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Probabilistic programming allows for automatic Bayesian inference on user-defined probabilistic models. Recent advances in Markov chain Monte Carlo (MCMC) sampling allow inference on increasingly complex models. This class of MCMC, known as Hamiltonian Monte Carlo, requires gradient information which is often not readily available. PyMC3 is a new open source probabilistic programming framework written in Python that uses Theano to compute gradients via automatic differentiation as well as compile probabilistic programs on-the-fly to C for increased speed. Contrary to other probabilistic programming languages, PyMC3 allows model specification directly in Python code. The lack of a domain specific language allows for great flexibility and direct interaction with the model. This paper is a tutorial-style introduction to this software package.

The diffusion model is a commonly used tool to infer latent psychological processes underlying decision-making, and to link them to neural mechanisms based on response times. Although efficient open source software has been made available to quantitatively fit the model to data, current estimation methods require an abundance of response time measurements to recover meaningful parameters, and only provide point estimates of each parameter. In contrast, hierarchical Bayesian parameter estimation methods are useful for enhancing statistical power, allowing for simultaneous estimation of individual subject parameters and the group distribution that they are drawn from, while also providing measures of uncertainty in these parameters in the posterior distribution. Here, we present a novel Python-based toolbox called HDDM (hierarchical drift diffusion model), which allows fast and flexible estimation of the the drift-diffusion model and the related linear ballistic accumulator model. HDDM requires fewer data per subject/condition than non-hierarchical methods, allows for full Bayesian data analysis, and can handle outliers in the data. Finally, HDDM supports the estimation of how trial-by-trial measurements (e.g., fMRI) influence decision-making parameters. This paper will first describe the theoretical background of the drift diffusion model and Bayesian inference. We then illustrate usage of the toolbox on a real-world data set from our lab. Finally, parameter recovery studies show that HDDM beats alternative fitting methods like the χ(2)-quantile method as well as maximum likelihood estimation. The software and documentation can be downloaded at: http://ski.clps.brown.edu/hddm_docs/

Cognitive deficits in depressed adults may reflect impaired decision-making. To investigate this possibility, we analyzed data from unmedicated adults with Major Depressive Disorder (MDD) and healthy controls as they performed a probabilistic reward task. The Hierarchical Drift Diffusion Model (HDDM) was used to quantify decision-making mechanisms recruited by the task, to determine if any such mechanism was disrupted by depression. Data came from two samples (Study 1: 258 MDD, 36 controls; Study 2: 23 MDD, 25 controls). On each trial, participants indicated which of two similar stimuli was presented; correct identifications were rewarded. Quantile-probability plots and the HDDM quantified the impact of MDD on response times (RT), speed of evidence accumulation (drift rate), and the width of decision thresholds, among other parameters. RTs were more positively skewed in depressed v. healthy adults, and the HDDM revealed that drift rates were reduced-and decision thresholds were wider-in the MDD groups. This pattern suggests that depressed adults accumulated the evidence needed to make decisions more slowly than controls did. Depressed adults responded slower than controls in both studies, and poorer performance led the MDD group to receive fewer rewards than controls in Study 1. These results did not reflect a sensorimotor deficit but were instead due to sluggish evidence accumulation. Thus, slowed decision-making-not slowed perception or response execution-caused the performance deficit in MDD. If these results generalize to other tasks, they may help explain the broad cognitive deficits seen in depression.

Humans survive and thrive through social exchange. Yet, social dependency also comes at a cost. Perceived social isolation, or loneliness, affects physical and mental health, cognitive performance, overall life expectancy, and increases vulnerability to Alzheimer’s disease-related dementias. Despite severe consequences on behavior and health, the neural basis of loneliness remains elusive. Using the UK Biobank population imaging-genetics cohort ( n  = ~40,000, aged 40–69 years when recruited, mean age = 54.9), we test for signatures of loneliness in grey matter morphology, intrinsic functional coupling, and fiber tract microstructure. The loneliness-linked neurobiological profiles converge on a collection of brain regions known as the ‘default network’. This higher associative network shows more consistent loneliness associations in grey matter volume than other cortical brain networks. Lonely individuals display stronger functional communication in the default network, and greater microstructural integrity of its fornix pathway. The findings fit with the possibility that the up-regulation of these neural circuits supports mentalizing, reminiscence and imagination to fill the social void. Here, using pattern-learning analyses of structural, functional, and diffusion brain scans in ~40,000 UK Biobank participants, the authors provide population-scale evidence that the default network is associated with perceived social isolation.

