A Generalized Gaussian Process Model for Computer Experiments With Binary Time Series

Abstract

Non-Gaussian observations such as binary responses are common in some computer experiments. Motivated by the analysis of a class of cell adhesion experiments, we introduce a generalized Gaussian process model for binary responses, which shares some common features with standard GP models. In addition, the proposed model incorporates a flexible mean function that can capture different types of time series structures. Asymptotic properties of the estimators are derived, and an optimal predictor as well as its predictive distribution are constructed. Their performance is examined via two simulation studies. The methodology is applied to study computer simulations for cell adhesion experiments. The fitted model reveals important biological information in repeated cell bindings, which is not directly observable in lab experiments.

Sequential Design of Computer Experiments with Quantitative and Qualitative Factors in Applications to HPC Performance Optimization

“…Finally, the proposed method is not limited to the continuous response. It will be interesting to investigate on how to extend the proposed method for computer experiments with noncontinuous output such as binary responses (Sung et al 2020).…”

Renewal Model for Dependent Binary Sequences

“…On the other hand, the Ising model is the only known parametric family that can cover all correlations of a finite number of binary variables. For this reason, in order to describe and generate infinite binary sequences, researchers have devised several approaches, each with its own advantages and disadvantages, which can be grouped in autoregressive models [7][8][9][10][11][12][13][14], latent factor models [15][16][17], and mixed models which combine autoregression with latent factors [7,20]. Autoregressive models are Markov chains with the property that the current probability of a symbol conditional on the past history is determined by a linear function of the previous outcomes [7], in a number corresponding to the order of the chain, linearity being postulated to not have explosion of parameters.…”

Renewal model for dependent binary sequences

“…Indeed, on the one hand the Ising model is the only known parametric family that covers all correlations, but on the other hand finite-dimensional distributions structured according to the Ising model are generally not consistent under marginalization, so that they cannot be regarded as children of a common probability measure associated with a stochastic process. For this reason, in order to describe and generate infinite binary sequences, researchers have devised several approaches, each with its own advantages and disadvantages, which can be grouped in autoregressive models [7][8][9][10][11][12][13][14], latent factor models [15][16][17], and mixed models which combine autoregression with latent factors [7,20]. Autoregressive models are Markov chains with the property that the current probability of a symbol conditional on the past history is determined by a linear function of the previous outcomes [7], in a number corresponding to the order of the chain, linearity being postulated to not have explosion of parameters.…”