Why Bayes Sample Clauses

Why Bayes. In this thesis, we make use of Bayesian inference. There are multiple reasons behind this choice. Bayesian inference allows us to integrate our beliefs and hypotheses into the data analysis process. It is done using prior distributions P (θ) in formula (1.5). While the likelihood part (P (yi|θ)) depends solely on the data itself and expresses how likely is the data point (yi) is given our hypothesis (θ), the prior part P (θ) gives us the prior possibility of our hypothesis (θ). In Bayesian inference, we multiply every data point with a probability distribution that we specify according to what we believe is going on in the world. By doing so, we give our hypotheses definite forms and allow us to formulate possible competing explanations of the data and test both of them against the data. ∏ P (θ|y) ∝ P (yi|θ)P (θ) (1.5) This procedure also allows us to decide how much we want to integrate from previous literature, which is made possible by the use of priors. In addition to our hypotheses, we can inform our model and calculations about previous behavioral data. For example, response times typically have a positive skew with a long tail following the central mass, as stated in ▇▇▇ and ▇▇▇▇▇▇▇▇▇ (2018) and ▇▇▇▇ (1991). Specifying this tendency in a model would deem some response time values less likely, and thus would diminish the effect of an outlier data point in our model. This also entails that not all experimental data are equal, and their contributions are equal. Moreover, the details of the prior distribution reflect our degree of confidence in that hypothesis. We can provide a very specific distribution with thin tails, which would mean that we are very confident about how the data is distributed. On the other hand, we can have a completely flat distribution, meaning that we have no information or prior evidence about the data. Lastly, it deals with uncertainty, which is an important aspect when we cannot gather all the possible data. If we were to use frequentist analyses and provide p-values in our models, we would have no way of knowing whether or not our p-value is a result of our sample size or the effect size. That is, having a small effect in magnitude and a large pool of participants and a larger effect in magnitude with fewer data points may give us the same p-value as a result. Thus, reported p-value would either tell us we have pinpointed a nice effect or we do not have enough participants. On this negative aspect of reporting p-values, a re...