Neural implementations of Bayesian inference

Bayesian inference has emerged as a general framework that captures how organisms make decisions under uncertainty. Recent experimental findings reveal disparate mechanisms for how the brain generates behaviors predicted by normative Bayesian theories. Here, we identify two broad classes of neural implementations for Bayesian inference: a modular class, where each probabilistic component of Bayesian computation is independently encoded and a transform class, where uncertain measurements are converted to Bayesian estimates through latent processes. Many recent experimental neuroscience findings studying probabilistic inference broadly fall into these classes. We identify potential avenues for synthesis across these two classes and the disparities that, at present, cannot be reconciled. We conclude that to distinguish among implementation hypotheses for Bayesian inference, we require greater engagement among theoretical and experimental neuroscientists in an effort that spans different scales of analysis, circuits, tasks, and species.     

Strong binding of myosin heads stretches and twists the actin helix

Calculation of the size of the power stroke of the myosin motor in contracting muscle requires knowledge of the compliance of the myofilaments. Current estimates of actin compliance vary significantly introducing uncertainty in the mechanical parameters of the motor. Using x-ray diffraction on small bundles of permeabilized fibers from rabbit muscle we show that strong binding of myosin heads changes directly the actin helix. The spacing of the 2.73-nm meridional x-ray reflection increased by 0.22% when relaxed fibers were put into low-tension rigor (<10 kN/m(2)) demonstrating that strongly bound myosin heads elongate the actin filaments even in the absence of external tension. The pitch of the 5.9-nm actin layer line increased by approximately 0.62% and that of the 5.1-nm layer line decreased by approximately 0.26%, suggesting that the elongation is accompanied by a decrease in its helical angle (approximately 166 degrees) by approximately 0.8 degrees. This effect explains the difference between actin compliance revealed from mechanical experiments with single fibers and from x-ray diffraction on whole muscles. Our measurement of actin compliance obtained by applying tension to fibers in rigor is consistent with the results of mechanical measurements.     

Humans Running at Stadiums and Beaches and the Accuracy of Speed Estimations from Fossil Trackways

The concept of dynamic similarity between mechanical properties of vertebrates and engineered structures has served in previous work to suggest that there is a power law relationship between vertebrate speeds and stride length. This relationship, with some additional assumptions about hind limb height, has permitted the calculation of speeds from fossil trackways of dinosaurs. However, there are claims that uncertainties are large. In this work we analyze the accuracy of speed calculations for fossil vertebrates based on fossil trackways by using data derived from both athletic competitions and an experiment with humans walking and running on a beach. Our results show that although there are somewhat different running regimes, in general terms human speed can be described in a simple way, and differences between observed and predicted speeds usually are no more than 10–15%. Thus, while recognizing that some uncertainty remains in the estimation of hind limb height, we conclude that reliable speed calculations can be obtained from vertebrate fossil trackways. Our results also show that very reliable speed estimates can be obtained from human fossil trackways directly from stride length measurements.     

Dynamics of in vivo power output and efficiency of Nasonia asynchronous flight muscle

By simultaneously measuring aerodynamic performance, wing kinematics, and metabolic activity, we have estimated the in vivo limits of mechanical power production and efficiency of the asynchronous flight muscle (IFM) in three species of ectoparasitoid wasps genus Nasonia (N. giraulti, N. longicornis, and N. vitripennis). The 0.6 mg animals were flown under tethered flight conditions in a flight simulator that allowed modulation of power production by employing an open-loop visual stimulation technique. At maximum locomotor capacity, flight muscles of Nasonia are capable to sustain 72.2 +/- 18.3 W kg(-1) muscle mechanical power at a chemo-mechanical conversion efficiency of approximately 9.8 +/- 0.9%. Within the working range of the locomotor system, profile power requirement for flight dominates induced power requirement suggesting that the cost to overcome wing drag places the primary limit on overall flight performance. Since inertial power is only approximately 25% of the sum of induced and profile power requirements, Nasonia spp. may not benefit from elastic energy storage during wing deceleration phases. A comparison between wing size-polymorphic males revealed that wing size reduction is accompanied by a decrease in total flight muscle volume, muscle mass-specific mechanical power production, and total flight efficiency. In animals with small wings maximum total flight efficiency is below 0.5%. The aerodynamic and power estimates reported here for Nasonia are comparable to values reported previously for the fruit fly Drosophila flying under similar experimental conditions, while muscle efficiency of the tiny wasp is more at the lower end of values published for various other insects.     

