A Fully Bayesian Inference Framework for Population Studies of the Brain Microstructure

SUMMARY Bayesian methods, powered by Markov Chain Monte Carlo estimates of posterior densities, have become a cornerstone of geophysical inverse theory. These methods have special relevance to the deep Earth, where data are sparse and uncertainties are large. We present a strategy for efficiently solving hierarchical Bayesian geophysical inverse problems for fixed parametrizations using Hamiltonian Monte Carlo sampling, and highlight an effective methodology for determining optimal parametrizations from a set of candidates by using efficient approximations to leave-one-out cross-validation for model complexity. To illustrate these methods, we use a case study of differential traveltime tomography of the lowermost mantle, using short period P-wave data carefully selected to minimize the contributions of the upper mantle and inner core. The resulting tomographic image of the lowermost mantle has a relatively weak degree 2—instead there is substantial heterogeneity at all low spherical harmonic degrees less than 15. This result further reinforces the dichotomy in the lowermost mantle between relatively simple degree 2 dominated long-period S-wave tomographic models, and more complex short-period P-wave tomographic models.

Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation (AD) is a powerful tool to automate the calculation of derivatives and is preferable to more traditional methods, especially when differentiating complex algorithms and mathematical functions. The implementation of AD, however, requires some care to insure efficiency. Modern differentiation packages deploy a broad range of computational techniques to improve applicability, run time, and memory management. Among these techniques are operation overloading, region‐based memory, and expression templates. There also exist several mathematical techniques which can yield high performance gains when applied to complex algorithms. For example, semi‐analytical derivatives can reduce by orders of magnitude the runtime required to numerically solve and differentiate an algebraic equation. Open and practical problems include the extension of current packages to provide more specialized routines, and finding optimal methods to perform higher‐order differentiation.This article is categorized under: Algorithmic Development > Scalable Statistical Methods

Myocardial T1 mapping using an instantaneous signal loss simulation modeling and a Bayesian estimation method: A robust T1 extraction method free of tuning parameters

Are there benefits from NHST?

Background: A review of sleep and athletic performance (Fullagar et al. , 2015) reported that lack of sleep could have a negative impact on cognitive and physical performance. Numerous factors (i.e. jet-lag , hotels, pre-competition anxiety, early start times) can potentially disturb the sleep routine of athletes during competition (Lastella, Lovell and Sargent, 2014). Similar research has been done during a 3-day cycling race (Lastella et al. , 2014) and during a simulated cycling grand tour (Lastella et al. , 2015). Purpose: The aim of the study was to investigate whether cyclists sleep parameters would worsen during a 5-day cycling competition. We hypothesised that total sleep time and sleep efficiency would decrease over the course of the race. Methods: 5 professional male cyclists from Androni Giocattoli – Sidermec Professional Cycling Team participated in this study during Vuelta a AndalucA­a 2019. (Mean ± SD; age: 32 ± 4 years; stature: 179.8 ± 4.2 cm; body mass 67.8 ± 1.9 kg). In order to monitor quantity and quality of sleep, actigraph watches (Actiwatch Spectrum PRO, Philips Respironics, Murrysville, PA, USA) and sleep diaries were used following a method applied several times in the literature (Halson et al. , 2014; Lastella et al. , 2014, 2015; Sargent, Halson and Roach, 2014). Data were collected for 5 days (from the night before the start of the race until the morning of the last day of competition). Since the number of cyclists per team is limited by race regulations, the Bayesian Statistical Analysis framework offers an advantage over null-hypothesis significance testing as not depending on large samples (van de Schoot and Depaoli, 2014). Results: Details of the Tour stages are shown in Table 1. A summary of the data collected are presented in Table 2. Results of Bayesian analysis can be found in Table 3. Get up time decreased over the stages (Figure 1). Cyclists woke up earlier on the first day of competition than the day before the start. Get up time was earlier the last day of competition than the first day of the race. Total sleep time decreased during the race (Figure 2) compared to the night before the start, cyclists slept less the first and the last night of the Tour, and sleep efficiency decreased during the event (Figure 3). Sleep efficiency was lower during the last night of competition compared to the night before the start of the Tour. The rest of the parameters were not affected by time. Discussion: The findings of this study demonstrate that some sleep parameters decreased over time during a multi-day cycling Tour. Sleep time decreased over the course of the Tour, with cyclists sleeping more the night before the start of the event than after the first stage. Sleep efficiency decreased during the Tour, particularly, the night prior to the final stage. Conclusions: The results of this study demonstrate that the sleep of professional cyclists is affected during a 5-day cycling Tour. These data emphasise the importance for athletes and coaches of sleep hygiene routines to optimise the quality and quantity of sleep, such as setup a consistent bedtime, control room temperature, avoid caffeine consumption 4-5h before going to bed, and reduce the use of electronic equipment prior to bedtime.

