Bayesian Model Selection Procedure Research Articles

A Bayesian phase I–II clinical trial design to find the biological optimal dose on drug combination

ABSTRACT In recent years, combined therapy shows expected treatment effect as they increase dose intensity, work on multiple targets and benefit more patients for antitumor treatment. However, dose -finding designs for combined therapy face a number of challenges. Therefore, under the framework of phase I–II, we propose a two-stage dose -finding design to identify the biologically optimal dose combination (BODC), defined as the one with the maximum posterior mean utility under acceptable safety. We model the probabilities of toxicity and efficacy by using linear logistic regression models and conduct Bayesian model selection (BMS) procedure to define the most likely pattern of dose–response surface. The BMS can adaptively select the most suitable model during the trial, making the results robust. We investigated the operating characteristics of the proposed design through simulation studies under various practical scenarios and showed that the proposed design is robust and performed well.

Bayesian model selection for structural equation models for myopia data

Structural equation models (SEMs) are extensively used in behavioral, social, and psychological research to model relationships between latent variables and observations. However, most models include redundant variables that are not important to relationships within the model. This study uses a Bayesian model selection procedure with mixture priors for SEMs to determine variables that have a meaningful relationship. The posterior probabilities for all possible models are calculated through the MCMC algorithm and the model with the largest probability is selected. The predictors of non-zero fixed-effect coefficients and/or non-zero random-effect variance components in the MCMC procedure are determined without the need for complex model selection criteria. The proposed methodologies are illustrated in a simulation and applied to a multidimensional longitudinal myopia data set in which the dimensionality of the parameter space is reduced and a more parsimonious model is selected.

Habituation in Aedes aegypti mosquito larvae is context specific.

Mosquito larvae live in water and perform a stereotyped escape response when a moving object projects its shadow on the water surface, indicating potential risk of predation. Repeated presentations of the shadow induce a decrease in the response as a result of habituation, a form of non-associative learning defined as the progressive and reversible decrease in response to a specific reiterative innocuous stimulus. Nevertheless, habituation can be context specific, which indicates an association between the context and the stimulus. The aim of this work was to study context specificity in habituation in mosquito larvae Aedes aegypti. Larvae were individually placed in Petri dishes positioned over black, white or black-white striped cardboard as background (visual context). Larvae were presented with a shadow produced by a cardboard square (training) over the course of 15 trials. After the 15th trial, the background was changed and the stimulus was presented once again (test). To analyse habituation in different contexts, we developed a series of learning curve models. We performed a Bayesian model selection procedure using those models and the data from the experiments to find which model best described the results. The selected model was a power law learning curve with six parameters (habituation rate; context-specific asymptotic habituation response, with one parameter per context, i.e. 3 parameters in total; response increase; and autocorrelation) describing the whole experimental setup with a generalised r2 of 0.96. According to the model, a single habituation rate would indicate that habituation was independent of the context, whilst asymptotic habituation would be context specific. If the background was changed after training, there was an increase in response in the test, evincing context specificity in habituation.

Neural surprise in somatosensory Bayesian learning.

Tracking statistical regularities of the environment is important for shaping human behavior and perception. Evidence suggests that the brain learns environmental dependencies using Bayesian principles. However, much remains unknown about the employed algorithms, for somesthesis in particular. Here, we describe the cortical dynamics of the somatosensory learning system to investigate both the form of the generative model as well as its neural surprise signatures. Specifically, we recorded EEG data from 40 participants subjected to a somatosensory roving-stimulus paradigm and performed single-trial modeling across peri-stimulus time in both sensor and source space. Our Bayesian model selection procedure indicates that evoked potentials are best described by a non-hierarchical learning model that tracks transitions between observations using leaky integration. From around 70ms post-stimulus onset, secondary somatosensory cortices are found to represent confidence-corrected surprise as a measure of model inadequacy. Indications of Bayesian surprise encoding, reflecting model updating, are found in primary somatosensory cortex from around 140ms. This dissociation is compatible with the idea that early surprise signals may control subsequent model update rates. In sum, our findings support the hypothesis that early somatosensory processing reflects Bayesian perceptual learning and contribute to an understanding of its underlying mechanisms.