One mechanism by which medial prefontal cortex (mPFC) exerts cognitive control is thought to involve the subthalamic nucleus (STN), which acts as a temporary brake on behavior. Here the authors found increases in mPFC and STN theta power as a function of decision conflict. Increases in mPFC theta power predicted increased decision thresholds. STN deep brain stimulation reversed this relationship, resulting in impulsive choice. It takes effort and time to tame one's impulses. Although medial prefrontal cortex (mPFC) is broadly implicated in effortful control over behavior, the subthalamic nucleus (STN) is specifically thought to contribute by acting as a brake on cortico-striatal function during decision conflict, buying time until the right decision can be made. Using the drift diffusion model of decision making, we found that trial-to-trial increases in mPFC activity (EEG theta power, 4–8 Hz) were related to an increased threshold for evidence accumulation (decision threshold) as a function of conflict. Deep brain stimulation of the STN in individuals with Parkinson's disease reversed this relationship, resulting in impulsive choice. In addition, intracranial recordings of the STN area revealed increased activity (2.5–5 Hz) during these same high-conflict decisions. Activity in these slow frequency bands may reflect a neural substrate for cortico–basal ganglia communication regulating decision processes.

PyMC is a probabilistic programming library for Python that provides tools for constructing and fitting Bayesian models. It offers an intuitive, readable syntax that is close to the natural syntax statisticians use to describe models. PyMC leverages the symbolic computation library PyTensor, allowing it to be compiled into a variety of computational backends, such as C, JAX, and Numba, which in turn offer access to different computational architectures including CPU, GPU, and TPU. Being a general modeling framework, PyMC supports a variety of models including generalized hierarchical linear regression and classification, time series, ordinary differential equations (ODEs), and non-parametric models such as Gaussian processes (GPs). We demonstrate PyMC’s versatility and ease of use with examples spanning a range of common statistical models. Additionally, we discuss the positive role of PyMC in the development of the open-source ecosystem for probabilistic programming.

Most data analyses rely on models. To complement statistical models, psychologists have developed cognitive models, which translate observed variables into psychologically interesting constructs. Response time models, in particular, assume that response time and accuracy are the observed expression of latent variables including 1) ease of processing, 2) response caution, 3) response bias, and 4) non-decision time. Inferences about these psychological factors, hinge upon the validity of the models’ parameters. Here, we use a blinded, collaborative approach to assess the validity of such model-based inferences. Seventeen teams of researchers analyzed the same 14 data sets. In each of these two-condition data sets, we manipulated properties of participants’ behavior in a two-alternative forced choice task. The contributing teams were blind to the manipulations, and had to infer what aspect of behavior was changed using their method of choice. The contributors chose to employ a variety of models, estimation methods, and inference procedures. Our results show that, although conclusions were similar across different methods, these \"modeler’s degrees of freedom\" did affect their inferences. Interestingly, many of the simpler approaches yielded as robust and accurate inferences as the more complex methods. We recommend that, in general, cognitive models become a typical analysis tool for response time data. In particular, we argue that the simpler models and procedures are sufficient for standard experimental designs. We finish by outlining situations in which more complicated models and methods may be necessary, and discuss potential pitfalls when interpreting the output from response time models.

Huntington's disease (HD) is genetically determined but with variability in symptom onset, leading to uncertainty as to when pharmacological intervention should be initiated. Here we take a computational approach based on neurocognitive phenotyping, computational modeling, and classification, in an effort to provide quantitative predictors of HD before symptom onset. A large sample of subjects-consisting of both pre-manifest individuals carrying the HD mutation (pre-HD), and early symptomatic-as well as healthy controls performed the antisaccade conflict task, which requires executive control and response inhibition. While symptomatic HD subjects differed substantially from controls in behavioral measures [reaction time (RT) and error rates], there was no such clear behavioral differences in pre-HD. RT distributions and error rates were fit with an accumulator-based model which summarizes the computational processes involved and which are related to identified mechanisms in more detailed neural models of prefrontal cortex and basal ganglia. Classification based on fitted model parameters revealed a key parameter related to executive control differentiated pre-HD from controls, whereas the response inhibition parameter declined only after symptom onset. These findings demonstrate the utility of computational approaches for classification and prediction of brain disorders, and provide clues as to the underlying neural mechanisms.

Rationale Repeated haloperidol treatment in rodents results in a day-to-day intensification of catalepsy (i.e., sensitization). Prior experiments suggest that this sensitization is context-dependent and resistant to extinction training. Objectives The aim of this study was to provide a neurobiological mechanistic explanation for these findings. Materials and methods We use a neurocomputational model of the basal ganglia and simulate two alternative models based on the reward prediction error and novelty hypotheses of dopamine function. We also conducted a behavioral rat experiment to adjudicate between these models. Twenty male Sprague–Dawley rats were challenged with 0.25 mg/kg haloperidol across multiple days and were subsequently tested in either a familiar or novel context. Results Simulation results show that catalepsy sensitization, and its context dependency, can be explained by “NoGo” learning via simulated D2 receptor antagonism in striatopallidal neurons, leading to increasingly slowed response latencies. The model further exhibits a non-extinguishable component of catalepsy sensitization due to latent NoGo representations that are prevented from being expressed, and therefore from being unlearned, during extinction. In the rat experiment, context dependency effects were not dependent on the novelty of the context, ruling out the novelty model’s account of context dependency. Conclusions Simulations lend insight into potential complex mechanisms leading to context-dependent catalepsy sensitization, extinction, and renewal.