Fully bayes parameter estimation
Fully Bayesian parameter estimation combines a prior distribution with observed-data likelihood to produce a posterior distribution over unknown parameters.
Causal AI
Bayesian estimation combines a prior distribution with observed data to produce a posterior distribution or estimate of parameters.
- How it is used
- Supplies parameter uncertainty to probabilistic predictions and to causal-effect inference after intervention on a fitted graphical model.
- How deep it goes
- Defines prior-to-posterior estimation, details a conjugate categorical case, and outlines a causal workflow without deriving general inference algorithms.
- Examples
- Uses pgmpy Dirichlet pseudo-counts for categorical probabilities and an online-game causal graph for a parameter-estimation workflow.
- What you can do after
- Apply it via pgmpy BayesianEstimator for conjugate point estimates, or use Pyro inference to obtain posterior samples for subsequent causal inference.
Read how Causal AI explains fully bayes parameter estimation →
Math and Architectures of Deep Learning
A Bayesian parameter-estimation approach that combines observed data likelihood with a prior distribution to obtain a posterior over the unknown parameter.
- How it is used
- Uses prior beliefs with observed data to estimate probability-distribution parameters for unsupervised generative modeling.
- How deep it goes
- Derives Gaussian and gamma posterior updates across known and unknown parameters, then connects them to PyTorch implementations.
- Examples
- Uses cat-image density modeling, unknown-mean Gaussian estimation, unknown-variance Gaussian estimation, and PyTorch code listings.
- What you can do after
- Apply Bayesian Gaussian estimation in PyTorch by updating posterior parameters for unknown means, variances, or precisions.
Read how Math and Architectures of Deep Learning explains fully bayes parameter estimation →
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.
- parameter estimationkind of · Parameter estimation is the process of inferring unknown numerical model parameters from observed data and, where applicable, substantive assumptions.
- bayesian statisticsuses · 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.
- prior probabilityuses · A prior probability distribution represents beliefs or assumptions about an unknown quantity before relevant observations or evidence are incorporated.
- Dirichlet distributionuses · A Dirichlet distribution is a continuous probability distribution over vectors of nonnegative components that sum to one, parameterized by positive concentration parameters.
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