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Bayesian Inference

Measuring dependence in the Wasserstein distance for Bayesian nonparametric models


Bayesian nonparametric (BNP) models are a prominent tool for performing flexible inference with a natural quantification of uncertainty. Notable examples for \(T\) include normalization for random probabilities (Regazzini et al., 2003), kernel mixtures for densities (Lo, 1984) and for hazards (Dykstra and Laud, 1981; James, 2005), exponential transformations for survival functions (Doksum, 1974) and cumulative transformations for cumulative hazards (Hjort, 1990). Very often, though, the data presents some structural heterogeneity one should carefully take into account, especially when analyzing data from different sources that are related in some way. For instance this happens in the study of clinical trials of a COVID-19 vaccine in different countries or when understanding the effects of a certain policy adopted by multiple regions. In these cases, besides modeling heterogeneity, one further aims at introducing some probabilistic mechanism that allows for borrowing information across different studies.

When to use Bayesian


Bayesian statistics is all about belief. We have some prior belief about the true model, and we combine that with the likelihood of our data to get our posterior belief about the true model. In some cases, we have knowledge about our domain before we see any of the data. Bayesian inference provides a straightforward way to encode that belief into a prior probability distribution. For example, say I am an economist predicting the effects of interest rates on tech stock price changes.

Learning Data Science from Real-World Projects


Mixed-integer programming saves the day. Taking a cue from consumer supply chains and the data-driven advances that have revolutionized them in recent decades, Gabe Verzino walks us through a scheduling program that would empower both patients and healthcare providers to use their time more efficiently. Bayes' Theorem might sound, well, theoretical. As Khuyen Tran shows in her recent tutorial (based on the traffic patterns of her own website), it can also be a powerful tool for detecting and analyzing change points in your data. The road to the perfect shot of espresso passes through a lot of data.

Bayesian Inference in Python


Originally published on Towards AI the World's Leading AI and Technology News and Media Company. If you are building an AI-related product or service, we invite you to consider becoming an AI sponsor. At Towards AI, we help scale AI and technology startups. Let us help you unleash your technology to the masses. Life is uncertain, and statistics can help us quantify certainty in this uncertain world by applying the concepts of probability and inference.

10 Mathematics for Data Science Free Courses You Must Know in 2022


Knowledge of Mathematics is essential to understand the data science basics. So if you want to learn Mathematics for Data Science, this article is for you. In this article, you will find the 10 Best Mathematics for Data Science Free Courses. For these courses, You don't need to pay a single buck. Now, without any further ado, let's get started- This is a completely FREE course for beginners and covers data visualization, probability, and many elementary statistics concepts like regression, hypothesis testing, and more.

Intuitive Bayes Introductory Course


All three of us are authors of the PyMC Probabilistic Programming Language, a production grade package used at leading organizations around the world. Ravin learned the power of Bayes Theorem at SpaceX when improving the supply chains of the world's most advanced rockets. He's now an advocate of applied Bayesian methods and has since authored a textbook about Bayes Theorem and writes about appllied data science on his blog. Thomas is enthusiastic about teaching statistics using code and examples, rather than arduous math. Through his many talks and blog posts, he has shown that there is a different way to teach statistics.

Steven Pinker Has His Reasons - Issue 108: Change


A few years ago, at the Princeton Club in Manhattan, I chanced on a memorable chat with the Harvard psychologist Steven Pinker. His spouse, the philosopher Rebecca Goldstein, with whom he was tagging along, had been invited onto a panel to discuss the conflict between religion and science and Einstein's so-called "God letter," which was being auctioned at Christie's. Pinker had recently published Enlightenment Now: The Case for Reason, Science, Humanism, and Progress. I was eager to pepper him with questions, mainly on religion, rationality, and evolutionary psychology. I remember I wanted Pinker's take on something Harvey Whitehouse, one of the founders of the cognitive science of religion, told me in an interview--that my own little enlightenment, of becoming an atheist in college, was probably mostly a product of merely changing my social milieu. I wasn't so much moved by rational arguments against the ethics and existence of God but by being distanced from my old life and meeting new, non-religious friends. I recall Pinker almost pouncing on that argument, defending reason's power to change our minds. He noted that people especially high in "intellectance," a personality trait now more commonly called "openness to experience," tend to be more curious, intelligent, and willing to entertain new ideas. I still think that Pinker's way of seeing things made more sense of my experience in those heady days. I really was, for the first time, trying my best to think things through, and it was exhilarating. We talked until the event staff shelved the wine, and parted ways at a chilly midtown intersection.

Bayesian Logistic Regression


If you've ever searched for evaluation metrics to assess model accuracy, chances are that you found many different options to choose from. Accuracy is in some sense the holy grail of prediction so it's not at all surprising that the machine learning community spends a lot time thinking about it. In a world where more and more high-stake decisions are being automated, model accuracy is in fact a very valid concern. But does this recipe for model evaluation seem like a sound and complete approach to automated decision-making? Some would argue that we need to pay more attention to model uncertainty. No matter how many times you have cross-validated your model, the loss metric that it is being optimized against as well as its parameters and predictions remain inherently random variables.

Making RL tractable by learning more informative reward functions: example-based control, meta-learning, and normalized maximum likelihood


After the user provides a few examples of desired outcomes, MURAL automatically infers a reward function that takes into account these examples and the agent's uncertainty for each state. Although reinforcement learning has shown success in domains such as robotics, chip placement and playing video games, it is usually intractable in its most general form. In particular, deciding when and how to visit new states in the hopes of learning more about the environment can be challenging, especially when the reward signal is uninformative. These questions of reward specification and exploration are closely connected -- the more directed and "well shaped" a reward function is, the easier the problem of exploration becomes. The answer to the question of how to explore most effectively is likely to be closely informed by the particular choice of how we specify rewards.

Naive Bayes Algorithm


This formula was devised and penned by respected Thomas Bayes, renowned statistician.It is an arithmetical formula for determining conditional probability. Conditional probability is the likelihood of an outcome occurring, based on a previous outcome occurring. This might be a bit brain-teasing as you are working backwards. Bayes' theorem may be derived from the definition of conditional probability, P(Do not launch Stock price increases) 0.4 0.30 0.12 Thus, there is a 57% probability that the company's share price will increase. Bayes' Theorem has several forms.