Bayesian Multiple Change-Points Detection in a Normal Model with Heterogeneous Variances

This study considers the problem of multiple change-points detection. For this problem, we develop an objective Bayesian multiple change-points detection procedure in a normal model with heterogeneous variances. Our Bayesian procedure is based on a combination of binary segmentation and the idea of the screening and ranking algorithm (Niu and Zhang in Ann Appl Stat 6:1306–1326, 2012). Using the screening and ranking algorithm, we can overcome the drawbacks of binary segmentation, as it cannot detect a small segment of structural change in the middle of a large segment or segments of structural changes with small jump magnitude. We propose a detection procedure based on a Bayesian model selection procedure to address this problem in which no subjective input is considered. We construct intrinsic priors for which the Bayes factors and model selection probabilities are well defined. We find that for large sample sizes, our method based on Bayes factors with intrinsic priors is consistent. Moreover, we compare the behavior of the proposed multiple change-points detection procedure with existing methods through a simulation study and two real data examples.

Agricultural Productivity in Space: an Econometric Assessment Based on Farm‐Level Data

This work aims to investigate scale, scope and nature of spatial dependence of agricultural total factor productivity (TFP) by using farm‐level survey data. TFP is measured using transitive index numbers, and the spatial properties of TFP are assessed within a dynamic spatial panel data model designed to separate production fundamentals from productivity spillovers. Because of the statistical issues that typically affect spatial analyses based on survey data, a Bayesian model selection procedure is used to inspect the spatial properties of TFP at different aggregation levels and to search for the most appropriate spatial scale to conduct the investigation. The application concerns Italian FADN farm‐level data over the period 2008–2015 then aggregated at the NUTS3 level. Results suggest that agricultural productivity spillovers significantly occur though over a limited spatial range. The cumulated effects of the estimated diffusion mechanism are described through a set of spatial indicators and presented graphically.

Causes of Effects via a Bayesian Model Selection Procedure

Summary In causal inference, and specifically in the causes-of-effects problem, one is interested in how to use statistical evidence to understand causation in an individual case, and in particular how to assess the so-called probability of causation. The answer involves the use of potential responses, which describe what would have happened to the outcome if we had observed a different value for the exposure. However, even given the best possible statistical evidence for the association between exposure and outcome, we can typically only provide bounds for the probability of causation. Dawid and his colleagues highlighted some fundamental conditions, namely exogeneity, comparability and sufficiency, that are required to obtain such bounds from experimental data. The aim of the present paper is to provide methods to find, in specific cases, the best subsample of the reference data set to satisfy these requirements. For this, we introduce a new variable, expressing the preference whether or not to be exposed, and we set the question up as a model selection problem. The best model is selected by using the marginal probability of the responses and a suitable prior over the model space. An application in the educational field is presented.

Bayesian Model Selection in Order-Restricted Two-Way ANOVA Mixed Models

In this article, we propose several Bayesian model selection procedures, based on the spike and slab priors, to select significant variables while accounting for some restrictions on them. We concentrate on the following methods: Kuo and Mallick, stochastic search variable selection (SSVS), Ishwaran and Rao (NMIG). Bayesian computation is straightforward via simple Gibbs sampling algorithm. The methods are illustrated using simulated data and an application to the blood lead levels data. Results indicate that the proposed approaches perform very well in various situations.

Bayesian model selection for metal yield models in high-velocity impact

The shock hydrodynamics code ALEGRA and the optimization and uncertainty quantification toolkit Dakota are used to calibrate and select between three competing steel yield models, taking uncertainties in the system into account. A Bayesian model selection procedure is used to choose between the models in a systematic, automated fashion, within an uncertainty quantification workflow. Time-series penetration data of a long tungsten-alloy rod impacting a hardened steel plate at approximately 1250 m/s, along with their measurement uncertainty, are used to calibrate and select between the models. The procedure finds that between the Johnson–Cook, Steinberg–Guinan–Lund, and Zerilli–Armstrong stress models, Zerilli–Armstrong performs the best.

Bayesian Empirical Likelihood Inference with Complex Survey Data

SummaryWe propose a Bayesian empirical likelihood approach to survey data analysis on a vector of finite population parameters defined through estimating equations. Our method allows overidentified estimating equation systems and is applicable to both smooth and non-differentiable estimating functions. Our proposed Bayesian estimator is design consistent for general sampling designs and the Bayesian credible intervals are calibrated in the sense of having asymptotically valid design-based frequentist properties under single-stage unequal probability sampling designs with small sampling fractions. Large sample properties of the Bayesian inference proposed are established for both non-informative and informative priors under the design-based framework. We also propose a Bayesian model selection procedure with complex survey data and show that it works for general sampling designs. An efficient Markov chain Monte Carlo procedure is described for the required computation of the posterior distribution for general vector parameters. Simulation studies and an application to a real survey data set are included to examine the finite sample performances of the methods proposed as well as the effect of different types of prior and different types of sampling design.

