Abstract Pricing decisions of companies require an understanding of the causal effect of a price change on the demand. When real-life pricing experiments are infeasible, data-driven decision-making must be based on alternative data sources such as purchase history (sales data) and conjoint studies where a group of customers is asked to make imaginary purchases in an artificial setup. We present an approach for price optimization that combines population statistics, purchase history and conjoint data in a systematic way.

Abstract Sequence analysis (SA) has gained increasing interest in social sciences for the holistic analysis of life course and other longitudinal data. The usual approach is to construct sequences, calculate dissimilarities, group similar sequences with cluster analysis, and use cluster membership as a dependent or independent variable in a linear or nonlinear regression model. This approach may be problematic as the cluster memberships are assumed to be fixed known characteristics of the subjects in subsequent analysis.

Abstract dynamite is an R package for Bayesian inference of intensive panel (time series) data comprising of multiple measurements per multiple individuals measured in time. The package supports joint modeling of multiple response variables, time-varying and time-invariant effects, a wide range of discrete and continuous distributions, group-specific random effects, latent factors, and customization of prior distributions of the model parameters. Models in the package are defined via a user-friendly formula interface, and estimation of the posterior distribution of the model parameters takes advantage of state-of-the-art Markov chain Monte Carlo methods.

Efficient methods for Bayesian inference of state space models via particle Markov chain Monte Carlo (MCMC) and MCMC based on parallel importance sampling type weighted estimators (Vihola, Helske, and Franks, 2020, doi:10.1111/sjos.12492). Gaussian, Poisson, binomial, negative binomial, and Gamma observation densities and basic stochastic volatility models with linear-Gaussian state dynamics, as well as general non-linear Gaussian models and discretised diffusion models are supported.

Bayesian generalized linear models with time-varying coefficients as in Helske (2020, arXiv:2009.07063). Gaussian, Poisson, and binomial observations are supported. The Markov chain Monte Carlo (MCMC) computations are done using Hamiltonian Monte Carlo provided by Stan, using a state space representation of the model in order to marginalise over the coefficients for efficient sampling. For non-Gaussian models, the package uses the importance sampling type estimators based on approximate marginal MCMC as in Vihola, Helske, Franks (2020, doi:10.

Panel data, consisting of various measurements from multiple subjects followed over several time points, are commonly studied in social sciences and other fields. Such data can naturally be analyzed in various ways, depending on the research questions and the characteristics of the data. Popular, somewhat overlapping modelling approaches include dynamic panel models, fixed effect models, and variations of cross-lagged panel models. In this talk, I extend the traditional cross-lagged panel model to handle time-varying effects and non-Gaussian response variables and show how Bayesian posterior predictive distributions can be used to evaluate long-term counterfactual predictions which take into account the dynamic structure of the assumed causal graph of the system. Finally, I give an overview of a new R package dynamite for Bayesian inference for panel data.

State space models are a flexible class of latent variable models commonly used in analysing time series data. The R package bssm is designed for Bayesian inference of general state space models with non-Gaussian and/or non-linear observational and state equations. The package provides easy-to-use and efficient functions for fully Bayesian inference with common time series models such as basic structural time series model with exogenous covariates, simple stochastic volatility models, and discretized diffusion models, making it straightforward and efficient to make predictions and other inference in a Bayesian setting. Unlike the existing packages, bssm allows for easy-to-use approximate inference based on Gaussian approximations such as the Laplace approximation and the extended Kalman filter. The inference is based on fully automatic, adaptive Markov chain Monte Carlo (MCMC) on the hyperparameters, with optional parallelizable importance sampling post-correction to eliminate any approximation bias. The bssm package implements also a direct pseudo-marginal MCMC and a delayed acceptance pseudo-marginal MCMC using intermediate approximations. The package supports directly models with linear-Gaussian state dynamics with non-Gaussian observation models and has an Rcpp interface for specifying custom non-linear and diffusion models.

We consider the problem of estimating causal effects of interventions from observational data when well-known back-door and front-door adjustments are not applicable. We show that when an identifiable causal effect is subject to an implicit functional constraint that is not deducible from conditional independence relations, the estimator of the causal effect can exhibit bias in small samples (where parameter estimation exhibits non-negligible uncertainty). This bias is related to variables that we call trapdoor variables. We use simulated data to study different strategies to account for trapdoor variables and suggest how the related trapdoor bias might be minimized. The importance of trapdoor variables in causal effect estimation is illustrated with real data from the Life Course 1971-2002 study. Using this dataset, we estimate the causal effect of education on income in the Finnish context. Using the Bayesian modelling approach allows us to take the parameter uncertainty into account and gives us the full interventional distribution instead of only average causal effect estimates.