Internal field strength measurements in chick forebrains at 50, 147, and 450 MHz.

This report describes some experimental measurements of the internal field levels induced within isolated chick-forebrains irradiated at 50, 147, and 450 MHz, under essentially the same conditions as those used in the in vitro calcium-ion efflux experiments. Ratios of incident power at 50/147 MHz and 147/450 MHz that are needed to establish the same probe output are given and comparisons made with values predicted by different spherical models. Data predicted by the layered-sphere model were found to be in close agreement with measured values for the 50/147-MHz ratio. Agreement for the 147/450-MHz ratio was poorer.     

Experimental validation of a statistical model for evaluating the past or future magnetic field exposures of a population living near power lines

This study was designed to provide an experimental validation for a statistical model predicting past or future exposures to magnetic fields (MF) from power lines. The model estimates exposure, combining the distribution of ambient MF in the absence of power lines with the distribution of past or future MF produced by power lines. In the study, validation is carried out by comparing exposures predicted by the model with the actual measurements obtained from a large-scale epidemiological study. The comparison was made for a group of 220 women living near a 735 kV power line. Knowing that the individual arithmetic means of MF exposures follow a log-normal distribution, the Pearson correlation between the log-transformed measured means and the calculated ones was determined and found to be 0.77. Predicted values of MF exposures were slightly lower than measured values. The calculated geometric mean of the group was 0.33 microT, compared to 0.38 microT for the measured geometric mean. The present study shows good agreement between the measured MF exposure of an individual inside a house near a 735 kV line and the MF exposure calculated using a statistical model.     

A TEST OF THE CONJECTURE THAT G‐MATRICES ARE MORE STABLE THAN B‐MATRICES

The G‐matrix occupies an important position in evolutionary biology both as a summary of the inheritance of quantitative traits and as an ingredient in predicting how those traits will respond to selection and drift. Consequently, the stability of G has an important bearing on the accuracy of predicted evolutionary trajectories. Furthermore, G should evolve in response to stable features of the adaptive landscape and their trajectories through time. Although the stability and evolution of G might be predicted from knowledge of selection in natural populations, most empirical comparisons of G‐matrices have been made in the absence of such a priori predictions. We present a theoretical argument that within‐sex G‐matrices should be more stable than between‐sex B‐matrices because they are more powerfully exposed to multivariate stabilizing selection. We tested this conjecture by comparing estimates of B‐ and within‐sex G‐matrices among three populations of the garter snake Thamnophis elegans. Matrix comparisons using Flury's hierarchical approach revealed that within‐sex G‐matrices had four principal components in common (full CPC), whereas B‐matrices had only a single principal component in common and eigenvalues that were more variable among populations. These results suggest that within‐sex G is more stable than B , as predicted by our theoretical argument.     

Linear independence of pairwise comparisons of DNA microarray data

MOTIVATION: For DNA microarrays, the gain in certainty by performing multiple experimental repeats is offset by the high cost of each experiment. In a typical experiment, two independent measurements (that is, data from two separate arrays) are combined to yield a single comparative index per gene. Thus, although one uses 2n arrays and performs 2n independent measurements, one obtains only n comparative measurements. We addressed the question: how many of the potential n2 comparisons derivable from such data are actually independent, and what effect do these additional comparisons have on the false positive rate. RESULTS: We show there are precisely 2n - 1 independent comparisons available from among the n2 possibilities. Applying these additional n - 1 independent comparisons to experimental and simulated data reduced the false positive rate by as much as 10-fold, with excellent agreement between experimental and theoretical false positive rates.     