Bayesian model for hydrological processes with jumping location and varying dispersion

This study proposes a Bayesian model for the nonstationary generalized extreme value (GEV) distributions with abrupt changes of location parameters and smooth change of scale parameters. Our motivation is that the quantiles of hydrological process depend on scale parameter as well as location parameter in the GEV distribution. The proposed model extends the nonstationary Bayesian model with jumping location parameters on the time domain, and it provides a wider class of models to explain abrupt location changes and smooth dispersion changes simultaneously as well as separately in the hydrological processes. This study also suggests the use of the Bayesian model selection procedure by logarithm of the pseudo marginal likelihood (LPML). Numerical study reveals that the proposed method can provide viable estimates of return levels through model selection. We apply the proposed method to analyze annual maximum precipitation acquired from the Korea Meteorological Administration.

Testing for time variation in the natural rate of interest

SummaryThis paper replicates in a wider sense the unobserved components model of Laubach and Williams (Review of Economics and Statistics, 2003, 85, 1063–1070) to estimate the natural rate of interest (NRI) and investigates the role of model uncertainty. A stochastic Bayesian model selection procedure is employed to test the hypothesis of time variation in the NRI against a constant NRI. The model selection confirms time variation in the NRI as a result of changes in potential output growth, but other determinants of the NRI are found constant.

BsamGP: An R Package for Bayesian Spectral Analysis Models Using Gaussian Process Priors

The Bayesian spectral analysis model (BSAM) is a powerful tool to deal with semiparametric methods in regression and density estimation based on the spectral representation of Gaussian process priors. The bsamGP package for R provides a comprehensive set of programs for the implementation of fully Bayesian semiparametric methods based on BSAM. Currently, bsamGP includes semiparametric additive models for regression, generalized models and density estimation. In particular, bsamGP deals with constrained regression models with monotone, convex/concave, S-shaped and U-shaped functions by modeling derivatives of regression functions as squared Gaussian processes. bsamGP also contains Bayesian model selection procedures for testing the adequacy of a parametric model relative to a non-specific semiparametric alternative and the existence of the shape restriction. To maximize computational efficiency, we carry out posterior sampling algorithms of all models using compiled Fortran code. The package is illustrated through Bayesian semiparametric analyses of synthetic data and benchmark data.

Objective Bayesian tests for Fieller–Creasy problem

From a statistical perspective, the Fieller–Creasy problem which involves inference about the ratio of two normal means has been quite challenging. In this study, we consider some solutions to this problem, based on an objective Bayesian model selection procedure. First, we develop the objective priors for testing the ratio of two normal means, based on measures of divergence between competing models. We then propose the intrinsic priors and the fractional priors for which the Bayes factors and model selection probabilities are well defined. In addition, we prove that the Bayes factors based on divergence-based priors, as well as intrinsic and fractional priors, are consistent for large sample sizes. Finally, we derive the Bayesian reference criterion from the Bayesian decision theory framework, based on the intrinsic discrepancy loss function. The behaviors of the Bayes factors are compared by undertaking a simulation study and using a case study example.

Intra-host interspecific larval parasitoid competition solved using modelling and bayesian statistics

Intraguild competition is a complex phenomenon that shapes parasitoid communities. When several species of parasitoids oviposit within the same individual host, a complex phenomenon of larval competitive interaction occurs. Within the same guild there is a specialization in competitive strategies, sometimes multiparasitism is avoided, but some species are facultative hyperparasitoids/predators of their competitors.As these interactions occur within a very small host and during a brief period of time, and that direct observation is very difficult to achieve, we used an alternative methodological approach. We analyzed intraguild host competition mechanisms via the combination of a series of competitive behavioral and functional response models, thurstonian competition model and set theory. These models were fitted via a reversible-jump bayesian model selection procedure to a series of competition experiments data using larvae of three species of Gonatocerus spp. (Hymenoptera: Mymaridae), egg parasitoids of the sharpshooter Tapajosa rubromarginata (Hemiptera: Cicadellidae) as a case-of-study. This study tests the influence of intrinsic interspecific competition between inmature stages within on an individual host, and parasitoid arrival order among the three parasitoid species.The results showed that the species differed in competitive behavior, some species were better competitors than others. Individuals arriving earlier had a competitive advantage, the weaker species were able to outcompete the stronger ones if the time advantage was longer than 18 h. All the species avoided already parasitized hosts, but in different degrees. The functional response was also different, with the best competitors having shorter estimated handling times. Using this analytical approach on a conventional experimental setup, we gained insights in the mechanism of competition, both on interference and exploitation, and in terms of host selection, all in a single analysis.

