tag:blogger.com,1999:blog-3240271627873788873.post3550020243435722577..comments2024-03-26T06:46:11.752-04:00Comments on Doing Bayesian Data Analysis: Decisions from posterior distributions: Tail probability or highest density interval?John K. Kruschkehttp://www.blogger.com/profile/17323153789716653784noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-3240271627873788873.post-50389647146596576252015-08-18T08:07:47.217-04:002015-08-18T08:07:47.217-04:00Right, by definition if invariance under reparamet...Right, by definition if invariance under reparameterization is the primary motivation, then the equal-tailed interval is more appropriate. <br /><br />It's relevant to point out that another consequence, often overlooked, is that the corresponding indicator of central tendency is the <i>median</i> of the distribution, not the mean. (When using highest density intervals, the corresponding indicator of central tendency is the mode, i.e., the point of highest density. Unfortunately the estimate of the mode from an MCMC sample is noisy.)John K. Kruschkehttps://www.blogger.com/profile/17323153789716653784noreply@blogger.comtag:blogger.com,1999:blog-3240271627873788873.post-50391406938776534492015-08-18T03:33:28.914-04:002015-08-18T03:33:28.914-04:00Link was broken... Here's the correct link:
h...Link was broken... Here's the correct link:<br /><br />https://docs.google.com/forms/d/1vfzd-ATu5a3Nh02EvLOPCr4iDFyuwz62Xv3_oAUR9xs/viewform?usp=send_formA.Grinstedhttps://www.blogger.com/profile/13909251015838896166noreply@blogger.comtag:blogger.com,1999:blog-3240271627873788873.post-16685327141304977802015-08-18T03:20:27.326-04:002015-08-18T03:20:27.326-04:00I am trying to get a feel for peoples preference o...I am trying to get a feel for peoples preference on equal-tailed -vs- highest density. So, I made a google-form mini survey here:<br /><br />https://docs.google.com/forms/d/1vfzd-ATu5<br /><br />Currently, with only very few respondents, the preference appears to be about balanced ETI vs HDI. <br /><br />For me personally the invariance to reparameterization of the equal tailed interval is very appealing. Lets say an astronomer does sine regression to characterize the dominant oscillation in a time series. I would expect consistent intervals regardless on whether a period or a frequency was used as the parameter. Often I am interested in the sign of a parameter, then i'd like to know the relative odds of positive vs negative (or simply the probability of negative as you show in green in your plots).A.Grinstedhttps://www.blogger.com/profile/13909251015838896166noreply@blogger.comtag:blogger.com,1999:blog-3240271627873788873.post-18191114547148861722014-03-22T17:42:40.687-04:002014-03-22T17:42:40.687-04:00Thanks for your interest in the book.
My short an...Thanks for your interest in the book.<br /><br />My short answer is that I don’t have an adequate answer. There are many relevant measures of effect size in the frequentist literature, of course, but we seek something for hierarchical Bayesian log-linear models. A measure of effect size is supposed to be an aggregated difference (i.e., the “effect”) standardized relative to some indicator of variance or noise in the data. Moreover, in a Bayesian setting, the effect size has a posterior distribution; it’s not just a point estimate. An example of posterior effect size for a difference between groups is given here: http://www.indiana.edu/~kruschke/BEST/<br />One possibility for describing effect size in hierarchical Bayesian ANOVA-style models (including log-linear models) is a ratio of estimated variance parameters. For example, the main effect of factor A might have an “effect size” given by sigma_A divided by sigma_y, where sigma_A is the scale parameter of the distribution of the factor-A deflections, and sigma_y is the scale parameter of the within-cell noise distribution. But that’s just off the top of my head.<br />Thanks again,<br />--John<br />John K. Kruschkehttps://www.blogger.com/profile/17323153789716653784noreply@blogger.comtag:blogger.com,1999:blog-3240271627873788873.post-10218744912716758602014-03-19T18:32:47.247-04:002014-03-19T18:32:47.247-04:00Dear Prof. Krushke, I'm working with ch 22 of ...Dear Prof. Krushke, I'm working with ch 22 of DBDA to analyse contingency tables. I'm curious to know where to look for a measure of effect size, both for the whole table and for individual interactions. Any tips you have would be much appreciated!<br />Thanks, BenBenhttps://www.blogger.com/profile/08993375645289421783noreply@blogger.comtag:blogger.com,1999:blog-3240271627873788873.post-34199252982022564152013-09-05T10:25:59.246-04:002013-09-05T10:25:59.246-04:00The question of whether to prefer a quantile-based...The question of whether to prefer a quantile-based interval or an HDI can be clarified by taking a statistical decision theory perspective. Consider two loss functions, both of which consist of a penalty proportional to the interval width plus another term that penalizes lack of coverage of the true value. For the first loss function, the lack-of-coverage penalty is the 0-1 loss; for the second loss function, the lack-of-coverage penalty is proportional to the distance by which the interval fails to cover the true value (if any). <a href="http://stats.stackexchange.com/questions/24681/what-is-the-decision-theoretic-justification-for-bayesian-credible-interval-proc" rel="nofollow">It turns out</a> that minimizing posterior expected loss leads to the HDI under the first loss function and to a quantile-based interval under the second loss function.Anonymousnoreply@blogger.com