Rejoinder

Rejoinder of "Statistical Inference: The Big Picture" by R. E. Kass [arXiv:1106.2895]Comment: Published in at http://dx.doi.org/10.1214/11-STS337REJ the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Information In The Non-Stationary Case

Information estimates such as the ``direct method'' of Strong et al. (1998) sidestep the difficult problem of estimating the joint distribution of response and stimulus by instead estimating the difference between the marginal and conditional entropies of the response. While this is an effective estimation strategy, it tempts the practitioner to ignore the role of the stimulus and the meaning of mutual information. We show here that, as the number of trials increases indefinitely, the direct (or ``plug-in'') estimate of marginal entropy converges (with probability 1) to the entropy of the time-averaged conditional distribution of the response, and the direct estimate of the conditional entropy converges to the time-averaged entropy of the conditional distribution of the response. Under joint stationarity and ergodicity of the response and stimulus, the difference of these quantities converges to the mutual information. When the stimulus is deterministic or non-stationary the direct estimate of information no longer estimates mutual information, which is no longer meaningful, but it remains a measure of variability of the response distribution across time

An Implementation of Bayesian Adaptive Regression Splines (BARS) in C with S and R Wrappers

BARS (DiMatteo, Genovese, and Kass 2001) uses the powerful reversible-jump MCMC engine to perform spline-based generalized nonparametric regression. It has been shown to work well in terms of having small mean-squared error in many examples (smaller than known competitors), as well as producing visually-appealing fits that are smooth (filtering out high-frequency noise) while adapting to sudden changes (retaining high-frequency signal). However, BARS is computationally intensive. The original implementation in S was too slow to be practical in certain situations, and was found to handle some data sets incorrectly. We have implemented BARS in C for the normal and Poisson cases, the latter being important in neurophysiological and other point-process applications. The C implementation includes all needed subroutines for fitting Poisson regression, manipulating B-splines (using code created by Bates and Venables), and finding starting values for Poisson regression (using code for density estimation created by Kooperberg). The code utilizes only freely-available external libraries (LAPACK and BLAS) and is otherwise self-contained. We have also provided wrappers so that BARS can be used easily within S or R.

Statistical Inference: The Big Picture

Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism, serves as a foundation for inference. Statistical pragmatism is inclusive and emphasizes the assumptions that connect statistical models with observed data. I argue that introductory courses often mischaracterize the process of statistical inference and I propose an alternative "big picture" depiction.Comment: Published in at http://dx.doi.org/10.1214/10-STS337 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Assessment of synchrony in multiple neural spike trains using loglinear point process models

Neural spike trains, which are sequences of very brief jumps in voltage across the cell membrane, were one of the motivating applications for the development of point process methodology. Early work required the assumption of stationarity, but contemporary experiments often use time-varying stimuli and produce time-varying neural responses. More recently, many statistical methods have been developed for nonstationary neural point process data. There has also been much interest in identifying synchrony, meaning events across two or more neurons that are nearly simultaneous at the time scale of the recordings. A natural statistical approach is to discretize time, using short time bins, and to introduce loglinear models for dependency among neurons, but previous use of loglinear modeling technology has assumed stationarity. We introduce a succinct yet powerful class of time-varying loglinear models by (a) allowing individual-neuron effects (main effects) to involve time-varying intensities; (b) also allowing the individual-neuron effects to involve autocovariation effects (history effects) due to past spiking, (c) assuming excess synchrony effects (interaction effects) do not depend on history, and (d) assuming all effects vary smoothly across time.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS429 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Approximate Methods for State-Space Models

State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace's method, an asymptotic series expansion, to approximate the state's conditional mean and variance, together with a Gaussian conditional distribution. This {\em Laplace-Gaussian filter} (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time.Comment: 31 pages, 4 figures. Different pagination from journal version due to incompatible style files but same content; the supplemental file for the journal appears here as appendices B--E

False discovery rate regression: an application to neural synchrony detection in primary visual cortex

