Bayes' Theorem allows a program to infer the probabilities of likely causes from the probabilities of their effects, when what it is given are the probabilities of effects, given the causes.
This is a complete Free course for statistics. In this course, you will learn how to estimate parameters of a population using sample statistics, hypothesis testing and confidence intervals, t-tests and ANOVA, correlation and regression, and chi-squared test. This course is taught by industry professionals and you will learn by doing various exercises.
As a data scientist, I am curious about knowing different analytical processes from a probabilistic point of view. There are two most popular ways of looking into any event, namely Bayesian and Frequentist . When Frequentist researchers look at any event from frequency of occurrence, Bayesian researchers focus more on probability of events happening. I will try to cover as much theory as possible with illustrative examples and sample codes so that readers can learn and practice simultaneously. As we all know Baye's rule is one of the most popular probability equation, which is defined as: P(a given b) P(a intersection b) / P(b) ….. (1) Here a and b are events that have taken place.
Photoacoustic tomography (PAT) is a hybrid biomedical imaging modality based on the photoacoustic effect [6, 44, 32]. In PAT, the imaged target is illuminated with a short pulse of light. Absorption of light creates localized areas of thermal expansion, resulting in localized pressure increases within the imaged target. This pressure distribution, called the initial pressure, relaxes as broadband ultrasound waves that are measured on the boundary of the imaged target. In the inverse problem of PAT, the initial pressure distribution is estimated from a set of measured ultrasound data.
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In the road so far, we have talked about MLP, CNN, and RNN architectures. These are discriminative models, that is models that can make predictions. Discriminative models essentially learn to estimate a conditional probability distribution p( x); that is, given a value, they try to predict the outcome based on what they learned about the probability distribution of x. Generative models are architectures of neural networks that learn the probability distribution of the data and learn how to generate data that seems to come from that probability distribution. Creating synthetic data is one use of generative models, but is not the only one.
Maximum Likelihood Estimation (MLE) is a probabilistic based approach to determine values for the parameters of the model. Parameters could be defined as blueprints for the model because based on that the algorithm works. MLE is a widely used technique in machine learning, time series, panel data and discrete data. The motive of MLE is to maximize the likelihood of values for the parameter to get the desired outcomes. Following are the topics to be covered.
The #52weeksofdatascience newsletter covers everything from Linear Regression to Neural Networks and beyond. So, if you like Data Science and Machine Learning, don't forget to subscribe! Main Idea: Bayesian Belief Network represents a set of variables and their conditional dependencies via a Directed Acyclic Graph (DAG) like the one displayed below. DAG allows us to determine the structure and relationship between different variables explicitly. Everyday use cases: BBN has many use cases, from helping to diagnose diseases to real-time predictions of a race outcome or advising marketing decisions.
Frequentist and Bayesian are two different versions of statistics. Frequentist is a more classical version, which, as the name suggests, rely on the long run frequency of events (data points) to calculate the variable of interest. Bayesian on the other hand, can also work without having a large number of events (in fact, it could work even with one data point!). The cardinal difference between the two is that: frequentist will give you a point estimate, whereas Bayesian will give you a distribution. Having a point estimate means that -- "we are certain that this is the output for this variable of interest". Whereas, having a distribution can be interpreted as -- "we have some belief that the mean of the distribution is the good estimate for this variable of interest, but there is uncertainty too, in the form of standard deviation".