Have you ever thought about how strong a prior is compared to observed data? It features a cyclic process with one event represented by the variable d. There is only 1 observation of that event so it means that maximum likelihood will always assign everything to this variable that cannot be explained by other data. In the plot below you will see the truth which is y and 3 lines corresponding to 3 independent samples from the fitted resulting posterior distribution. Before you start to argue with my reasoning take a look at the plots where we plot the last prior vs the posterior and the point estimate from our generating process.

As we talked about in the last paper, understanding that a marginal likelihood uses the prior predictive distribution is a key to understanding why it's so fragile when used for model comparison. That is, the data generated using the prior (and the fixed elements of the design, in this case the spatial locations and the covariate values) should cover the range of "reasonable" data values and a little beyond. In the end, prior predictive checks and posterior predictive checks are both important in the statistical workflow. But your prior predictive checks make most sense before you do things with your data, and posterior predictive checks make most sense after.

Applying cross-validation prevents overfitting and a good out-of-sample performance, low generalisation error in unseen data, indicates not an overfit. Aim In this post, we will give an intuition on why model validation as approximating generalization error of a model fit and detection of overfitting can not be resolved simultaneously on a single model. Let's use the following functional form, from classic text of Bishop, but with an added Gaussian noise We generate large enough set, 100 points to avoid sample size issue discussed in Bishop's book, see Figure 2. Overtraining is not overfitting Overtraining means a model performance degrades in learning model parameters against an objective variable that effects how model is build, for example, an objective variable can be a training data size or iteration cycle in neural network.

First, we will discuss how to correctly interpret p-values, effect sizes, confidence intervals, Bayes Factors, and likelihood ratios, and how these statistics answer different questions you might be interested in. Then, you will learn how to design experiments where the false positive rate is controlled, and how to decide upon the sample size for your study, for example in order to achieve high statistical power. In practical, hands on assignments, you will learn how to simulate t-tests to learn which p-values you can expect, calculate likelihood ratio's and get an introduction the binomial Bayesian statistics, and learn about the positive predictive value which expresses the probability published research findings are true. You will calculate effect sizes, see how confidence intervals work through simulations, and practice doing a-priori power analyses.

It seems like, a kind of an urban legend or a meme, a folklore is circulating in data science or allied fields with the following statement: Applying cross-validation prevents overfitting and a good out-of-sample performance, low generalisation error in unseen data, indicates not an overfit. Aim In this post, we will give an intuition on why model validation as approximating generalization error of a model fit and detection of overfitting can not be resolved simultaneously on a single model. Let's use the following functional form, from classic text of Bishop, but with an added Gaussian noise $$ f(x) sin(2\pi x) \mathcal{N}(0,0.1).$$ We generate large enough set, 100 points to avoid sample size issue discussed in Bishop's book, see Figure 2. Overtraining is not overfitting Overtraining means a model performance degrades in learning model parameters against an objective variable that effects how model is build, for example, an objective variable can be a training data size or iteration cycle in neural network.

Contextual Adaptation -- Where systems construct contextual explanatory models for classes of real world phenomena. I write about these two in previous articles (see: "The Only Way to Make Deep Learning Interpretable is to have it Explain Itself" and "The Meta Model and Meta Meta Model of Deep Learning" DARPA's presentation nails it, by highlighting what's going on in current state-of-the-art research. Deep Learning systems have flaws analogous to our own intuitions having flaws. Just to recap, here's the roadmap that I have ( explained here): It's a Deep Learning roadmap and does not cover developments in other AI fields.

Today the company employs a team from a diverse range of scientific backgrounds and uses a combination of data science and machine learning techniques to manage significant amounts of client money. Anthony Ledford, Man AHL's chief scientist, emphasises the importance of diversity in all things and knows never to have too much faith in any one prediction model. If you ask me how much faith do I have in any particular model or being able to predict an individual price of a financial instrument, well I have very little faith in it. The way you can turn that into something that makes sense from an investment point of view, is to distil those tiny statistical edges down into something that, at the portfolio level, makes sense as an investment product," he said.

Batch training How to train a model using only minibatches of data at a time. Linear mixed effects models Linear modeling of fixed and random effects. Inference networks How to amortize computation for training and testing models. If you're interested in contributing a tutorial, checking out the contributing page.

Andrew Gelman: Bayesian statistics uses the mathematical rules of probability to combines data with "prior information" to give inferences which (if the model being used is correct) are more precise than would be obtained by either source of information alone. You can reproduce the classical methods using Bayesian inference: In a regression prediction context, setting the prior of a coefficient to uniform or "noninformative" is mathematically equivalent to including the corresponding predictor in a least squares or maximum likelihood estimate; setting the prior to a spike at zero is the same as excluding the predictor, and you can reproduce a pooling of predictors thorough a joint deterministic prior on their coefficients. When Bayesian methods work best, it's by providing a clear set of paths connecting data, mathematical/statistical models, and the substantive theory of the variation and comparison of interest. Bayesian methods offer a clarity that comes from the explicit specification of a so-called "generative model": a probability model of the data-collection process and a probability model of the underlying parameters.

In an earlier blog, "Need for DYNAMICAL Machine Learning: Bayesian exact recursive estimation", I introduced the need for Dynamical ML as we now enter the "Walk" stage of "Crawl-Walk-Run" evolution of machine learning. How DYNAMICAL Machine Learning is practiced is discussed in Generalized Dynamical Machine Learning and associated articles describing the theory, algorithms, examples and MATLAB code (in Systems Analytics: Adaptive Machine Learning workbook). In Machine Learning, (1) a Data Model is chosen; (2) a Learning Method is selected to obtain model parameters & (3) data are processed in a "batch" or "in-stream" (or sequential) mode. For a complete discussion of Kalman Filter use for Dynamical machine learning, see SYSTEMS Analytics book.