BackgroundThe ChIP-chip technology has been used in a wide range of biomedical studies, such as identification of human transcription factor binding sites, investigation of DNA methylation, and investigation of histone modifications in animals and plants. Various methods have been proposed in the literature for analyzing the ChIP-chip data, such as the sliding window methods, the hidden Markov model-based methods, and Bayesian methods. Although, due to the integrated consideration of uncertainty of the models and model parameters, Bayesian methods can potentially work better than the other two classes of methods, the existing Bayesian methods do not perform satisfactorily. They usually require multiple replicates or some extra experimental information to parametrize the model, and long CPU time due to involving of MCMC simulations.ResultsIn this paper, we propose a Bayesian latent model for the ChIP-chip data. The new model mainly differs from the existing Bayesian models, such as the joint deconvolution model, the hierarchical gamma mixture model, and the Bayesian hierarchical model, in two respects. Firstly, it works on the difference between the averaged treatment and control samples. This enables the use of a simple model for the data, which avoids the probe-specific effect and the sample (control/treatment) effect. As a consequence, this enables an efficient MCMC simulation of the posterior distribution of the model, and also makes the model more robust to the outliers. Secondly, it models the neighboring dependence of probes by introducing a latent indicator vector. A truncated Poisson prior distribution is assumed for the latent indicator variable, with the rationale being justified at length.ConclusionThe Bayesian latent method is successfully applied to real and ten simulated datasets, with comparisons with some of the existing Bayesian methods, hidden Markov model methods, and sliding window methods. The numerical results indicate that the Bayesian latent method can outperform other methods, especially when the data contain outliers.

Bayesian marginal influence assessment

Despite more than half a century of criticism, significance testing continues to be used commonly by ecologists. Significance tests are widely misused and misunderstood, and even when properly used, they are not very informative for most ecological data. Problems of misuse and misinterpretation include: (i) invalid logic; (ii) rote use; (iii) equating statistical significance with biological importance; (iv) regarding the P‐value as the probability that the null hypothesis is true; (v) regarding the P‐value as a measure of effect size; and (vi) regarding the P‐value as a measure of evidence. Significance tests are poorly suited for inference because they pose the wrong question. In addition, most null hypotheses in ecology are point hypotheses already known to be false, so whether they are rejected or not provides little additional understanding. Ecological data rarely fit the controlled experimental setting for which significance tests were developed. More satisfactory methods of inference assess the degree of support which data provide for hypotheses, measured in terms of information theory (model‐based inference), likelihood ratios (likelihood inference) or probability (Bayesian inference). Modern statistical methods allow multiple data sets to be combined into a single likelihood framework, avoiding the loss of information that can occur when data are analyzed in separate steps. Inference based on significance testing is compared with model‐based, likelihood and Bayesian inference using data on an endangered porpoise,Phocoena sinus. All of the alternatives lead to greater understanding and improved inference than provided by a P‐value and the associated statement of statistical significance.

The role of hydrophilic (polyethylene glycol) and hydrophobic (light liquid paraffin wax) chemicals as self-curing compounds to improve the curing efficiency of self-compacting concrete (SCC) was investigated in terms of performance and microstructure. The parameters considered in the investigation were the concrete grade, dosage of self-curing compound, curing regime, temperature and duration of curing. Performance investigations included water retention tests, compressive strength test and durability studies (porosity, sorptivity, rapid chloride permeability and accelerated corrosion permeability tests). Microstructural analyses studies (X-ray diffraction analysis and scanning electron microscopy) were conducted to confirm the results obtained from the macrostructural studies. Two grades of concretes, with compressive strengths of 70 MPa and 50 MPa, were used. Based on experimentation and microstructural studies, it was concluded that the addition of optimum dosages of hydrophilic and hydrophobic chemicals arrested loss of moisture, resulting in improved water retention and progressive hydration of SCC.

Suprathreshold fiber cluster statistics: Leveraging white matter geometry to enhance tractography statistical analysis

A microstructural examination of concrete has recently attracted people's interest. For the study of concrete microstructure, many research studies attempt a microstructural examination of concrete. A microstructural analysis aids in the investigation of the microstructure in concrete in order to better understand the performance of concrete ingredients. This study focuses on the different sophisticated microstructural analysis approaches. Self-compacting concrete (SCC) applications are becoming more popular around the world as the construction of megastructures progresses. This is a major driving force behind the topic of self-compacting concrete microstructural analysis methodologies. This literature review studies the sophisticated instrumental techniques and gives a brief presentation about particular usage of all the techniques. The information could be utilized as a guide in growing the use of microstructural analysis methods for the research in the microstructural properties of SCC and other type of concrete. The microstructural characteristics of SCC in the plastic and hard stages are thoroughly examined. Concrete's microstructure has a considerable impact on qualities like as strength and durability. The microstructure of SCC is greatly influenced by the addition of various components, and the effect on fresh and mechanical characteristics of SCC is visualised. With the use of microstructural analysis methodologies, researchers were able to alter the behaviour of SCC by varying the ingredients. As a result, microstructural analysis provides a tool for studying the microstructure of SCC, as well as the interactions between various alternative materials and self-compacting concrete.

