PhD Pre-Submission Progress review talk
You are invited to attend the following PhD Pre-Submission Progress review talk.
- Wednesday 09 December 2020 12:00 pm (Add to calendar)
- Paul Kabaila
- Presented by:
- Nishika Ranathunga
- Type of Event:
Title: Confidence Intervals in General Regression Models that Utilize Uncertain Prior Information
We consider a general regression model, without a scale parameter. We construct a confidence interval for a scalar parameter of interest that utilizes the uncertain prior information that a distinct scalar parameter takes the specified value. This confidence interval has good coverage properties. It also has scaled expected length, where the scaling is with respect to the usual confidence interval, that is (a) substantially less than 1 when the prior information is correct, (b) has a maximum value that is not too large and (c) is close to 1 when the data and prior information are highly discordant.
Furthermore, in Kabaila and Ranathunga (2020), we solve the problem of numerically evaluating the expected value of a smooth bounded function of a chi-distributed random variable, divided by the square root of the number of degrees of freedom, using Mori's transformation followed by the trapezoidal rule, which is exponentially convergent for suitable integrands. This problem arises in simultaneous inference, selection and ranking of populations, the evaluation of multivariate t probabilities and the assessment of coverage and expected volume properties of non-standard confidence regions.
We apply this solution in the R package ciuupi2 that computes the Kabaila and Giri (2009) confidence interval, which utilizes the uncertain prior information in a linear regression model with unknown error variance. Previous computations of this interval used MATLAB programs that were time-consuming to run. By writing these programs in R, the computation time is greatly reduced and they become freely available. We also assess a new definition of scaled expected length.
Finally, we compare the computations of the log-likelihood function for generalized linear mixed models using (a) adaptive Gauss-Hermite quadrature and (b) importance sampling, where both methods share the same initial step (Kabaila and Ranathunga, 2019).
- Kabaila, P., & Giri, K. (2009). Confidence intervals in regression utilizing prior information. Journal of Statistical Planning and Inference, 139, 3419-3429.
- Kabaila P. and Ranathunga N. (2019) On Adaptive Gauss-Hermite Quadrature for Estimation in GLMM’s. In: Nguyen H. (eds) Statistics and Data Science. RSSDS 2019. Communications in Computer and Information Science, vol 1150. Springer, Singapore.
- Kabaila, P., & Ranathunga, N. (2020). Computation of the expected value of a chi-distributed random variable. Computational Statistics.
ZOOM LINK: https://latrobe.zoom.us/j/98357628534