and diagnosis.

Automated probabilistic estimation framework in real-time simultaneous objects tracking

State-of-the-art in real-time simultaneous objects tracking through automated probabilistic estimation framework has been considered. The approach proposed here is dealt with in association with a novel self-correcting particle filter to track a number of moving objects. This idea is applicable to track most of simultaneous non-rigid objects, since 3D image is analyzed. Due to the fact that the captured frames are taken into account as two dimensional data matrices, some appropriate extracted features of the processed frames could be utilized to make the third dimension. The whole of suitable features of moving objects, which cannot directly be applied to the process of posterior probability calculation, need to be fed to a neural network for the purpose of making the third dimension. Subsequently, the probabilistic estimation of the present self-correcting particle filter in each frame is corrected through the neural network results to estimate each identified object, appropriately, in its current frame. The effectiveness of the proposed approach performance is guaranteed, once the results of three known particle filter-based procedures are taken into real consideration as benchmark approaches. Experimental results demonstrate that the proposed approach outperforms the traditional tracking systems for various challenging scenarios. It is shown that the accuracy of the proposed approach is improved, while its tracking error is correspondingly decreased.

A New Naive Bayes Text Classification Algorithm

Aiming at the phenomenon that in text classification the calculation of prior probability is time-consuming and has little effect on the classification results and the error propagation of posterior probability affects the accuracy of classification, this paper improves the classical naive bayes algorithm and proposes a new text classification algorithm which accelerates the speed by removing the calculation of prior probability and reduces the accuracy loss of error propagation by adding an amplification factor .The experiments prove that removing the calculation of prior probability can accelerate the classification speed obviously and has little effect on the classification accuracy, and adding an amplification factor in the calculation of posterior probability can reduce the effect of error propagation and improve the classification accuracy. DOI : http://dx.doi.org/10.11591/telkomnika.v12i2.4180

Disease Mapping and Regression with Count Data in the Presence of Overdispersion and Spatial Autocorrelation: A Bayesian Model Averaging Approach

This paper applies the generalised linear model for modelling geographical variation to esophageal cancer incidence data in the Caspian region of Iran. The data have a complex and hierarchical structure that makes them suitable for hierarchical analysis using Bayesian techniques, but with care required to deal with problems arising from counts of events observed in small geographical areas when overdispersion and residual spatial autocorrelation are present. These considerations lead to nine regression models derived from using three probability distributions for count data: Poisson, generalised Poisson and negative binomial, and three different autocorrelation structures. We employ the framework of Bayesian variable selection and a Gibbs sampling based technique to identify significant cancer risk factors. The framework deals with situations where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. The evidence from applying the modelling methodology suggests that modelling strategies based on the use of generalised Poisson and negative binomial with spatial autocorrelation work well and provide a robust basis for inference.

The use of DNA barcoding to monitor the marine mammal biodiversity along the French Atlantic coast

In the last ten years, 14 species of cetaceans and five species of pinnipeds stranded along the Atlantic coast of Brittany in the North West of France. All species included, an average of 150 animals strand each year in this area. Based on reports from the stranding network operating along this coast, the most common stranding events comprise six cetacean species (Delphinus delphis, Tursiops truncatus, Stenella coeruleoalba, Globicephala melas, Grampus griseus, Phocoena phocoena)and one pinniped species (Halichoerus grypus). Rare stranding events include deep-diving or exotic species, such as arctic seals. In this study, our aim was to determine the potential contribution of DNA barcoding to the monitoring of marine mammal biodiversity as performed by the stranding network.We sequenced more than 500 bp of the 5’ end of the mitochondrial COI gene of 89 animals of 15 different species (12 cetaceans, and three pinnipeds). Except for members of the Delphininae, all species were unambiguously discriminated on the basis of their COI sequences. We then applied DNA barcoding to identify some “undetermined” samples. With again the exception of the Delphininae, this was successful using the BOLD identification engine. For samples of the Delphininae, we sequenced a portion of the mitochondrial control region (MCR), and using a non-metric multidimentional scaling plot and posterior probability calculations we were able to determine putatively each species. We then showed, in the case of the harbour porpoise, that COI polymorphisms, although being lower than MCR ones, could also be used to assess intraspecific variability. All these results show that the use of DNA barcoding in conjunction with a stranding network could clearly increase the accuracy of the monitoring of marine mammal biodiversity.