A stochastic version of the brass PF ratio adjustment of age-specific fertility schedules

Estimates of age-specific fertility rates based on survey data are known to suffer down-bias associated with incomplete reporting. Previously, William Brass (1964, 1965, 1968) proposed a series of adjustments of such data to reflect more appropriate levels of fertility through comparison with data on children-ever-born by age, a measure of cohort-specific cumulative fertility. His now widely-used Parity/Fertility or PF ratio method makes a number of strong assumptions, which have been the focus of an extended discussion in the literature on indirect estimation. However, while it is clear that the measures used in making adjusted age-specific fertility estimates with this method are captured with statistical uncertainty, little discussion of the nature of this uncertainty around PF-ratio based estimates of fertility has been entertained in the literature. Since both age-specific risk of childbearing and cumulative parity (children ever born) are measured with statistical uncertainty, an unknown credibility interval must surround every PF ratio-based estimate. Using the standard approach, this is unknown, limiting the ability to make statistical comparisons of fertility between groups or to understand stochasticity in population dynamics. This paper makes use of approaches applied to similar problems in engineering, the natural sciences, and decision analysis--often discussed under the title of uncertainty analysis or stochastic modeling--to characterize this uncertainty and to present a new method for making PF ratio-based fertility estimates with 95 percent uncertainty intervals. The implications for demographic analysis, between-group comparisons of fertility, and the field of statistical demography are explored.     

A Bayesian approach to functional-based multilevel modeling of longitudinal data: applications to environmental epidemiology

Flexible multilevel models are proposed to allow for cluster-specific smooth estimation of growth curves in a mixed-effects modeling format that includes subject-specific random effects on the growth parameters. Attention is then focused on models that examine between-cluster comparisons of the effects of an ecologic covariate of interest (e.g. air pollution) on nonlinear functionals of growth curves (e.g. maximum rate of growth). A Gibbs sampling approach is used to get posterior mean estimates of nonlinear functionals along with their uncertainty estimates. A second-stage ecologic random-effects model is used to examine the association between a covariate of interest (e.g. air pollution) and the nonlinear functionals. A unified estimation procedure is presented along with its computational and theoretical details. The models are motivated by, and illustrated with, lung function and air pollution data from the Southern California Children's Health Study.     

Refining Estimates of Bird Collision and Electrocution Mortality at Power Lines in the United States

Collisions and electrocutions at power lines are thought to kill large numbers of birds in the United States annually. However, existing estimates of mortality are either speculative (for electrocution) or based on extrapolation of results from one study to all U.S. power lines (for collision). Because national-scale estimates of mortality and comparisons among threats are likely to be used for prioritizing policy and management strategies and for identifying major research needs, these estimates should be based on systematic and transparent assessment of rigorously collected data. We conducted a quantitative review that incorporated data from 14 studies meeting our inclusion criteria to estimate that between 12 and 64 million birds are killed each year at U.S. power lines, with between 8 and 57 million birds killed by collision and between 0.9 and 11.6 million birds killed by electrocution. Sensitivity analyses indicate that the majority of uncertainty in our estimates arises from variation in mortality rates across studies; this variation is due in part to the small sample of rigorously conducted studies that can be used to estimate mortality. Little information is available to quantify species-specific vulnerability to mortality at power lines; the available literature over-represents particular bird groups and habitats, and most studies only sample and present data for one or a few species. Furthermore, additional research is needed to clarify whether, to what degree, and in what regions populations of different bird species are affected by power line-related mortality. Nonetheless, our data-driven analysis suggests that the amount of bird mortality at U.S. power lines is substantial and that conservation management and policy is necessary to reduce this mortality.     

