Phantom perception as a Bayesian inference problem: a pilot study.

Tinnitus is the perception of a continuous sound in the absence of an external source. Although the role of the auditory system is well investigated, there is a gap in how multisensory signals are integrated to produce a single percept in tinnitus. Here, we train participants to learn a new sensory environment by associating a cue with a target signal that varies in perceptual threshold. In the test phase, we present only the cue to see whether the person perceives an illusion of the target signal. We perform two separate experiments to observe the behavioral and electrophysiological responses to the learning and test phases in 1) healthy young adults and 2) people with continuous subjective tinnitus and matched control subjects. We observed that in both parts of the study the percentage of false alarms was negatively correlated with the 75% detection threshold. Additionally, the perception of an illusion goes together with increased evoked response potential in frontal regions of the brain. Furthermore, in patients with tinnitus, we observe no significant difference in behavioral or evoked response in the auditory paradigm, whereas patients with tinnitus were more likely to report false alarms along with increased evoked activity during the learning and test phases in the visual paradigm. This emphasizes the importance of integrity of sensory pathways in multisensory integration and how this process may be disrupted in people with tinnitus. Furthermore, the present study also presents preliminary data supporting evidence that tinnitus patients may be building stronger perceptual models, which needs future studies with a larger population to provide concrete evidence on.NEW & NOTEWORTHY Tinnitus is the continuous phantom perception of a ringing in the ears. Recently, it has been suggested that tinnitus may be a maladaptive inference of the brain to auditory anomalies, whether they are detected or undetected by an audiogram. The present study presents empirical evidence for this hypothesis by inducing an illusion in a sensory domain that is damaged (auditory) and one that is intact (visual). It also presents novel information about how people with tinnitus process multisensory stimuli in the audio-visual domain.

Perceptual axioms are irreconcilable with Euclidean geometry.

There are different definitions of axioms, but the one that seems to have general approval is that axioms are statements whose truths are universally accepted but cannot be proven; they are the foundation from which further propositional truths are derived. Previous attempts, led by David Hilbert, to show that all of mathematics can be built into an axiomatic system that is complete and consistent failed when Kurt Gödel proved that there will always be statements which are known to be true but can never be proven within the same axiomatic system. But Gödel and his followers took no account of brain mechanisms that generate and mediate logic. In this largely theoretical paper, but backed by previous experiments and our new ones reported below, we show that in the case of so-called 'optical illusions', there exists a significant and irreconcilable difference between their visual perception and their description according to Euclidean geometry; when participants are asked to adjust, from an initial randomised state, the perceptual geometric axioms to conform to the Euclidean description, the two never match, although the degree of mismatch varies between individuals. These results provide evidence that perceptual axioms, or statements known to be perceptually true, cannot be described mathematically. Thus, the logic of the visual perceptual system is irreconcilable with the cognitive (mathematical) system and cannot be updated even when knowledge of the difference between the two is available. Hence, no one brain reality is more 'objective' than any other.

Historical controls in clinical trials: a note on linking Pocock's model with the robust mixture priors.

Several Bayesian methods have been proposed to borrow information dynamically from historical controls in clinical trials. In this note, we identify key features of the relationship between the first method proposed, the bias-variance method, which is strongly related to the commensurate prior approach, and a more recent and widely used approach called robust mixture priors (RMP). We focus on the two key terms that need to be chosen to define the RMP, namely $w$, the prior probability that the new trial differs systematically from the historical trial, and $s_v^2$, the variance of the vague component of the RMP. The relationship with Pocock's prior reveals that different combinations of these two terms can express similar prior beliefs about the amount of information provided by the historical data. This demonstrates the value of fixing $s_v^2$, e.g., so the vague component is "worth one subject." Prior belief about the relevance of the historical data is then driven by a single value, the prespecified weight $w$.

Resolution enhancement, noise suppression, and joint T2* decay estimation in dual-echo sodium-23 MR imaging using anatomically guided reconstruction.