Scalable Bayesian Variable Selection Using Nonlocal Prior Densities in Ultrahigh-dimensional Settings.

Bayesian model selection procedures based on nonlocal alternative prior densities are extended to ultrahigh dimensional settings and compared to other variable selection procedures using precision-recall curves. Variable selection procedures included in these comparisons include methods based on g-priors, reciprocal lasso, adaptive lasso, scad, and minimax concave penalty criteria. The use of precision-recall curves eliminates the sensitivity of our conclusions to the choice of tuning parameters. We find that Bayesian variable selection procedures based on nonlocal priors are competitive to all other procedures in a range of simulation scenarios, and we subsequently explain this favorable performance through a theoretical examination of their consistency properties. When certain regularity conditions apply, we demonstrate that the nonlocal procedures are consistent for linear models even when the number of covariates p increases sub-exponentially with the sample size n. A model selection procedure based on Zellner's g-prior is also found to be competitive with penalized likelihood methods in identifying the true model, but the posterior distribution on the model space induced by this method is much more dispersed than the posterior distribution induced on the model space by the nonlocal prior methods. We investigate the asymptotic form of the marginal likelihood based on the nonlocal priors and show that it attains a unique term that cannot be derived from the other Bayesian model selection procedures. We also propose a scalable and efficient algorithm called Simplified Shotgun Stochastic Search with Screening (S5) to explore the enormous model space, and we show that S5 dramatically reduces the computing time without losing the capacity to search the interesting region in the model space, at least in the simulation settings considered. The S5 algorithm is available in an R package BayesS5 on CRAN.

Detection of Parametric Roll Resonance using Bayesian Discrete-Frequency Model Selection

This paper explores the use of two discrete-frequency models and a probabilistic Bayesian model selection procedure to detect the inception of parametric resonance in ships. We exploit knowledge of the coupling between roll and pitch due to the restoring forces arising from the shape of the hull to propose a single and a double discrete-frequency model. These models are then used within a Bayesian framework to compute the posterior distribution of the frequencies and amplitudes of the two models and this information is used for model selection. The latter is based on the computation of the probability that each one of the models is correct given the data analysed within a past window of samples. The algorithm is tested with data from a scale-model experiment for both regular and irregular sea states. The results indicate the proposed detector is effective in accusing the inception of parametric resonance.

Military L2 immersion

Abstract The purpose of the present study was to examine some of the motivations and longitudinal consequences of military service in L2 Swedish for L1 Finnish conscripts in Finland’s only Swedish language garrison. Cross-sectional data (N = 42), analyzed with Bayesian path analysis, indicates that promotional instrumentality enhanced participants’ L2 ideal selves, but integrative orientation did not. The L2 ideal self predicts L2 learning intentions in the army, but only among learners with low L2 proficiency at the beginning of military service. Longitudinal data (N = 17), analyzed with a Bayesian model selection procedure, shows that after six months in the army, participants reported higher levels of L2 proficiency, lower levels of L2 use anxiety and more positive attitudes towards L2 speakers than at the beginning of military service.

Bayesian meta-analysis: The role of the between-sample heterogeneity.

The random effect approach for meta-analysis was motivated by a lack of consistent assessment of homogeneity of treatment effect before pooling. The random effect model assumes that the distribution of the treatment effect is fully heterogenous across the experiments. However, other models arising by grouping some of the experiments are plausible. We illustrate on simulated binary experiments that the fully heterogenous model gives a poor meta-inference when fully heterogeneity is not the true model and that the knowledge of the true cluster model considerably improves the inference. We propose the use of a Bayesian model selection procedure for estimating the true cluster model, and Bayesian model averaging to incorporate into the meta-analysis the clustering estimation. A well-known meta-analysis for six major multicentre trials to assess the efficacy of a given dose of aspirin in post-myocardial infarction patients is reanalysed.

Objective Bayesian testing on the common mean of several normal distributions under divergence-based priors

This paper considers the problem of testing on the common mean of several normal distributions. We propose a solution based on a Bayesian model selection procedure in which no subjective input is considered. We construct the proper priors for testing hypotheses about the common mean based on measures of divergence between competing models. This method is called the divergence-based priors (Bayarri and Garcia-Donato in J R Stat Soc B 70:981---1003, 2008). The behavior of the Bayes factors based DB priors is compared with the fractional Bayes factor in a simulation study and compared with the existing tests in two real examples.