Hierarchical Inference Research Articles

THE SL2S GALAXY-SCALE LENS SAMPLE. V. DARK MATTER HALOS AND STELLAR IMF OF MASSIVE EARLY-TYPE GALAXIES OUT TO REDSHIFT 0.8

We investigate the cosmic evolution of the internal structure of massive early-type galaxies over half of the age of the Universe. We perform a joint lensing and stellar dynamics analysis of a sample of 81 strong lenses from the SL2S and SLACS surveys and combine the results with a hierarchical Bayesian inference method to measure the distribution of dark matter mass and stellar IMF across the population of massive early-type galaxies. Lensing selection effects are taken into account. We find that the dark matter mass projected within the inner 5 kpc increases for increasing redshift, decreases for increasing stellar mass density, but is roughly constant along the evolutionary tracks of early-type galaxies. The average dark matter slope is consistent with that of an NFW profile, but is not well constrained. The stellar IMF normalization is close to a Salpeter IMF at $\log{M_*} = 11.5$ and scales strongly with increasing stellar mass. No dependence of the IMF on redshift or stellar mass density is detected. The anti-correlation between dark matter mass and stellar mass density supports the idea of mergers being more frequent in more massive dark matter halos.

Hierarchical statistical framework to combine generalized depletion models and biomass dynamic models in the stock assessment of the Chilean sea urchin (Loxechinus albus) fishery

Generalized depletion models are useful for representing catch dynamics when biological compositional data are lacking but high frequency records of catch and effort are available. A shortcoming of these models is that although they estimate vulnerable abundance they do not provide direct information on the productivity of the stocks. Here we combine generalized depletion models with a biomass dynamic model of the Pella–Tomlinson type. The inference framework is hierarchical, with initial biomass estimates from generalized depletion models being used as input to the biomass dynamic model to estimate its hyper-parameters. Two hierarchical inference approaches are employed: the standard state-space framework and a new hybrid marginal-estimated approximation to the likelihood function, which make different simplifying assumptions. We apply this assessment approach to the first Chilean fishery with a Management Plan, the southern sea urchin fishery. Results from both hierarchical inference methods show a stock fluctuating between high and low biomass levels, for which maximum sustainable yield appears as a risk-prone annual harvest policy. Given this we propose an alternative annual harvest rate corresponding to the average latent productivity over the years of peaks and troughs of biomass fluctuations.

Using Fuzzy Inference System to Predict Iron and Manganese Accumulation Potential in Water Distribution Networks

Abstract The occurrence of discolored drinking water at customers’ taps, which is mainly caused by the deposition and release of iron (Fe) and manganese (Mn) in water distribution networks (WDNs), is a major worry for both customers and water companies. In this paper, two hierarchical fuzzy inference systems (FISs) to predict Fe and Mn accumulation potential in WDNs were developed. They were also able to indicate the causes of Fe and Mn accumulation potential failures. The FISs could be of great benefit to water resource engineers and drinking water supply companies in managing water discoloration.

Precision and neuronal dynamics in the human posterior parietal cortex during evidence accumulation

Primate studies show slow ramping activity in posterior parietal cortex (PPC) neurons during perceptual decision-making. These findings have inspired a rich theoretical literature to account for this activity. These accounts are largely unrelated to Bayesian theories of perception and predictive coding, a related formulation of perceptual inference in the cortical hierarchy. Here, we tested a key prediction of such hierarchical inference, namely that the estimated precision (reliability) of information ascending the cortical hierarchy plays a key role in determining both the speed of decision-making and the rate of increase of PPC activity. Using dynamic causal modelling of magnetoencephalographic (MEG) evoked responses, recorded during a simple perceptual decision-making task, we recover ramping-activity from an anatomically and functionally plausible network of regions, including early visual cortex, the middle temporal area (MT) and PPC. Precision, as reflected by the gain on pyramidal cell activity, was strongly correlated with both the speed of decision making and the slope of PPC ramping activity. Our findings indicate that the dynamics of neuronal activity in the human PPC during perceptual decision-making recapitulate those observed in the macaque, and in so doing we link observations from primate electrophysiology and human choice behaviour. Moreover, the synaptic gain control modulating these dynamics is consistent with predictive coding formulations of evidence accumulation.

Attentional modulation of alpha/beta and gamma oscillations reflect functionally distinct processes.

