Prior probability
A prior probability distribution represents beliefs or assumptions about an unknown quantity before relevant observations or evidence are incorporated.
Math and Architectures of Deep Learning
The distribution over parameters before observing data.
- How it is used
- Injects beliefs or constraints into Bayesian parameter estimation when observed training data alone is insufficient.
- How deep it goes
- Derives priors through MAP and Gaussian, gamma, and normal-gamma posterior estimation, then applies them to mixtures and VAEs.
- Examples
- Uses small-magnitude parameter penalties, Gaussian mean and precision estimation, class-selection weights, height data, and latent Gaussian priors.
- What you can do after
- Apply it via PyTorch distributions to compute posterior distributions and MAP estimates for Gaussian model parameters.
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Grokking Machine Learning
A prior probability is the initial probability assigned to an event or hypothesis before new evidence is considered.
- How it is used
- Supplies the starting probability that Bayes’ theorem revises when new evidence arrives.
- How deep it goes
- Defines the prior and calculates it from counts, then follows its revision through medical tests and email words.
- Examples
- Uses a rain forecast, medical-test counts, a 100-email spam example and a labeled email dataset.
- What you can do after
- Apply it via pandas to estimate spam and ham priors from labeled emails before making word-based predictions.
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Fabulous Adventures in Data Structures and Algorithms
A prior is a probability distribution representing beliefs about a hypothesis before incorporating new evidence.
- How it is used
- Supplies the starting belief used to infer causes from observed effects.
- How deep it goes
- Develops priors from survey counts into weighted distributions, joint calculations, and posterior updates, including integer-weight implementation.
- Examples
- Uses a cold-and-sneeze survey, a rare-condition blood test, and repeated coin flips.
- What you can do after
- Apply it via ToCategorical, ToJoint, and Posterior to construct discrete priors and update them after observations.
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Bayesian Optimization in Action
A prior distribution is a probability distribution representing beliefs about an unknown quantity before incorporating observations.
- How it is used
- Frames initial uncertainty so Bayesian updating and information-theoretic search can incorporate existing beliefs.
- How deep it goes
- Defines priors through examples and distributions, then shows posterior effects while treating Bayes’ theorem only at a high level.
- Examples
- Uses house prices, a psychic-number test, and a phone-drop floor-search problem.
- What you can do after
- Apply it via entropy search to choose trials under uncertainty while accounting for nonuniform beliefs.
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AI-Powered Search
A prior distribution is a probability distribution representing an initial belief about an unknown quantity before incorporating case-specific observations.
- How it is used
- Uses a beta prior to temper click-derived relevance judgments without discarding rarely examined results from LTR training.
- How deep it goes
- Works through configurable prior values, click-count updates, posterior grades, and a Python implementation.
- Examples
- Compares raw and adjusted grades for “blue ray” search results and supplies Python calculations.
- What you can do after
- Operate/configure a beta prior to produce confidence-adjusted judgments for an LTR pipeline.
Build a Robo-Advisor with Python (From Scratch)
A prior distribution is a probability distribution representing beliefs about an unknown quantity before incorporating observed data.
- How it is used
- Anchors Black–Litterman expected returns before investor views update them into optimization inputs.
- How deep it goes
- Defines priors through Bayes’ rule and specifies multivariate-normal update formulas, while deferring their mathematical derivation.
- Examples
- Uses professional basketball and height events, then multivariate expected returns and uncertain investor views.
- What you can do after
- Apply it via Python functions to update equilibrium return estimates and covariance before asset-allocation optimization.
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Causal AI
A prior distribution is a probability distribution expressing beliefs about unknown quantities before observing the relevant data.
- How it is used
- Frames beliefs about unknown parameters before data and constrains plausible causal graph structures during discovery.
- How deep it goes
- Explains priors, hyperparameters, posterior distributions, and uncertainty, while stopping short of specifying particular prior families or computations.
- Examples
- Uses parameter estimation and required or forbidden graph edges as examples of prior information.
- What you can do after
- Evaluate parameter uncertainty and incorporate it into predictions or causal discovery constraints.
Machine Learning Algorithms in Depth
A prior distribution represents probability beliefs about model parameters or latent variables before observing the current data.
- How it is used
- Represents initial beliefs about parameters or latent variables and combines them with observed data to produce a posterior.
- How deep it goes
- Defines prior types, conjugacy, and normalization, then works through Beta-Bernoulli updating but defers high-dimensional normalization techniques.
- Examples
- Uses uniform and experience-based priors, a Bayes-engine update diagram, and a Beta prior for repeated coin flips.
- What you can do after
- Apply it via Bayes rule to update beliefs and compute a closed-form Beta posterior for coin-flip data.
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Related concepts
- posterior probabilityproduces · A posterior probability or distribution expresses the probability assigned to an event, hypothesis, or unknown quantity conditional on observed evidence and prior information.
- bayesian statisticsused by · Bayesian statistics is a framework for statistical inference that combines prior probability distributions with observed-data likelihoods to update probabilities over hypotheses or unknown quantities.
- conjugacyincludes · Conjugacy is the property whereby a prior distribution and a specified likelihood yield a posterior distribution in the same family as the prior.
- probability distributionkind of · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
- Bayesian modelpart of · A Bayesian model represents uncertain quantities with prior distributions, likelihoods, and posterior distributions updated using observed data.
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