PURPOSE: Sodium MRI is challenging because of the low tissue concentration of the 23 Na nucleus and its extremely fast biexponential transverse relaxation rate. In this article, we present an iterative reconstruction framework using dual-echo 23 Na data and exploiting anatomical prior information (AGR) from high-resolution, low-noise, 1 H MR images. This framework enables the estimation and modeling of the spatially varying signal decay due to transverse relaxation during readout (AGRdm), which leads to images of better resolution and reduced noise resulting in improved quantification of the reconstructed 23 Na images. METHODS: The proposed framework was evaluated using reconstructions of 30 noise realizations of realistic simulations of dual echo twisted projection imaging (TPI) 23 Na data. Moreover, three dual echo 23 Na TPI brain datasets of healthy controls acquired on a 3T Siemens Prisma system were reconstructed using conventional reconstruction, AGR and AGRdm. RESULTS: Our simulations show that compared to conventional reconstructions, AGR and AGRdm show improved bias-noise characteristics in several regions of the brain. Moreover, AGR and AGRdm images show more anatomical detail and less noise in the reconstructions of the experimental data sets. Compared to AGR and the conventional reconstruction, AGRdm shows higher contrast in the sodium concentration ratio between gray and white matter and between gray matter and the brain stem. CONCLUSION: AGR and AGRdm generate 23 Na images with high resolution, high levels of anatomical detail, and low levels of noise, potentially enabling high-quality 23 Na MR imaging at 3T.

Manipulating Prior Beliefs Causally Induces Under- and Overconfidence.

Humans differ vastly in the confidence they assign to decisions. Although such under- and overconfidence relate to fundamental life outcomes, a computational account specifying the underlying mechanisms is currently lacking. We propose that prior beliefs in the ability to perform a task explain confidence differences across participants and tasks, despite similar performance. In two perceptual decision-making experiments, we show that manipulating prior beliefs about performance during training causally influences confidence in healthy adults (N = 50 each; Experiment 1: 8 men, one nonbinary; Experiment 2: 5 men) during a test phase, despite unaffected objective performance. This is true when prior beliefs are induced via manipulated comparative feedback and via manipulated training-phase difficulty. Our results were accounted for within an accumulation-to-bound model, explicitly modeling prior beliefs on the basis of earlier task exposure. Decision confidence is quantified as the probability of being correct conditional on prior beliefs, causing under- or overconfidence. We provide a fundamental mechanistic insight into the computations underlying under- and overconfidence.

Navigating Visual Challenges: How Parkinson's Disease Alters Cognitive Priorities in Visual Search.

OBJECTIVE: Parkinson's disease (PD) hampers visual search tasks such as reading, driving, and navigation. We examined expectations from past experiences, guiding cognition and contextual priors, on visual search in PD. METHODS: We compared eye movements as PD and healthy participants searched for a hidden object (target) in cluttered real-world scenes. RESULTS: PD participants prolonged fixation on high-probability (high-prior) locations for the target, consistent across expected and unexpected scenario. Such emphasis on contextual visual priors, evidenced by high fixation duration on high-probability areas, was beneficial when the target was at the expected location but presented challenges when the target was situated in an unlikely place. CONCLUSION: This study contributes to understanding how PD impacts visual search behavior and cognitive processing. The findings indicate that PD alters attention allocation and visual processing by affecting the utilization of contextual visual priors. It provides insights for potential interventions targeting visuo-cognitive deficits in PD patients. Published 2024. This article is a U.S. Government work and is in the public domain in the USA.

Robotically-induced auditory-verbal hallucinations: combining self-monitoring and strong perceptual priors.

BACKGROUND: Inducing hallucinations under controlled experimental conditions in non-hallucinating individuals represents a novel research avenue oriented toward understanding complex hallucinatory phenomena, avoiding confounds observed in patients. Auditory-verbal hallucinations (AVH) are one of the most common and distressing psychotic symptoms, whose etiology remains largely unknown. Two prominent accounts portray AVH either as a deficit in auditory-verbal self-monitoring, or as a result of overly strong perceptual priors. METHODS: In order to test both theoretical models and evaluate their potential integration, we developed a robotic procedure able to induce self-monitoring perturbations (consisting of sensorimotor conflicts between poking movements and corresponding tactile feedback) and a perceptual prior associated with otherness sensations (i.e. feeling the presence of a non-existing another person). RESULTS: Here, in two independent studies, we show that this robotic procedure led to AVH-like phenomena in healthy individuals, quantified as an increase in false alarm rate in a voice detection task. Robotically-induced AVH-like sensations were further associated with delusional ideation and to both AVH accounts. Specifically, a condition with stronger sensorimotor conflicts induced more AVH-like sensations (self-monitoring), while, in the otherness-related experimental condition, there were more AVH-like sensations when participants were detecting other-voice stimuli, compared to detecting self-voice stimuli (strong-priors). CONCLUSIONS: By demonstrating an experimental procedure able to induce AVH-like sensations in non-hallucinating individuals, we shed new light on AVH phenomenology, thereby integrating self-monitoring and strong-priors accounts.

A scaled kernel density estimation prior for dynamic borrowing of historical information with application to clinical trial design.