The brain adapts to dynamic environments by adjusting the attentional gain or precision afforded to salient and predictable sensory input. Previous research suggests that this involves the regulation of cortical excitability (reflected in prestimulus alpha oscillations) before stimulus onset that modulates subsequent stimulus processing (reflected in stimulus-bound gamma oscillations). We present two spatial attention experiments in humans, where we first replicate the classic finding of prestimulus attentional alpha modulation and poststimulus gamma modulation. In the second experiment, the task-relevant target was a stimulus change that occurred after stimulus onset. This enabled us to show that attentional alpha modulation reflects the predictability (precision) of an upcoming sensory target, rather than an attenuation of alpha activity induced by neuronal excitation related to stimulus onset. In particular, we show that the strength of attentional alpha modulations increases with the predictability of the anticipated sensory target, regardless of current afferent drive. By contrast, we show that the poststimulus attentional gamma enhancement is stimulus-bound and decreases when the subsequent target becomes more predictable. Hence, this pattern suggests that the strength of gamma oscillations is not merely a function of cortical excitability, but also depends on the relative mismatch of predictions and sensory evidence. Together, these findings support recent theoretical proposals for distinct roles of alpha/beta and gamma oscillations in hierarchical perceptual inference and predictive coding.

Cholinergic stimulation enhances Bayesian belief updating in the deployment of spatial attention.

The exact mechanisms whereby the cholinergic neurotransmitter system contributes to attentional processing remain poorly understood. Here, we applied computational modeling to psychophysical data (obtained from a spatial attention task) under a psychopharmacological challenge with the cholinesterase inhibitor galantamine (Reminyl). This allowed us to characterize the cholinergic modulation of selective attention formally, in terms of hierarchical Bayesian inference. In a placebo-controlled, within-subject, crossover design, 16 healthy human subjects performed a modified version of Posner's location-cueing task in which the proportion of validly and invalidly cued targets (percentage of cue validity, % CV) changed over time. Saccadic response speeds were used to estimate the parameters of a hierarchical Bayesian model to test whether cholinergic stimulation affected the trial-wise updating of probabilistic beliefs that underlie the allocation of attention or whether galantamine changed the mapping from those beliefs to subsequent eye movements. Behaviorally, galantamine led to a greater influence of probabilistic context (% CV) on response speed than placebo. Crucially, computational modeling suggested this effect was due to an increase in the rate of belief updating about cue validity (as opposed to the increased sensitivity of behavioral responses to those beliefs). We discuss these findings with respect to cholinergic effects on hierarchical cortical processing and in relation to the encoding of expected uncertainty or precision.

The ejected mass distribution of Type Ia supernovae: a significant rate of non-Chandrasekhar-mass progenitors

The ejected mass distribution of type Ia supernovae directly probes progenitor evolutionary history and explosion mechanisms, with implications for their use as cosmological probes. Although the Chandrasekhar mass is a natural mass scale for the explosion of white dwarfs as type Ia supernovae, models allowing type Ia supernovae to explode at other masses have attracted much recent attention. Using an empirical relation between the ejected mass and the light curve width, we derive ejected masses $M_\mathrm{ej}$ and $^{56}$Ni masses $M_\mathrm{Ni}$ for a sample of 337 type Ia supernovae with redshifts $z < 0.7$ used in recent cosmological analyses. We use hierarchical Bayesian inference to reconstruct the joint $M_\mathrm{ej}$-$M_\mathrm{Ni}$ distribution, accounting for measurement errors. The inferred marginal distribution of $M_\mathrm{ej}$ has a long tail towards sub-Chandrasekhar masses, but cuts off sharply above 1.4 $M_\odot$. Our results imply that 25\%-50\% of normal type Ia supernovae are inconsistent with Chandrasekhar-mass explosions, with almost all of these being sub-Chandrasekhar-mass; super-Chandrasekhar-mass explosions make up no more than 1\% of all spectroscopically normal type Ia supernovae. We interpret the type Ia supernova width-luminosity relation as an underlying relation between $M_\mathrm{ej}$ and $M_\mathrm{Ni}$, and show that the inferred relation is not naturally explained by the predictions of any single known explosion mechanism.