Many approaches for multiple testing begin with the assumption that all tests in a given study should be combined into a global false-discovery-rate analysis. But this may be inappropriate for many of today's large-scale screening problems, where auxiliary information about each test is often available, and where a combined analysis can lead to poorly calibrated error rates within different subsets of the experiment. To address this issue, we introduce an approach called false-discovery-rate regression that directly uses this auxiliary information to inform the outcome of each test. The method can be motivated by a two-groups model in which covariates are allowed to influence the local false discovery rate, or equivalently, the posterior probability that a given observation is a signal. This poses many subtle issues at the interface between inference and computation, and we investigate several variations of the overall approach. Simulation evidence suggests that: (1) when covariate effects are present, FDR regression improves power for a fixed false-discovery rate; and (2) when covariate effects are absent, the method is robust, in the sense that it does not lead to inflated error rates. We apply the method to neural recordings from primary visual cortex. The goal is to detect pairs of neurons that exhibit fine-time-scale interactions, in the sense that they fire together more often than expected due to chance. Our method detects roughly 50% more synchronous pairs versus a standard FDR-controlling analysis. The companion R package FDRreg implements all methods described in the paper

An Implementation of Bayesian Adaptive Regression Splines (BARS) in C with S and R Wrappers

BARS (DiMatteo, Genovese, and Kass 2001) uses the powerful reversible-jump MCMC engine to perform spline-based generalized nonparametric regression. It has been shown to work well in terms of having small mean-squared error in many examples (smaller than known competitors), as well as producing visually-appealing fits that are smooth (filtering out high-frequency noise) while adapting to sudden changes (retaining high-frequency signal). However, BARS is computationally intensive. The original implementation in S was too slow to be practical in certain situations, and was found to handle some data sets incorrectly. We have implemented BARS in C for the normal and Poisson cases, the latter being important in neurophysiological and other point-process applications. The C implementation includes all needed subroutines for fitting Poisson regression, manipulating B-splines (using code created by Bates and Venables), and finding starting values for Poisson regression (using code for density estimation created by Kooperberg). The code utilizes only freely-available external libraries (LAPACK and BLAS) and is otherwise self-contained. We have also provided wrappers so that BARS can be used easily within S or R

Channel Openings Are Necessary but not Sufficient for Use-dependent Block of Cardiac Na+ Channels by Flecainide: Evidence from the Analysis of Disease-linked Mutations

Na+ channel blockers such as flecainide have found renewed usefulness in the diagnosis and treatment of two clinical syndromes arising from inherited mutations in SCN5A, the gene encoding the α subunit of the cardiac voltage–gated Na+ channel. The Brugada syndrome (BrS) and the LQT-3 variant of the Long QT syndrome are caused by disease-linked SCN5A mutations that act to change functional and pharmacological properties of the channel. Here we have explored a set of SCN5A mutations linked both to BrS and LQT-3 to determine what disease-modified channel properties underlie distinct responses to the Na+ channel blocker flecainide. We focused on flecainide block that develops with repetitive channel activity, so-called use-dependent block (UDB). Our results indicate that mutation-induced changes in the voltage-dependence of channel availability (inactivation) may act as determinants of flecainide block. The data further indicate that UDB by flecainide requires channel opening, but is not likely due to open channel block. Rather, flecainide appears to interact with inactivation states that follow depolarization-induced channel opening, and mutation-induced changes in channel inactivation will alter flecainide block independent of the disease to which the mutation is linked. Analysis of flecainide block of mutant channels linked to these rare disorders has provided novel insight into the molecular determinants of drug action

Teaching Computation in Neuroscience: Notes on the 2019 Society for Neuroscience Professional Development Workshop on Teaching

The 2019 Society for Neuroscience Professional 1Development Workshop on Teaching reviewed current tools, approaches, and examples for teaching computation in neuroscience. Robert Kass described the statistical foundations that students need to properly analyze data. Pascal Wallisch compared MATLAB and Python as programming languages for teaching students. Adrienne Fairhall discussed computational methods, training opportunities, and curricular considerations. Walt Babiec provided a view from the trenches on practical aspects of teaching computational neuroscience. Mathew Abrams concluded the session with an overview of resources for teaching and learning computational modeling in neuroscience