Chapter 3 provides a brief overview of null hypothesis significance testing and points out its primary defects. It then outlines the neo-Fisherian account of tests of statistical significance, along with a second option contained in the philosophy of statistics known as the error-statistical philosophy, both of which are defensible. Tests of statistical significance are the most widely used means for evaluating hypotheses and theories in psychology. A massive critical literature has developed in psychology, and the behavioral sciences more generally, regarding the worth of these tests. The chapter provides a list of important lessons learned from the ongoing debates about tests of significance.

Bayesian methods in family business research

<p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d612827e85"> <b>Objectives:</b> The utility and feasibility of Neural network (NN) and Bayesian in PK-PD analysis were investigated. Recently, Hierarchical Deep Compartment Modeling (HDCM) workflow was shown to be able to quantify uncertainty of NN model predicted parameters and was successfully tested on synthetic data from 10 subjects [ <a class="xref-link" href="#r1">1</a>]. While conceptually appealing, this approach incurs prohibitive run time for typical clinical datasets due to the complexity of the high-dimensional Bayesian posterior distribution. <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d612827e93">To enable the full covariate modeling in PK-PD analyses with practical run time, this research utilized flow-based generative deep learning [ <a class="xref-link" href="#r2">2</a>] in addition to NN and Bayesian inference. A novel approach was developed, which trains normalizing flows (NFs) [ <a class="xref-link" href="#r2">2</a>] to generate both samples and their associated probabilities from the posterior distribution. This approach allows breaking down Bayesian inference from a large dataset into manageable subtasks that can be completed sequentially while accumulating all information from the whole dataset. <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d612827e101"> <b>Methods:</b> The workflow was implemented in Julia to perform PopPK/PD analysis on simulated dataset for a hypothetical small molecule drug with pharmacodynamic activity following stimulatory response function. The data included 302 subjects from phase 1 and phase 2 studies, with formulation, subject type, weight, gender, age as PK covariates and 3 PD covariates (PDcov1-3). <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d612827e106">The covariate-PK/PD parameter relationships were modeled by NN. Loose priors and standard normal distributions were set for fixed, random effect and NN parameters. The initial analysis step processed one sub-dataset (first subtask). The No-U-Turn Sampler (NUTS) [ <a class="xref-link" href="#r3">3</a>] was used to draw samples from the intermediate posterior distribution. A NF [ <a class="xref-link" href="#r2">2</a>] was trained to establish a probability distribution from these samples. The NF-induced distribution became the prior distribution input for the second analysis step, with the likelihood evaluated only for the next sub-dataset. This iterative procedure was repeated until the whole dataset was analyzed. <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d612827e114"> <b>Results:</b> A six-step RealNVP[ <a class="xref-link" href="#r4">4</a>] architecture using NN conditioners of 2 hidden layers, width 100, was adequate for carrying posterior information forward across 30 sub-datasets. NUTS produced well-mixing chains (R^ &lt; 1.01). Full covariate analysis testing was completed within 3 days on a 64-core compute node. Posterior predictive checks confirmed that predicted concentrations/PD responses based on the posterior distributions captured observed drug concentrations/responses. Forest plots generated from the NN-predicted covariate effects correctly identified covariate-parameter relationships consistent with NONMEM-based Stepwise Covariate Modeling approach [ <a class="xref-link" href="#r5">5</a>]. <p xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" dir="auto" id="d612827e125"> <b>Conclusions:</b> Bayesian updates enabled by normalizing flows was shown to be a promising direction for improving scalability of NN-based PopPK/PD analyses. The newly developed method adds flexibility to analysis planning, allowing the posterior distribution to be provisionally generated from existing data while waiting for additional clinical studies, from which new information can be readily incorporated.

Missing data are frequently encountered in longitudinal clinical trials. To better monitor and understand the progress over time, one must handle the missing data appropriately and examine whether the missing data mechanism is ignorable or nonignorable. In this article, we develop a new probit model for longitudinal binary response data. It resolves a challenging issue for estimating the variance of the random effects, and substantially improves the convergence and mixing of the Gibbs sampling algorithm. We show that when improper uniform priors are specified for the regression coefficients of the joint multinomial model via a sequence of one-dimensional conditional distributions for the missing data indicators under nonignorable missingness, the joint posterior distribution is improper. A variation of Jeffreys prior is thus established as a remedy for the improper posterior distribution. In addition, an efficient Gibbs sampling algorithm is developed using a collapsing technique. Two model assessment criteria, the deviance information criterion (DIC) and the logarithm of the pseudomarginal likelihood (LPML), are used to guide the choices of prior specifications and to compare the models under different missing data mechanisms. We report on extensive simulations conducted to investigate the empirical performance of the proposed methods. The proposed methodology is further illustrated using data from an HIV prevention clinical trial.