Non-informative hierarchical Bayesian inference for non-negative matrix factorization

Non-negative matrix factorization (NMF) is an intuitive, non-negative, and interpretable approximation method. Canonical NMF approach could derive some basic components to represent original data, while probabilistic NMF approaches try to introduce some reasonable constraints to optimize the canonical NMF model. However, both of them cannot handle ground-truth bases discovering and model order determination problems. In general, the model order of basis matrix needs to be pre-defined. The model order determines the capability and accuracy of data structure discovering. However, how to accurately infer the model order of basis matrix has not been well investigated. In this paper, we propose a method called non-informative hierarchical Bayesian non-negative matrix factorization (NHBNMF) to automatically determine the model order and discover the data structure. They are achieved through hierarchical Bayesian inference model, maximum a posteriori (MAP) criterion, and non-informative parameters. In NHBNMF method, we first introduce a structure with two-level parameters to enable the entire model to approach the distributions of ground-truth bases. Then we use non-informative parameter scheme to eliminate the hyper-parameter to enable automatic searching. Finally, the model order and ground-truth bases are discovered by using MAP criterion and L2-norm selection. The experiments are conducted based on both synthetic and real-world datasets to show the effectiveness of our algorithm. The results demonstrate that our algorithm can accurately estimate the model order and discover the ground-truth bases. Even for the complicated FERET facial dataset, our algorithm still obtained interpretable bases and achieved satisfactory accuracy of the model order estimation.

What visual illusions teach us about schizophrenia.

Illusion, namely a mismatch between the objective and perceived properties of an object present in the environment, is a common feature of visual perception, both in normal and pathological conditions. This makes illusion a valuable tool with which to explore normal perception and its impairments. Although still debated, the hypothesis of a modified, and typically diminished, susceptibility to illusions in schizophrenia patients is supported by a growing number of studies. The current paper aimed to review how illusions have been used to explore and reveal the core features of visual perception in schizophrenia from a psychophysical, neurophysiological and functional point of view. We propose an integration of these findings into a common hierarchical Bayesian inference framework. The Bayesian formalism considers perception as the optimal combination between sensory evidence and prior knowledge, thereby highlighting the interweaving of perceptions and beliefs. Notably, it offers a holistic and convincing explanation for the perceptual changes observed in schizophrenia that might be ideally tested using illusory paradigms, as well as potential paths to explore neural mechanisms. Implications for psychopathology (in terms of positive symptoms, subjective experience or behavior disruptions) are critically discussed.

The role of abstraction in non-native speech perception

The end-result of perceptual reorganization in infancy is currently viewed as a reconfigured perceptual space, “warped” around native-language phonetic categories, which then acts as a direct perceptual filter on any non-native sounds: naïve-listener discrimination of non-native-sounds is determined by their mapping onto native-language phonetic categories that are acoustically/articulatorily most similar. We report results that suggest another factor in non-native speech perception: some perceptual sensitivities cannot be attributed to listeners' warped perceptual space alone, but rather to enhanced general sensitivity along phonetic dimensions that the listeners' native language employs to distinguish between categories. Specifically, we show that the knowledge of a language with short and long vowel categories leads to enhanced discrimination of non-native consonant length contrasts. We argue that these results support a view of perceptual reorganization as the consequence of learners' hierarchical inductive inferences about the structure of the language's sound system: infants not only acquire the specific phonetic category inventory, but also draw higher-order generalizations over the set of those categories, such as the overall informativity of phonetic dimensions for sound categorization. Non-native sound perception is then also determined by sensitivities that emerge from these generalizations, rather than only by mappings of non-native sounds onto native-language phonetic categories.

The Dopaminergic Midbrain Encodes the Expected Certainty about Desired Outcomes.

Dopamine plays a key role in learning; however, its exact function in decision making and choice remains unclear. Recently, we proposed a generic model based on active (Bayesian) inference wherein dopamine encodes the precision of beliefs about optimal policies. Put simply, dopamine discharges reflect the confidence that a chosen policy will lead to desired outcomes. We designed a novel task to test this hypothesis, where subjects played a “limited offer” game in a functional magnetic resonance imaging experiment. Subjects had to decide how long to wait for a high offer before accepting a low offer, with the risk of losing everything if they waited too long. Bayesian model comparison showed that behavior strongly supported active inference, based on surprise minimization, over classical utility maximization schemes. Furthermore, midbrain activity, encompassing dopamine projection neurons, was accurately predicted by trial-by-trial variations in model-based estimates of precision. Our findings demonstrate that human subjects infer both optimal policies and the precision of those inferences, and thus support the notion that humans perform hierarchical probabilistic Bayesian inference. In other words, subjects have to infer both what they should do as well as how confident they are in their choices, where confidence may be encoded by dopaminergic firing.