Mixed-effects statistical model for comparative LC-MS proteomics studies

Comparing a protein's concentrations across two or more treatments is the focus of many proteomics studies. A frequent source of measurements for these comparisons is a mass spectrometry (MS) analysis of a protein's peptide ions separated by liquid chromatography (LC) following its enzymatic digestion. Alas, LC-MS identification and quantification of equimolar peptides can vary significantly due to their unequal digestion, separation, and ionization. This unequal measurability of peptides, the largest source of LC-MS nuisance variation, stymies confident comparison of a protein's concentration across treatments. Our objective is to introduce a mixed-effects statistical model for comparative LC-MS proteomics studies. We describe LC-MS peptide abundance with a linear model featuring pivotal terms that account for unequal peptide LC-MS measurability. We advance fitting this model to an often incomplete LC-MS data set with REstricted Maximum Likelihood (REML) estimation, producing estimates of model goodness-of-fit, treatment effects, standard errors, confidence intervals, and protein relative concentrations. We illustrate the model with an experiment featuring a known dilution series of a filamentous ascomycete fungus Trichoderma reesei protein mixture. For 781 of the 1546 T. reesei proteins with sufficient data coverage, the fitted mixed-effects models capably described the LC-MS measurements. The LC-MS measurability terms effectively accounted for this major source of uncertainty. Ninety percent of the relative concentration estimates were within 0.5-fold of the true relative concentrations. Akin to the common ratio method, this model also produced biased estimates, albeit less biased. Bias decreased significantly, both absolutely and relative to the ratio method, as the number of observed peptides per protein increased. Mixed-effects statistical modeling offers a flexible, well-established methodology for comparative proteomics studies integrating common experimental designs with LC-MS sample processing plans. It favorably accounts for the unequal LC-MS measurability of peptides and produces informative quantitative comparisons of a protein's concentration across treatments with objective measures of uncertainties.     

A molecular dynamics method for calculating molecular volume changes appropriate for biomolecular simulation

Photothermal methods permit measurement of molecular volume changes of solvated molecules over nanosecond timescales. Such experiments are an important tool in investigating complex biophysical phenomena including identifying transient species in solution. Developing a microscopic understanding of the origin of volume changes in the condensed phase is needed to complement the experimental measurements. A molecular dynamics (MD) method exploiting available simulation methodology is demonstrated here that both mimics experimental measurements and provides microscopic resolution to the thermodynamic measurements. To calculate thermodynamic volume changes over time, isothermal-isobaric (NPT) MD is performed on a solution for a chosen length of time and the volume of the system is thus established. A further simulation is then performed by "plucking" out a solute molecule of interest to determine the volume of the system in its absence. The difference between these volumes is the thermodynamic volume of the solute molecule. NPT MD allows the volume of the system to fluctuate over time and this results in a statistical uncertainty in volumes that are calculated. It is found in the systems investigated here that simulations lasting a few nanoseconds can discern volume changes of approximately 1.0 ml/mole. This precision is comparable to that achieved empirically, making the experimental and theoretical techniques synergistic. The technique is demonstrated here on model systems including neat water, both charged and neutral aqueous methane, and an aqueous beta-sheet peptide.     

Simulated and experimental estimates of hydrodynamic drag from bio-logging tags

Drag force acting on swimming marine mammals is difficult to measure directly. Researchers often use simple modeling and kinematic measurements from animals, or computational fluid dynamics (CFD) simulations to estimate drag. However, studies that compare these methods are lacking. Here, computational simulation and physical experiments were used to estimate drag forces on gliding bottlenose dolphins (Tursiops truncatus). To facilitate comparison, variable drag loading (no-tag, tag, tag + 4, tag + 8) was used to increase force in both simulations and experiments. During the experiments, two dolphins were trained to perform controlled glides with variable loading. CFD simulations of dolphin/tag geometry in steady flow (1–6 m/s) were used to model drag forces. We expect both techniques will capture relative changes created by experimental conditions, but absolute forces predicted by the methods will differ. CFD estimates were within a calculated 90% confidence interval of the experimental results for all but the tag condition. Relative drag increase predicted by the simulation vs. experiment, respectively, differed by between 21% and 31%: tag, 4% vs. 33%; tag + 4, 47% vs. 68%; and tag + 8, 108% vs. 77%. The results from this work provide a direct comparison of computational and experimental estimates of drag, and provide a framework to quantify uncertainty.     

