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Computational statistics develops and studies computational procedures for statistical inference. It includes numerical evaluation of likelihood functions, simulation from probability distributions and assessment of uncertainty when an exact symbolic calculation is unavailable. The statistical question and the numerical approximation both need error control.

For example, if independent simulations $X_1,\dots ,X_M$ follow a model and $g(X)$ has finite variance, the Monte Carlo estimator $\hat{\mu }=M^{-1}{\sum }_{j}g(X_j)$ estimates $\mu =\mathbb{E}[g(X)]$, with variance $\mathrm{Var}(g(X))/M$. Halving its standard deviation therefore requires four times as many independent simulations. An optimization routine finding a maximum of a likelihood function and a simulation routine estimating an integral solve different computational tasks, even when both are steps in the same analysis.

Giacomo Zanella develops methods in computational statistics, applied probability theory and machine learning, especially Bayesian computation. His research statement identifies Markov chain Monte Carlo, random measures and variable selection among these interests.^[ref]

With Gareth Roberts, he proposed the Tempered Gibbs sampler. A modified coordinate-selection rule can explore difficult high-dimensional targets more effectively; importance sampling weights then recover averages under the desired probability distribution. Their analysis includes applications to Bayesian variable selection.^[ref]

Nathaniel E. Helwig develops statistical methods at the intersection of psychology and computational statistics. His University of Minnesota research biography emphasizes multivariate and nonparametric statistics for complex observations.^[ref]

His Generalized Linear Models in R by Nathaniel E. Helwig explains how a link function connects a response's conditional expected value with a linear predictor. For logistic regression, the predictor represents log odds; for Poisson regression, a logarithmic link ensures a positive fitted mean. This separates the model for the mean from the response's probability distribution, while making deviance and dispersion part of model assessment.^[ref]