Dynamic and Succinct Statistical Analysis of Neuroscience Data

Modern neuroscientific recording technologies are increasingly generating rich, multimodal data that provide unique opportunities to investigate the intricacies of brain function. However, our ability to exploit the dynamic, interactive interplay among neural processes is limited by the lack of appropriate analysis methods. In this paper, some challenging issues in neuroscience data analysis are described, and some general-purpose approaches to address such challenges are proposed. Specifically, we discuss statistical methodologies with a theme of loss functions, and hierarchical Bayesian inference methodologies from the perspective of constructing optimal mappings. These approaches are demonstrated on both simulated and experimentally acquired neural data sets to assess causal influences and track time-varying interactions among neural processes on a fine time scale.

Receiver function deconvolution using transdimensional hierarchical Bayesian inference

S U M M A R Y Teleseismic waves can convert from shear to compressional (Sp) or compressional to shear (Ps) across impedance contrasts in the subsurface. Deconvolving the parent waveforms (P for Ps or S for Sp) from the daughter waveforms (S for Ps or P for Sp) generates receiver functions which can be used to analyse velocity structure beneath the receiver. Though a variety of deconvolution techniques have been developed, they are all adversely affected by background and signal-generated noise. In order to take into account the unknown noise characteristics, we propose a method based on transdimensional hierarchical Bayesian inference in which both the noise magnitude and noise spectral character are parameters in calculating the likelihood probability distribution. We use a reversible-jump implementation of a Markov chain Monte Carlo algorithm to find an ensemble of receiver functions whose relative fits to the data have been calculated while simultaneously inferring the values of the noise parameters. Our noise parametrization is determined from pre-event noise so that it approximates observed noise characteristics. We test the algorithm on synthetic waveforms contaminated with noise generated from a covariance matrix obtained from observed noise. We show that the method retrieves easily interpretable receiver functions even in the presence of high noise levels. We also show that we can obtain useful estimates of noise amplitude and frequency content. Analysis of the ensemble solutions produced by our method can be used to quantify the uncertainties associated with individual receiver functions as well as with individual features within them, providing an objective way for deciding which features warrant geological interpretation. This method should make possible more robust inferences on subsurface structure using receiver function analysis, especially in areas of poor data coverage or under noisy station conditions.

Bayesian noise-reduction in Arabia/Somalia and Nubia/Arabia finite rotations since ∼20 Ma: Implications for Nubia/Somalia relative motion

Knowledge of Nubia/Somalia relative motion since the Early Neogene is of particular importance in the Earth Sciences, because it (i) impacts on inferences on African dynamic topography; and (ii) allows us to link plate kinematics within the Indian realm with those within the Atlantic basin. The contemporary Nubia/Somalia motion is well known from geodetic observations. Precise estimates of the past-3.2-Myr average motion are also available from paleo-magnetic observations. However, little is known of the Nubia/Somalia motion prior to ∼3.2 Ma, chiefly because the Southwest Indian Ridge spread slowly, posing a challenge to precisely identify magnetic lineations. This also makes the few observations available particularly prone to noise. Here we reconstruct Nubia/Somalia relative motions since ∼20 Ma from the alternative plate-circuit Nubia-Arabia-Somalia. We resort to trans-dimensional hierarchical Bayesian Inference, which has proved effective in reducing finite-rotation noise, to unravel the Arabia/Somalia and Arabia/Nubia motions. We combine the resulting kinematics to reconstruct the Nubia/Somalia relative motion since ∼20 Ma. We verify the validity of the approach by comparing our reconstruction with the available record for the past ∼3.2 Myr, obtained through Antarctica. Results indicate that prior to ∼11 Ma the total motion between Nubia and Somalia was faster than today. Furthermore, it featured a significant strike-slip component along the Nubia/Somalia boundary. It is only since ∼11 Ma that Nubia diverges away from Somalia at slower rates, comparable to the present-day one. Kinematic changes of some 20% might have occurred in the period leading to the present-day, but plate-motion steadiness is also warranted within the uncertainties.

REDBACK: Open-source software for efficient noise-reduction in plate kinematic reconstructions

Knowledge of past plate motions derived from ocean-floor finite rotations is an important asset of the Earth Sciences, because it allows linking a variety of shallow-rooted and deep-rooted geological processes. Efforts have recently been taken toward inferring finite rotations at the unprecedented temporal resolution of 1 Myr or less, and more data are anticipated in the near future. These reconstructions, like any data set, feature a degree of noise that compromises significantly our ability to make geodynamical inferences. Bayesian Inference has been recently shown to be effective in reducing the impact of noise on plate kinematics inferred from high-temporal-resolution finite-rotation data sets. We describe REDBACK, an open-source software that implements transdimensional hierarchical Bayesian Inference for efficient noise-reduction in plate kinematic reconstructions. Algorithm details are described and illustrated by means of a synthetic test.