Nested Sampling for Bayesian Model Comparison in the Context of Salmonella Disease Dynamics

Understanding the mechanisms underlying the observed dynamics of complex biological systems requires the statistical assessment and comparison of multiple alternative models. Although this has traditionally been done using maximum likelihood-based methods such as Akaike's Information Criterion (AIC), Bayesian methods have gained in popularity because they provide more informative output in the form of posterior probability distributions. However, comparison between multiple models in a Bayesian framework is made difficult by the computational cost of numerical integration over large parameter spaces. A new, efficient method for the computation of posterior probabilities has recently been proposed and applied to complex problems from the physical sciences. Here we demonstrate how nested sampling can be used for inference and model comparison in biological sciences. We present a reanalysis of data from experimental infection of mice with Salmonella enterica showing the distribution of bacteria in liver cells. In addition to confirming the main finding of the original analysis, which relied on AIC, our approach provides: (a) integration across the parameter space, (b) estimation of the posterior parameter distributions (with visualisations of parameter correlations), and (c) estimation of the posterior predictive distributions for goodness-of-fit assessments of the models. The goodness-of-fit results suggest that alternative mechanistic models and a relaxation of the quasi-stationary assumption should be considered.

Two Fagan nomograms for the (genetic) evidence in a judicial context

While there are many computer programs that derive the likelihood ratio for genetic and other types of evidence, the Bayesian method of combination of prior probability coupled with the likelihood ratio, used by courts to ascertain posterior probability, has less support from software and other practical aids. Without proper instructions to a court, Bayes’ rule is either applied subconsciously by the judge, or prior probability is, by default, assigned a flat 50% probability by a forensic expert. In the worst case, it can be interpreted wrongly. A graphical representation using a nomogram is a proven way of representing Bayes’ theorem but remains underused in the field of forensics and the law. For this paper, I used the freeware package PyNomo to prepare two simple forensic nomograms allowing the graphical calculation of posterior probability by increasing or decreasing the prior probability due to evidence.

Bayesian inference of signaling network topology in a cancer cell line.

Protein signaling networks play a key role in cellular function, and their dysregulation is central to many diseases, including cancer. To shed light on signaling network topology in specific contexts, such as cancer, requires interrogation of multiple proteins through time and statistical approaches to make inferences regarding network structure. In this study, we use dynamic Bayesian networks to make inferences regarding network structure and thereby generate testable hypotheses. We incorporate existing biology using informative network priors, weighted objectively by an empirical Bayes approach, and exploit a connection between variable selection and network inference to enable exact calculation of posterior probabilities of interest. The approach is computationally efficient and essentially free of user-set tuning parameters. Results on data where the true, underlying network is known place the approach favorably relative to existing approaches. We apply these methods to reverse-phase protein array time-course data from a breast cancer cell line (MDA-MB-468) to predict signaling links that we independently validate using targeted inhibition. The methods proposed offer a general approach by which to elucidate molecular networks specific to biological context, including, but not limited to, human cancers. http://mukherjeelab.nki.nl/DBN (code and data).

Sequential Markov Chain Monte Carlo (MCMC) model discrimination

AbstractIn this paper a new approach to model discrimination is presented that takes advantage of Markov Chain Monte Carlo (MCMC) methods. It combines an experimental criterion first proposed by Roth (Roth, Design of Experiments for Discrimination Among rival Models, PhD, Thesis, Princeton University, New Jersey, USA, 1965) with an adaptation of a model selection method described by Chib and Jeliazkov [Chib and Jeliazkov, Stat. Neerl. 59, 30–44 (2005)], which uses an Acceptance–Rejection Metropolis–Hastings algorithm to evaluate the model marginal likelihood thus enabling the calculation of model posterior probabilities. It does so without requiring any linearisation of nonlinear models. In designing model discrimination experiments using the Roth criterion, MCMC methods are again used to find the mean of the predicted values by integrating over the entire parameter probability density function. The method is illustrated using the well‐known chemical reaction kinetics example first discussed by Box and Hill [Box and Hill, Technometrics 9, 57–71 (1967)]. The results indicate that the method is very successful in identifying the correct model. Higher error levels and more complex kinetics require on average more model discrimination experiments. © 2012 Canadian Society for Chemical Engineering

A Bayesian approach to the evaluation of comparisons of individually value-assigned reference materials

Several recent international comparison studies used a relatively novel experimental design to evaluate the measurement capabilities of participating organizations. These studies compared the values assigned by each participant to one or more qualitatively similar materials with measurements made on all of the materials by one laboratory under repeatability conditions. A statistical model was then established relating the values to the repeatability measurements; the extent of agreement between the assigned value(s) and the consensus model reflected the participants' measurement capabilities. Since each participant used their own supplies, equipment, and methods to produce and value-assign their material(s), the agreement between the assigned value(s) and the model was a fairer reflection of their intrinsic capabilities than provided by studies that directly compared time- and material-constrained measurements on unknown samples prepared elsewhere. A new statistical procedure is presented for the analysis of such data. The procedure incorporates several novel concepts, most importantly a leave-one-out strategy for the estimation of the consensus value of the measurand, model fitting via Bayesian posterior probabilities, and posterior coverage probability calculation for the assigned 95% uncertainty intervals. The benefits of the new procedure are illustrated using data from the CCQM-K54 comparison of eight cylinders of n-hexane in methane.