Incorporating historical data into a current data analysis can improve estimation of parameters shared across both datasets and increase the power to detect associations of interest while reducing the time and cost of new data collection. Several methods for prior distribution elicitation have been introduced to allow for the data-driven borrowing of historical information within a Bayesian analysis of the current data. We propose scaled Gaussian kernel density estimation (SGKDE) prior distributions as potentially more flexible alternatives. SGKDE priors directly use posterior samples collected from a historical data analysis to approximate probability density functions, whose variances depend on the degree of similarity between the historical and current datasets, which are used as prior distributions in the current data analysis. We compare the performances of the SGKDE priors with some existing approaches using a simulation study. Data from a recently completed phase III clinical trial of a maternal vaccine for respiratory syncytial virus are used to further explore the properties of SGKDE priors when designing a new clinical trial while incorporating historical data. Overall, both studies suggest that the new approach results in improved parameter estimation and power in the current data analysis compared to the considered existing methods.

Ecologically informed priors improve Bayesian model estimates of species richness and occupancy for undetected species.

Detection error can bias observations of ecological processes, especially when some species are never detected during sampling. In many communities, the probable identity of these missing species is known from previous research and natural history collections, but this information is rarely incorporated into subsequent models. Here, I present prior aggregation as a method for including information from external sources in Bayesian hierarchical detection models. Prior aggregation combines information from multiple prior distributions, in this case, an ecologically informative, species-level prior, and an uninformative community-level prior. This approach incorporates external information into the model without sacrificing the advantages of modeling species in the context of the community. Using simulated data supplied to a multispecies occupancy model, I demonstrated that prior aggregation improves estimates of (1) metacommunity richness and (2) environmental covariates were associated with species-specific occupancy probabilities. When applied to a dataset of small mammals in Vermont, prior aggregation allowed the model to estimate occupancy correlates of the Eastern cottontail Sylvilagus floridanus, a species observed at several sites in the region but never captured. Prior aggregation can be used to improve the analysis of several important metrics in population and community ecology, including abundance, survivorship, and diversity.

Spatial-temporal Bayesian accelerated failure time models for survival endpoints with applications to prostate cancer registry data.

Prostate cancer is the most common cancer after non-melanoma skin cancer and the second leading cause of cancer deaths in US men. Its incidence and mortality rates vary substantially across geographical regions and over time, with large disparities by race, geographic regions (i.e., Appalachia), among others. The widely used Cox proportional hazards model is usually not applicable in such scenarios owing to the violation of the proportional hazards assumption. In this paper, we fit Bayesian accelerated failure time models for the analysis of prostate cancer survival and take dependent spatial structures and temporal information into account by incorporating random effects with multivariate conditional autoregressive priors. In particular, we relax the proportional hazards assumption, consider flexible frailty structures in space and time, and also explore strategies for handling the temporal variable. The parameter estimation and inference are based on a Monte Carlo Markov chain technique under a Bayesian framework. The deviance information criterion is used to check goodness of fit and to select the best candidate model. Extensive simulations are performed to examine and compare the performances of models in different contexts. Finally, we illustrate our approach by using the 2004-2014 Pennsylvania Prostate Cancer Registry data to explore spatial-temporal heterogeneity in overall survival and identify significant risk factors.

Explanatory power by vagueness. Challenges to the strong prior hypothesis on hallucinations exemplified by the Charles-Bonnet-Syndrome.

Predictive processing models are often ascribed a certain generality in conceptually unifying the relationships between perception, action, and cognition or the potential to posit a 'grand unified theory' of the mind. The limitations of this unification can be seen when these models are applied to specific cognitive phenomena or phenomenal consciousness. Our article discusses these shortcomings for predictive processing models of hallucinations by the example of the Charles-Bonnet-Syndrome. This case study shows that the current predictive processing account omits essential characteristics of stimulus-independent perception in general, which has critical phenomenological implications. We argue that the most popular predictive processing model of hallucinatory conditions - the strong prior hypothesis - fails to fully account for the characteristics of nonveridical perceptual experiences associated with Charles-Bonnet-Syndrome. To fill this explanatory gap, we propose that the strong prior hypothesis needs to include reality monitoring to apply to more than just veridical percepts.

Effects of sceptical priors on the performance of adaptive clinical trials with binary outcomes.