A Hierarchical Bayesian Modeling Approach to Searching and Stopping in Multi‐Attribute Judgment

In most decision-making situations, there is a plethora of information potentially available to people. Deciding what information to gather and what to ignore is no small feat. How do decision makers determine in what sequence to collect information and when to stop? In two experiments, we administered a version of the German cities task developed by Gigerenzer and Goldstein (1996), in which participants had to decide which of two cities had the larger population. Decision makers were not provided with the names of the cities, but they were able to collect different kinds of cues for both response alternatives (e.g., "Does this city have a university?") before making a decision. Our experiments differed in whether participants were free to determine the number of cues they examined. We demonstrate that a novel model, using hierarchical latent mixtures and Bayesian inference (Lee & Newell, ) provides a more complete description of the data from both experiments than simple conventional strategies, such as the take-the-best or the Weighted Additive heuristics.

Predictive codes of interoception, emotion, and the self

Interoception is the ability to perceive and integrate physiological signals from within the body. It is closely related to the autonomic system and is a key component in the generation of affective states and abstract representations of the self (Critchley et al., 2004; Ainley and Tsakiris, 2013). Seth proposes a predictive coding (PC) model of interoception that involves a free-energy based explanation of emotion awareness and selfhood. In this model, emotions, and in turn the sense of self, rely on predictions of the causes of interoceptive signals. Within this framework, the interoceptive system minimizes free-energy, or the discrepancy between predictions and interoceptive signals. Free-energy can be minimized either by updating predictions about the causes of the sensory signals (perceptual updating), or by acting to change autonomic states such that bodily states are more predictable (active inference).

Spatial Latent Gaussian Models: Application to House Prices Data in Tehran City

Latent Gaussian models are flexible models that are applied in several statistical applications. When posterior marginals or full conditional distributions in hierarchical Bayesian inference from these models are not available in closed form, Markov chain Monte Carlo methods are implemented. The component dependence of the latent field usually causes increase in computational time and divergence of algorithms. In this paper, an integrated nested Laplace approximation is used to solve these problems, in which the Laplace approximation and the numerical integration methods are combined in an efficient way so that hard simulations are replaced by fast computation and accurate approximation. Finally the relationship between house price data, floor size, age, number of rooms, building frame, type of proprietorship and facilities such as electricity, landline, water, gas, central heating and cooling system, kitchen goods, bath and toilet are modeled by using spatial latent Gaussian models. The fitted model can be used for predicting the house price in Tehran city.

A cooperative Cuckoo Search – hierarchical adaptive neuro-fuzzy inference system approach for predicting student academic performance

The accurate prediction of student academic performance facilitates admission decisions and enhances educational services at tertiary institutions. This raises the need to have an effective model that predicts student performance in university that is based on the results of standardized exams and other influential factors, such as socio-economic background. In this study, a novel approach to the prediction of student academic performance based on the Cuckoo Search (CS) – hierarchical Adaptive Neuro-Fuzzy Inference System (HANFIS) model is proposed. Firstly, the most appropriate factors were selected and a dataset was constructed. Then, the proposed model was used to predict academic performance. In the model, a hierarchical structure of ANFIS was suggested to solve the curse-of-dimensionality problem, the CS algorithm was utilized to optimize the clustering parameters which helped form the rule base, and ANFIS optimized the parameters in the antecedent and consequent parts of each sub-model. The findings showed that the proposed model is accurate and reliable. The results were also compared with those obtained from the Artificial Neural Network (ANN), GA-HANFIS (the combination of Genetic algorithm and HANFIS), and HANFIS models, indicating the proposed approach performed better. It is expected that this work may be used to assist in student admission procedures and strengthen the service system in educational institutions.

Function formula oriented construction of Bayesian inference nets for diagnosis of cardiovascular disease.

An intelligent cardiovascular disease (CVD) diagnosis system using hemodynamic parameters (HDPs) derived from sphygmogram (SPG) signal is presented to support the emerging patient-centric healthcare models. To replicate clinical approach of diagnosis through a staged decision process, the Bayesian inference nets (BIN) are adapted. New approaches to construct a hierarchical multistage BIN using defined function formulas and a method employing fuzzy logic (FL) technology to quantify inference nodes with dynamic values of statistical parameters are proposed. The suggested methodology is validated by constructing hierarchical Bayesian fuzzy inference nets (HBFIN) to diagnose various heart pathologies from the deduced HDPs. The preliminary diagnostic results show that the proposed methodology has salient validity and effectiveness in the diagnosis of cardiovascular disease.