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Today we will talk about how to confront models with experimental data. Does my model capture the behavior of my participant, or its neural activity? Does the data support my model against alternatives? Which component in the model is needed? Do parameters in the model vary systematically between two subject populations? We will cover the basic concepts and tools to address these questions, starting with a general overview in the intro. You will learn how to estimate the parameters of simple regression models from the data in Tutorials 1 & 2, and then how to estimate the uncertainty about these values in Tutorial 3. Then you will learn how to select from models of different complexity the one that best accounts for your data (Tutorial 4-6). The outro illustrates some of these techniques in real research examples.
Fitting and comparing models to data is really the bread of butter of data analysis in neuroscience. You have learned during Model Types Day (W1D1) about a whole zoo of different types of models that we’re interested in in neuroscience. So here you will learn about generic concepts and techniques that apply for fitting and comparing any type of models, which is arguably pretty useful! You will apply these tools again when dealing with GLMs (W1D4), latent models (W1D5), deep networks (W2D1), dynamical models (W2D2), decision models, reinforcement learning models… it’s everywhere! On top of this, we will cover linear regression models - the typical regression model when the dependent variable is continuous (e.g. BOLD activity) – and use it throughout the day, to illustrate the concepts and methods we learn. In the GLM day, you will see how to generalize regression models when the dependent variable is binary (e.g. choices) or an integer (e.g. spike counts).
Almost all statistical and data analysis methods rely either explicitly or implicitly on fitting some model to the data. The concepts and tools you will learn today are crucial to be able to test your hypothesis about how behavior or neural activity is formed. A typical way this is done is that you formulate a computational (stochastic) model that embodies your hypothesis, and then one or more control models. Then you fit each or your models to your experimental data, say the pattern of choices of one experimental subject, or the spiking activity from one recorded neuron. Simulating your fitted models allows validating that your model indeed captures the effects of interest in your data. Then you use model comparison techniques to tell which one or your main or control model(s) provides a better description of the data. Also, you could assess whether some parameter in your model changes between experimental conditions or subject populations.
In the content and tutorials today, you will be using vectors and matrices (W0D3 T1/T2), probability distributions (W0D5 T1), and likelihoods (W0D5 T2). Please review this material if necessary!