Passive deformations and active motions of leukocytes

The purpose of this paper is to review the development of continuum mechanics models of single leukocytes in both passive deformations and active motions and to indicate some future directions. Models of passive deformations describe the overall rheological behavior of single leukocytes under externally applied forces and predict the average mechanical properties from experimental data. Various "apparent" viscoelastic coefficients are obtained depending on the models assumed and the types of test used. Models of spontaneous motions postulate active driving mechanisms which must be derived internally from the cell itself and probably have different bases for different kind of motions. For pseudopod protrusion on leukocytes, energy transduction from chemical potential to mechanical work associated with actin polymerization at the tip of the projection is assumed to supply the motive power. For pseudopod retraction, active contraction due to actin-myosin interaction is assumed to be the driving force. The feasibility of the hypotheses are tested via numerical examples and comparison of the theoretical results with experimental measurements.     

Uncertainty in techno-economic estimates of cellulosic ethanol production due to experimental measurement uncertainty

ABSTRACT: BACKGROUND: Cost-effective production of lignocellulosic biofuels remains a major financial and technical challenge at the industrial scale. A critical tool in biofuels process development is the techno-economic (TE) model, which calculates biofuel production costs using a process model and an economic model. The process model solves mass and energy balances for each unit, and the economic model estimates capital and operating costs from the process model based on economic assumptions. The process model inputs include experimental data on the feedstock composition and intermediate product yields for each unit. These experimental yield data are calculated from primary measurements. Uncertainty in these primary measurements is propagated to the calculated yields, to the process model, and ultimately to the economic model. Thus, outputs of the TE model have a minimum uncertainty associated with the uncertainty in the primary measurements. RESULTS: We calculate the uncertainty in the Minimum Ethanol Selling Price (MESP) estimate for lignocellulosic ethanol production via a biochemical conversion process: dilute sulfuric acid pretreatment of corn stover followed by enzymatic hydrolysis and co-fermentation of the resulting sugars to ethanol. We perform a sensitivity analysis on the TE model and identify the feedstock composition and conversion yields from three unit operations (xylose from pretreatment, glucose from enzymatic hydrolysis, and ethanol from fermentation) as the most important variables. The uncertainty in the pretreatment xylose yield arises from multiple measurements, whereas the glucose and ethanol yields from enzymatic hydrolysis and fermentation, respectively, are dominated by a single measurement: the fraction of insoluble solids (fIS) in the biomass slurries. CONCLUSIONS: We calculate a $0.15/gal uncertainty in MESP from the TE model due to uncertainties in primary measurements. This result sets a lower bound on the error bars of the TE model predictions. This analysis highlights the primary measurements that merit further development to reduce the uncertainty associated with their use in TE models. While we develop and apply this mathematical framework to a specific biorefinery scenario here, this analysis can be readily adapted to other types of biorefining processes and provides a general framework for propagating uncertainty due to analytical measurements through a TE model.     

ESTIMATING DIVERSIFICATION RATES: HOW USEFUL ARE DIVERGENCE TIMES?

