Dealing with groups that don't conform to a MVN distribution

[Rachael-H14]

Hi there,

I have stable isotope data for several different groups of consumers at three different sites. I plan to use SIBER to produced SEA and layman metrics, to compare trophic structure between these communities.

A few of my groups do not conform to the assumption of a multivariate normal distribution. In most cases, it seems likely that the non normal distribution is due to small sample size (7 - 10). My initial plan is to simulate a multivariate normal distribution based off of my data for these non-normal groups - guesstimating what the mean and variance would be if I had a larger samples size - and then use that to make more informative priors for those groups.

My question is whether it's possible to make specific priors for each group, maintaining the standard priors for groups with a MVN distribution, but using the simulated values for the groups that do not conform to this assumption? And if so, how?

Many thanks in advance,
Rachael

[AndrewLJackson]

Hi Rachael I probably would not simulate up to larger sample sizes, since that is pretty much what the Bayesian MCMC approach is doing. The simulations in my J Anim Ecol paper show that small sample sizes can still yield unbiased estimates of the population means and variances, albeit with reduced precision. Also looking at, or simulating from the data, contravenes the concept of what a prior should be… i.e. your prior expectation of the statistics before considering the data. Personally, I think that normality tests are overly punitive and tend to lead to analysts wanting to reject the distribution. Even if its slightly non-normal, what are you going to use instead? Often we are stuck with the normal distribution as a catch-all, and unless there is strong evidence that the shape is different and there is a suitable alternative distribution I think taking the normal as an a priori assumption is justified in many cases. Your choice of distribution for the likelihood in a Bayesian analysis can be part of the prior in this regard. Best wishes Andrew From: Rachael-H14 ***@***.***> Date: Tuesday, 22 August 2023 at 18:02 To: AndrewLJackson/SIBER ***@***.***> Cc: Subscribed ***@***.***> Subject: [AndrewLJackson/SIBER] Dealing with groups that don't conform to a MVN distribution (Issue #99) Hi there, I have stable isotope data for several different groups of consumers at three different sites. I plan to use SIBER to produced SEA and layman metrics, to compare trophic structure between these communities. A few of my groups do not conform to the assumption of a multivariate normal distribution. In most cases, it seems likely that the non normal distribution is due to small sample size (7 - 10). My initial plan is to simulate a multivariate normal distribution based off of my data for these non-normal groups - guesstimating what the mean and variance would be if I had a larger samples size - and then use that to make more informative priors for those groups. My question is whether it's possible to make specific priors for each group, maintaining the standard priors for groups with a MVN distribution, but using the simulated values for the groups that do not conform to this assumption? And if so, how? Many thanks in advance, Rachael — Reply to this email directly, view it on GitHub<#99>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AAZLLMFWP3ORCIPM67MYSTTXWTQZ5ANCNFSM6AAAAAA32HEOXI>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***>

[Rachael-H14]

Hi Andrew, Thank you for getting back to me so quickly with your response. That is really clear and helpful, thank you. Best wishes, Rachael From: Andrew Jackson ***@***.***> Sent: Wednesday, August 23, 2023 9:55 AM To: AndrewLJackson/SIBER ***@***.***> Cc: Hall, Rachael E ***@***.***>; Author ***@***.***> Subject: Re: [AndrewLJackson/SIBER] Dealing with groups that don't conform to a MVN distribution (Issue #99) **************************************************************** Caution: This email originated from a sender outside Heriot-Watt University. Do not follow links or open attachments if you doubt the authenticity of the sender or the content. **************************************************************** Hi Rachael I probably would not simulate up to larger sample sizes, since that is pretty much what the Bayesian MCMC approach is doing. The simulations in my J Anim Ecol paper show that small sample sizes can still yield unbiased estimates of the population means and variances, albeit with reduced precision. Also looking at, or simulating from the data, contravenes the concept of what a prior should be… i.e. your prior expectation of the statistics before considering the data. Personally, I think that normality tests are overly punitive and tend to lead to analysts wanting to reject the distribution. Even if its slightly non-normal, what are you going to use instead? Often we are stuck with the normal distribution as a catch-all, and unless there is strong evidence that the shape is different and there is a suitable alternative distribution I think taking the normal as an a priori assumption is justified in many cases. Your choice of distribution for the likelihood in a Bayesian analysis can be part of the prior in this regard. Best wishes Andrew From: Rachael-H14 ***@***.***<mailto:***@***.***>> Date: Tuesday, 22 August 2023 at 18:02 To: AndrewLJackson/SIBER ***@***.***<mailto:***@***.***>> Cc: Subscribed ***@***.***<mailto:***@***.***>> Subject: [AndrewLJackson/SIBER] Dealing with groups that don't conform to a MVN distribution (Issue #99) Hi there, I have stable isotope data for several different groups of consumers at three different sites. I plan to use SIBER to produced SEA and layman metrics, to compare trophic structure between these communities. A few of my groups do not conform to the assumption of a multivariate normal distribution. In most cases, it seems likely that the non normal distribution is due to small sample size (7 - 10). My initial plan is to simulate a multivariate normal distribution based off of my data for these non-normal groups - guesstimating what the mean and variance would be if I had a larger samples size - and then use that to make more informative priors for those groups. My question is whether it's possible to make specific priors for each group, maintaining the standard priors for groups with a MVN distribution, but using the simulated values for the groups that do not conform to this assumption? And if so, how? Many thanks in advance, Rachael — Reply to this email directly, view it on GitHub<#99>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AAZLLMFWP3ORCIPM67MYSTTXWTQZ5ANCNFSM6AAAAAA32HEOXI>. You are receiving this because you are subscribed to this thread.Message ID: ***@***.***<mailto:***@***.***>> — Reply to this email directly, view it on GitHub<#99 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/BCBOY77UEQKGCEWJS6NQO63XWXANHANCNFSM6AAAAAA32HEOXI>. You are receiving this because you authored the thread.Message ID: ***@***.******@***.***>>

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