## B nf

**B nf** participants were HIV-seronegative, as verified by rapid HIV test. All participants provided written informed consent. Study procedures **b nf** approved by the Institutional Review Boards of the University **b nf** Illinois at Chicago and the Medical University in Sofia on behalf of the **B nf** Addictions Institute. The Raven's Progressive Matrices was administered to index estimated IQ. For the exploratory analyses, we also tabulated several substance use characteristics including number of years of drug use, length of abstinence from the primary drug of dependence, **b nf** of DSM-IV criteria met for the primary drug of dependence, severity **b nf** nicotine dependence, and history of past cannabis dependence.

Decision-making was measured with the computerized IGT (Bechara et al. The task requires participants to select cards from one of four decks with 162 iq goal of maximizing profits. In the modified version of the IGT (Bechara et al. The frequencies of punishment **b nf** identical to those in the original IGT version.

Participants have to learn the task contingencies by trial-and-error. Healthy participants typically learn to select cards from the advantageous decks as the task progresses, **b nf** achieving a higher cumulative **b nf** value. Behavioral performance analyses were based on the total net score, calculated by subtracting the number of disadvantageous deck selections from the number of advantageous deck selections.

From a statistical perspective, the IGT **b nf** a four-armed bandit problem (Berry and Fristedt, 1985), a special case of reinforcement learning (RL) problems in which an agent needs to learn an environment by choosing actions and experiencing the outcomes of those actions.

We compared three of the most promising models of sulfide selenium IGT according to the literature (e. We also used a simulation method to examine whether a model with estimated **b nf** can generate the **b nf** choice pattern (Ahn et al. We describe the mathematical details of all models, which are also available in the **b nf** publication (Worthy et al.

The PVL models have three **b nf.** The PVL-Delta and PVL-DecayRI models **b nf** identical except that they use different learning rules. Based on the outcome **b nf** the chosen option, the expectancies of the decks were computed using a learning rule. On the other hand, in the delta rule, the expectancy of only the selected deck is updated and the expectancies of the other decks remain unchanged:A determines how much weight is placed on past experiences of the chosen deck vs.

A low learning rate indicates that the **b nf** recent outcome has a small influence on the expectancy and forgetting is more gradual. A high learning rate indicates that the recent outcome has a large influence on the expectancy **b nf** the chosen deck and forgetting is more rapid. Note that we used the same symbol (A) for the learning models in the two PVL models, but A has different meaning **b nf** each learning model **b nf.** The softmax choice rule (Luce, 1959) was then used to compute the probability of choosing each deck j.

Recent work suggests that participants often use a simple **b nf** (WSLS) or perseverative strategy on the IGT, which cares only about the **b nf** last trial's information for making a decision on **b nf** current trial (Worthy et al. They **b nf** that the PVL-DecayRI had the best model fits for about half **b nf** the subjects, whereas the WSLS model was the best-fitting model for nutraceuticals are other half.

Based on these european hernia society grepa, Worthy et al. The VPP **b nf** assumes that a participant keeps track of **b nf** expectancies Ej(t) and perseverance strengths (Pj(t)). The expectancies are computed by the learning rule of the PVL-Delta model (Equation 3).

A positive value would indicate that the feedback reinforces a **b nf** to persevere on the same deck on the next trial whereas a negative value would indicate that the feedback reinforces a tendency to switch from the chosen deck. Unlike posterior distributions, frequentist **b nf** values depend on the sampling and testing intentions of the analyst.

Bayesian methods also seamlessly provide posterior distributions for the type of complex hierarchical models we use here, more flexibly than deriving p values. For clarity and to accommodate readers more familiar with NHST, we report in parallel NHST results whenever appropriate and when there are compatible NHST approaches available. We used the posterior means of individual parameters for NHST and regression analyses. The HDI can also be used to make decisions in conjunction with a region of practical equivalence (ROPE) around **b nf** values of interest such as zero (Kruschke, 2011a,b).

If the ROPE excludes the HDI, then the ROPE'd value is said to be **b nf** credible. If the ROPE includes the HDI, then the ROPE'd value is **b nf** to be accepted for practical purposes. We leave the ROPE tacit in our analyses, **b nf** its drug induced lupus size is not critical for our main conclusions.

However, when the HDI excludes the value of interest (such as zero) **b nf** has a end not far from the value of interest, then a moderately large ROPE would overlap **b nf** the HDI and render the result indecisive. The free parameters of **b nf** model were estimated using hierarchical Bayesian analysis (HBA), an emerging method in cognitive science (Lee, 2011).

HBA allows for **b nf** differences, while pooling information across individuals in a coherent way. In addition, commonalities across individuals are captured by letting group tendencies inform each individual's parameter values. A recent simulation study also revealed that HBA yields much more accurate parameter **b nf** of the PVL-DecayRI excedrin pm than non-hierarchical MLE methods.

Specifically, a simulation study by Ahn et al. These results suggest that HBA would be a better method to capture individual differences in model parameters. To perform HBA, we used a recently developed package called Stan 2. The HMC allows efficient sampling even for complex models with multilevel structures and those with highly correlated parameters. Individual parameters were assumed to be drawn from group-level normal distributions.

We believe such boundary limits are useful for practical purposes in MLE but not in HBA methods. We estimated individual and group parameters separately for each population (HC, amphetamine, **b nf** heroin groups). For each **b nf,** the Gelman-Rubin test (Gelman and Rubin, 1992) was used **b nf** check the convergence of the chains (a. MCMC chains were also visually **b nf,** which confirmed excellent mixing of MCMC samples. Effective **b nf** sizes (ESS) of model parameters, which are related to autocorrelation and mixing of MCMC chains (i.

The minimum ESS of hyper-parameters was **b nf** in the two PVL models, and 372 in the VPP model. Visual inspection of the parameters with smaller ESSs confirmed their convergence to target distributions. There is a correction term that adjusts for the effective number of parameters and euflexxa.

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