The dynamics of species diversification rates are a key component of macroevolutionary patterns. Although not absolutely necessary, the use of divergence times inferred from sequence data has led to development of more powerful methods for inferring diversification rates. However, it is unclear what impact uncertainty in age estimates have on diversification rate inferences. Here, we quantify these effects using both Bayesian and frequentist methodology. Through simulation, we demonstrate that adding sequence data results in more precise estimates of internal node ages, but a reasonable approximation of these node ages is often sufficient to approach the theoretical minimum variance in speciation rate estimates. We also find that even crude estimates of divergence times increase the power of tests of diversification rate differences between sister clades. Finally, because Bayesian and frequentist methods provided similar assessments of error, novel Bayesian approaches may provide a useful framework for tests of diversification rates in more complex contexts than are addressed here.     

Feasibility and Uncertainty in Behavior Genetics for the Nonhuman Primate

The analysis of phenotypic covariances among genetically related individuals is the basis for estimations of genetic and phenotypic effects on phenotypes. Beyond heritability, there are several other estimates that can be made with behavior genetic models of interest to primatologists. Some of these estimates are feasible with primate samples because they take advantage of the types of relatives available to compare in primate species and because most behaviors are expressed orders of magnitude more often and in a greater variety of contexts than morphological or life-history traits. The hypotheses that can be tested with these estimates are contrasted with hypotheses that will be difficult to achieve in primates because of sample size limitations. Feasible comparisons include the proportion of variance from interaction effects, the variation of genetic effects across environments, and the genetics of growth and development. Simulation shows that uncertainty of genetic parameters can be reduced by sampling each individual more than once. Because sample sizes are likely to remain relatively small in most primate behavior genetics, expressing uncertainty in parameter estimates is needed to move our inferences forward.     

Estimating Uncertainty in Ecosystem Budget Calculations

Ecosystem nutrient budgets often report values for pools and fluxes without any indication of uncertainty, which makes it difficult to evaluate the significance of findings or make comparisons across systems. We present an example, implemented in Excel, of a Monte Carlo approach to estimating error in calculating the N content of vegetation at the Hubbard Brook Experimental Forest in New Hampshire. The total N content of trees was estimated at 847 kg ha⁻¹ with an uncertainty of 8%, expressed as the standard deviation divided by the mean (the coefficient of variation). The individual sources of uncertainty were as follows: uncertainty in allometric equations (5%), uncertainty in tissue N concentrations (3%), uncertainty due to plot variability (6%, based on a sample of 15 plots of 0.05 ha), and uncertainty due to tree diameter measurement error (0.02%). In addition to allowing estimation of uncertainty in budget estimates, this approach can be used to assess which measurements should be improved to reduce uncertainty in the calculated values. This exercise was possible because the uncertainty in the parameters and equations that we used was made available by previous researchers. It is important to provide the error statistics with regression results if they are to be used in later calculations; archiving the data makes resampling analyses possible for future researchers. When conducted using a Monte Carlo framework, the analysis of uncertainty in complex calculations does not have to be difficult and should be standard practice when constructing ecosystem budgets.     

Spectra of intracellular Fura-2.

In the theory of measurement of calcium ion activity by determination of Fura-2 fluorescence at two excitation wavelengths, the accuracy of the result depends upon the accuracy both of the sample measurements and of the calibration measurements which are made on calcium-bound and free dye. Two factors underlie adequate calibration and accuracy. The first is the elimination of systematic error due to spectral shifts arising from the intracellular environment felt by the dye. To this end, detailed comparisons between complete spectra of both calcium-bound and calcium-free Fura-2 can be used to help separate spectral effects due to light absorption by cellular constituents versus polarity and viscosity of the intracellular milieu. The second major factor which determines accuracy is the experimental uncertainty (in both sample and calibration measurements). For samples in which the ratio of bound to free dye is large, the uncertainty in the ratio is also large, even when it is expressed as a percentage of the ratio itself. The errors in calibration measurements impact on the accuracy of the method primarily through the measurements made at wavelengths which are off the spectral peaks of the bound or free dye, since these are the least accurate. In order to obtain a guide to the choice of wavelengths and estimation of the reliability of results, a mathematical expression is derived for the dependence of the accuracy of the method on the accuracy of both sample and calibration measurements.