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Bayesian Estimation as an Alternative to Monte Carlo Analysis in Financial Planning: An Application Using S&P 500 Returns
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A majority of statistically educated scientists draw incorrect conclusions based on the most commonly used statistical technique: null hypothesis significance testing (NHST). Frequentist techniques are often claimed to be incorrectly interpreted as Bayesian outcomes, which suggests that a Bayesian framework may fit better to inferences researchers frequently want to make (Briggs, 2012). The current study set out to test this proposition. Firstly, we investigated whether there is a discrepancy between what researchers think they can conclude and what they want to be able to conclude from NHST. Secondly, we investigated to what extent researchers want to incorporate prior study results and their personal beliefs in their statistical inference. Results show the expected discrepancy between what researchers think they can conclude from NHST and what they want to be able to conclude. Furthermore, researchers were interested in incorporating prior study results, but not their personal beliefs, into their statistical inference.
Leave-one-out cross-validation (LOO) and the widely applicable information criterion (WAIC) are methods for estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model using the log-likelihood evaluated at the posterior simulations of the parameter values. LOO and WAIC have various advantages over simpler estimates of predictive error such as AIC and DIC but are less used in practice because they involve additional computational steps. Here we lay out fast and stable computations for LOO and WAIC that can be performed using existing simulation draws. We introduce an efficient computation of LOO using Pareto-smoothed importance sampling (PSIS), a new procedure for regularizing importance weights. Although WAIC is asymptotically equal to LOO, we demonstrate that PSIS-LOO is more robust in the finite case with weak priors or influential observations. As a byproduct of our calculations, we also obtain approximate standard errors for estimated predictive errors and for comparison of predictive errors between two models. We implement the computations in an R package called loo and demonstrate using models fit with the Bayesian inference package Stan.
Markov Chain Monte–Carlo (MCMC) is an increasingly popular method for obtaining information about distributions, especially for estimating posterior distributions in Bayesian inference. This article provides a very basic introduction to MCMC sampling. It describes what MCMC is, and what it can be used for, with simple illustrative examples. Highlighted are some of the benefits and limitations of MCMC sampling, as well as different approaches to circumventing the limitations most likely to trouble cognitive scientists.
The use of significance tests in science has been debated from the invention of these tests until the present time. Apart from theoretical critiques on their appropriateness for evaluating scientific hypotheses, significance tests also receive criticism for inviting mi- sinterpretations. We presented six common misinterpretations to psychologists who work in German universities and found out that they are still surprisingly widespread - even among instructors who teach statistics to psychology students. Although these mi- sinterpretations are well documented among students, until now there has been little research on pedagogical methods to remove them. Rather, they are considered "hard facts" that are impervious to correction. We discuss the roots of these misinterpretations and propose a pedagogical concept to teach significance tests, which involves explaining the meaning of statistical significance in an appropriate way.
The authors considered an individual investor who holds a financial portfolio with funds in at least two of the following accounts: a taxable account, a tax-deferred account, and a tax-exempt account. They examined various strategies for withdrawing these funds in retirement. Conventional wisdom suggests that the investor should withdraw funds first from the taxable account, then from the tax-deferred account, and finally from the tax-exempt account. The authors provide the underlying intuition for more tax-efficient withdrawal strategies and demonstrate that these strategies can add more than three years to the portfolio’s longevity relative to the strategy suggested by the conventional wisdom.
The use of Bayesian methods for data analysis is creating a revolution in fields ranging from genetics to marketing. Yet, results of our literature review, including more than 10,000 articles published in 15 journals from January 2001 and December 2010, indicate that Bayesian approaches are essentially absent from the organizational sciences. Our article introduces organizational science researchers to Bayesian methods and describes why and how they should be used. We use multiple linear regression as the framework to offer a step-by-step demonstration, including the use of software, regarding how to implement Bayesian methods. We explain and illustrate how to determine the prior distribution, compute the posterior distribution, possibly accept the null value, and produce a write-up describing the entire Bayesian process, including graphs, results, and their interpretation. We also offer a summary of the advantages of using Bayesian analysis and examples of how specific published research based on frequentist analysis-based approaches failed to benefit from the advantages offered by a Bayesian approach and how using Bayesian analyses would have led to richer and, in some cases, different substantive conclusions. We hope that our article will serve as a catalyst for the adoption of Bayesian methods in organizational science research.
Exploring the Retirement Consumption Puzzles
- David Blanchett
Model-based clustering of non-Gaussian panel data based on skew-t distributions
- R Hoekstra
Capital Market Expectations, Asset Allocation, and Safe Withdrawal Rates
- D Mcneish