It is unclear how sceptical priors impact adaptive trials. We assessed the influence of priors expressing a spectrum of scepticism on the performance of several Bayesian, multi-stage, adaptive clinical trial designs using binary outcomes under different clinical scenarios. Simulations were conducted using fixed stopping rules and stopping rules calibrated to keep type 1 error rates at approximately 5%. We assessed total sample sizes, event rates, event counts, probabilities of conclusiveness and selecting the best arm, root mean squared errors (RMSEs) of the estimated treatment effect in the selected arms, and ideal design percentages (IDPs; which combines arm selection probabilities, power, and consequences of selecting inferior arms), with RMSEs and IDPs estimated in conclusive trials only and after selecting the control arm in inconclusive trials. Using fixed stopping rules, increasingly sceptical priors led to larger sample sizes, more events, higher IDPs in simulations ending in superiority, and lower RMSEs, lower probabilities of conclusiveness/selecting the best arm, and lower IDPs when selecting controls in inconclusive simulations. With calibrated stopping rules, the effects of increased scepticism on sample sizes and event counts were attenuated, and increased scepticism increased the probabilities of conclusiveness/selecting the best arm and IDPs when selecting controls in inconclusive simulations without substantially increasing sample sizes. Results from trial designs with gentle adaptation and non-informative priors resembled those from designs with more aggressive adaptation using weakly-to-moderately sceptical priors. In conclusion, the use of somewhat sceptical priors in adaptive trial designs with binary outcomes seems reasonable when considering multiple performance metrics simultaneously.

Direction-of-Arrival Estimation via Sparse Bayesian Learning Exploiting Hierarchical Priors with Low Complexity.

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

Comparing various Bayesian random-effects models for pooling randomized controlled trials with rare events.

The meta-analysis of rare events presents unique methodological challenges owing to the small number of events. Bayesian methods are often used to combine rare events data to inform decision-making, as they can incorporate prior information and handle studies with zero events without the need for continuity corrections. However, the comparative performances of different Bayesian models in pooling rare events data are not well understood. We conducted a simulation to compare the statistical properties of four parameterizations based on the binomial-normal hierarchical model, using two different priors for the treatment effect: weakly informative prior (WIP) and non-informative prior (NIP), pooling randomized controlled trials with rare events using the odds ratio metric. We also considered the beta-binomial model proposed by Kuss and the random intercept and slope generalized linear mixed models. The simulation scenarios varied based on the treatment effect, sample size ratio between the treatment and control arms, and level of heterogeneity. Performance was evaluated using median bias, root mean square error, median width of 95% credible or confidence intervals, coverage, Type I error, and empirical power. Two reviews are used to illustrate these methods. The results demonstrate that the WIP outperforms the NIP within the same model structure. Among the compared models, the model that included the treatment effect parameter in the risk model for the control arm did not perform well. Our findings confirm that rare events meta-analysis faces the challenge of being underpowered, highlighting the importance of reporting the power of results in empirical studies.

Enhancing View Synthesis with Depth-Guided Neural Radiance Fields and Improved Depth Completion.

Neural radiance fields (NeRFs) leverage a neural representation to encode scenes, obtaining photorealistic rendering of novel views. However, NeRF has notable limitations. A significant drawback is that it does not capture surface geometry and only renders the object surface colors. Furthermore, the training of NeRF is exceedingly time-consuming. We propose Depth-NeRF as a solution to these issues. Specifically, our approach employs a fast depth completion algorithm to denoise and complete the depth maps generated by RGB-D cameras. These improved depth maps guide the sampling points of NeRF to be distributed closer to the scene's surface, benefiting from dense depth information. Furthermore, we have optimized the network structure of NeRF and integrated depth information to constrain the optimization process, ensuring that the termination distribution of the ray is consistent with the scene's geometry. Compared to NeRF, our method accelerates the training speed by 18%, and the rendered images achieve a higher PSNR than those obtained by mainstream methods. Additionally, there is a significant reduction in RMSE between the rendered scene depth and the ground truth depth, which indicates that our method can better capture the geometric information of the scene. With these improvements, we can train the NeRF model more efficiently and achieve more accurate rendering results.

Sharing information across patient subgroups to draw conclusions from sparse treatment networks.

