Bayesian Analysis of Generalized Hierarchical Indian Buffet Processes for Within and Across Group Sharing of Latent Features

Bayesian nonparametric hierarchical priors provide flexible models for sharing of information within and across groups. We focus on latent feature allocation models, where the data structures correspond to multisets or unbounded sparse matrices. The fundamental development in this regard is the Hierarchical Indian Buffet process (HIBP), devised by Thibaux and Jordan (2007). However, little is known in terms of explicit tractable descriptions of the joint, marginal, posterior and predictive distributions of the HIBP. We provide explicit novel descriptions of these quantities, in the Bernoulli HIBP and general spike and slab HIBP settings, which allows for exact sampling and simpler practical implementation. We then extend these results to the more complex setting of hierarchies of general HIBP (HHIBP). The generality of our framework allows one to recognize important structure that may otherwise be masked in the Bernoulli setting, and involves characterizations via dynamic mixed Poisson random count matrices. Our analysis shows that the standard choice of hierarchical Beta processes for modeling across group sharing is not ideal in the classic Bernoulli HIBP setting proposed by Thibaux and Jordan (2007), or other spike and slab HIBP settings, and we thus indicate tractable alternative priors.Comment: This is an extensive re-write and extension of arXiv:2103.11407 where variations of the results for the HIBP (but not HHIBP) were establishe

Attitudes towards vaccines and intention to vaccinate against COVID-19: a cross-sectional analysis - implications for public health communications in Australia

Objective To examine SARS-CoV-2 vaccine confidence, attitudes and intentions in Australian adults as part of the iCARE Study. Design and setting Cross-sectional online survey conducted when free COVID-19 vaccinations first became available in Australia in February 2021. Participants Total of 1166 Australians from general population aged 18-90 years (mean 52, SD of 19). Main outcome measures Primary outcome: responses to question € If a vaccine for COVID-19 were available today, what is the likelihood that you would get vaccinated?'. Secondary outcome: analyses of putative drivers of uptake, including vaccine confidence, socioeconomic status and sources of trust, derived from multiple survey questions. Results Seventy-eight per cent reported being likely to receive a SARS-CoV-2 vaccine. Higher SARS-CoV-2 vaccine intentions were associated with: increasing age (OR: 2.01 (95% CI 1.77 to 2.77)), being male (1.37 (95% CI 1.08 to 1.72)), residing in least disadvantaged area quintile (2.27 (95% CI 1.53 to 3.37)) and a self-perceived high risk of getting COVID-19 (1.52 (95% CI 1.08 to 2.14)). However, 72% did not believe they were at a high risk of getting COVID-19. Findings regarding vaccines in general were similar except there were no sex differences. For both the SARS-CoV-2 vaccine and vaccines in general, there were no differences in intentions to vaccinate as a function of education level, perceived income level and rurality. Knowing that the vaccine is safe and effective and that getting vaccinated will protect others, trusting the company that made it and vaccination recommended by a doctor were reported to influence a large proportion of the study cohort to uptake the SARS-CoV-2 vaccine. Seventy-eight per cent reported the intent to continue engaging in virus-protecting behaviours (mask wearing, social distancing, etc) postvaccine. Conclusions Most Australians are likely to receive a SARS-CoV-2 vaccine. Key influencing factors identified (eg, knowing vaccine is safe and effective, and doctor's recommendation to get vaccinated) can inform public health messaging to enhance vaccination rates

How well do covariates perform when adjusting for sampling bias in online COVID-19 research? Insights from multiverse analyses

: COVID-19 research has relied heavily on convenience-based samples, which-though often necessary-are susceptible to important sampling biases. We begin with a theoretical overview and introduction to the dynamics that underlie sampling bias. We then empirically examine sampling bias in online COVID-19 surveys and evaluate the degree to which common statistical adjustments for demographic covariates successfully attenuate such bias. This registered study analysed responses to identical questions from three convenience and three largely representative samples (total N = 13,731) collected online in Canada within the International COVID-19 Awareness and Responses Evaluation Study ( www.icarestudy.com ). We compared samples on 11 behavioural and psychological outcomes (e.g., adherence to COVID-19 prevention measures, vaccine intentions) across three time points and employed multiverse-style analyses to examine how 512 combinations of demographic covariates (e.g., sex, age, education, income, ethnicity) impacted sampling discrepancies on these outcomes. Significant discrepancies emerged between samples on 73% of outcomes. Participants in the convenience samples held more positive thoughts towards and engaged in more COVID-19 prevention behaviours. Covariates attenuated sampling differences in only 55% of cases and increased differences in 45%. No covariate performed reliably well. Our results suggest that online convenience samples may display more positive dispositions towards COVID-19 prevention behaviours being studied than would samples drawn using more representative means. Adjusting results for demographic covariates frequently increased rather than decreased bias, suggesting that researchers should be cautious when interpreting adjusted findings. Using multiverse-style analyses as extended sensitivity analyses is recommended.COVID-19 research has relied heavily on convenience-based samples, which-though often necessary-are susceptible to important sampling biases. We begin with a theoretical overview and introduction to the dynamics that underlie sampling bias. We then empirically examine sampling bias in online COVID-19 surveys and evaluate the degree to which common statistical adjustments for demographic covariates successfully attenuate such bias. This registered study analysed responses to identical questions from three convenience and three largely representative samples (total N = 13,731) collected online in Canada within the International COVID-19 Awareness and Responses Evaluation Study (www.icarestudy.com). We compared samples on 11 behavioural and psychological outcomes (e.g., adherence to COVID-19 prevention measures, vaccine intentions) across three time points and employed multiverse-style analyses to examine how 512 combinations of demographic covariates (e.g., sex, age, education, income, ethnicity) impacted sampling discrepancies on these outcomes. Significant discrepancies emerged between samples on 73% of outcomes. Participants in the convenience samples held more positive thoughts towards and engaged in more COVID-19 prevention behaviours. Covariates attenuated sampling differences in only 55% of cases and increased differences in 45%. No covariate performed reliably well. Our results suggest that online convenience samples may display more positive dispositions towards COVID-19 prevention behaviours being studied than would samples drawn using more representative means. Adjusting results for demographic covariates frequently increased rather than decreased bias, suggesting that researchers should be cautious when interpreting adjusted findings. Using multiverse-style analyses as extended sensitivity analyses is recommended