Network meta-analysis (NMA) usually provides estimates of the relative effects with the highest possible precision. However, sparse networks with few available studies and limited direct evidence can arise, threatening the robustness and reliability of NMA estimates. In these cases, the limited amount of available information can hamper the formal evaluation of the underlying NMA assumptions of transitivity and consistency. In addition, NMA estimates from sparse networks are expected to be imprecise and possibly biased as they rely on large-sample approximations that are invalid in the absence of sufficient data. We propose a Bayesian framework that allows sharing of information between two networks that pertain to different population subgroups. Specifically, we use the results from a subgroup with a lot of direct evidence (a dense network) to construct informative priors for the relative effects in the target subgroup (a sparse network). This is a two-stage approach where at the first stage, we extrapolate the results of the dense network to those expected from the sparse network. This takes place by using a modified hierarchical NMA model where we add a location parameter that shifts the distribution of the relative effects to make them applicable to the target population. At the second stage, these extrapolated results are used as prior information for the sparse network. We illustrate our approach through a motivating example of psychiatric patients. Our approach results in more precise and robust estimates of the relative effects and can adequately inform clinical practice in presence of sparse networks.

HBMIRT: A SAS macro for estimating uni- and multidimensional 1- and 2-parameter item response models in small (and large!) samples.

Item response theory (IRT) has evolved as a standard psychometric approach in recent years, in particular for test construction based on dichotomous (i.e., true/false) items. Unfortunately, large samples are typically needed for item refinement in unidimensional models and even more so in the multidimensional case. However, Bayesian IRT approaches with hierarchical priors have recently been shown to be promising for estimating even complex models in small samples. Still, it may be challenging for applied researchers to set up such IRT models in general purpose or specialized statistical computer programs. Therefore, we developed a user-friendly tool - a SAS macro called HBMIRT - that allows to estimate uni- and multidimensional IRT models with dichotomous items. We explain the capabilities and features of the macro and demonstrate the particular advantages of the implemented hierarchical priors in rather small samples over weakly informative priors and traditional maximum likelihood estimation with the help of a simulation study. The macro can also be used with the online version of SAS OnDemand for Academics that is freely accessible for academic researchers.

An Objective and Robust Bayes Factor for the Hypothesis Test One Sample and Two Population Means.

It has been over 100 years since the discovery of one of the most fundamental statistical tests: the Student's t test. However, reliable conventional and objective Bayesian procedures are still essential for routine practice. In this work, we proposed an objective and robust Bayesian approach for hypothesis testing for one-sample and two-sample mean comparisons when the assumption of equal variances holds. The newly proposed Bayes factors are based on the intrinsic and Berger robust prior. Additionally, we introduced a corrected version of the Bayesian Information Criterion (BIC), denoted BIC-TESS, which is based on the effective sample size (TESS), for comparing two population means. We studied our developed Bayes factors in several simulation experiments for hypothesis testing. Our methodologies consistently provided strong evidence in favor of the null hypothesis in the case of equal means and variances. Finally, we applied the methodology to the original Gosset sleep data, concluding strong evidence favoring the hypothesis that the average sleep hours differed between the two treatments. These methodologies exhibit finite sample consistency and demonstrate consistent qualitative behavior, proving reasonably close to each other in practice, particularly for moderate to large sample sizes.

Transfer Learning in Multiple Hypothesis Testing.

In this investigation, a synthesis of Convolutional Neural Networks (CNNs) and Bayesian inference is presented, leading to a novel approach to the problem of Multiple Hypothesis Testing (MHT). Diverging from traditional paradigms, this study introduces a sequence-based uncalibrated Bayes factor approach to test many hypotheses using the same family of sampling parametric models. A two-step methodology is employed: initially, a learning phase is conducted utilizing simulated datasets encompassing a wide spectrum of null and alternative hypotheses, followed by a transfer phase applying this fitted model to real-world experimental sequences. The outcome is a CNN model capable of navigating the complex domain of MHT with improved precision over traditional methods, also demonstrating robustness under varying conditions, including the number of true nulls and dependencies between tests. Although indications of empirical evaluations are presented and show that the methodology will prove useful, more work is required to provide a full evaluation from a theoretical perspective. The potential of this innovative approach is further illustrated within the critical domain of genomics. Although formal proof of the consistency of the model remains elusive due to the inherent complexity of the algorithms, this paper also provides some theoretical insights and advocates for continued exploration of this methodology.

Objective Priors for Invariant e-Values in the Presence of Nuisance Parameters.

This paper aims to contribute to refining the e-values for testing precise hypotheses, especially when dealing with nuisance parameters, leveraging the effectiveness of asymptotic expansions of the posterior. The proposed approach offers the advantage of bypassing the need for elicitation of priors and reference functions for the nuisance parameters and the multidimensional integration step. For this purpose, starting from a Laplace approximation, a posterior distribution for the parameter of interest is only considered and then a suitable objective matching prior is introduced, ensuring that the posterior mode aligns with an equivariant frequentist estimator. Consequently, both Highest Probability Density credible sets and the e-value remain invariant. Some targeted and challenging examples are discussed.