Simpson's paradox is a commonly used example to introduce confounders and how they can cause problems if not handled appropriately. I'm going to piggyback on the specific example from (Bottou et al, 2013), another excellent paper that should be on your reading list if you haven't read it already. We're looking at data about the success rate of two different treatments, A and B, for kidney stone removal:
Look at the first column "Overall" first. The average success rate of treatment A is 78%, while the success rate of treatment B is 83%. You might stop here and conclude that treatment B is better because it's successful in a higher percentage of cases, and continue recommending treatment B to everyone. Not so fast! Look at what happens if we group the data by the size of kidney stone. Now we see that in the group of patients with small stones, treatment A is better, in the group with large stones we also see that treatment A is better. How can treatment A be superior in both group of patients, but treatment B be better overall?
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The obvious limitation of this method - and the authors are very transparent about this - is that it cannot deal with single-cause confounders. You have to assume if there is a confounder in your problem, you will be able to find another cause variable causally influenced by the same confounder in order to use this method.
The other limitation is the assumption that the assignments follow a factor model distribution marginally. While this may seem like a relatively OK assumption, it rules a couple of interesting cases out. For example, the assumption implies that the treatments cannot directly causally influence each other. In many applications this is not a reasonable assumption. If I make you watch Lord of the Rings it will definitely causally influence whether you will want to watch Lord of the Rings II. Similarly, some treatments in hospitals may be given or ruled out because of other treatments.
Finally, while the argument guarantees that all multi-cause confounders will be contained in the substitute confounder, there is no guarantee that the method will identify a minimal set of confounders. Indeed, if there are factors which influence multiple $A$s but are unrelated to the outcome, those variables will be covered by $Z$ as well. It is not difficult to create toy examples where the majority of the information captured in $Z$ is redundant.
In the second paper, Wang et al (2018) use this method to the specific problem of training recommender systems. The issue here is that vanilla ML approaches work only when items and users are randomly sampled in the dataset, which is rarely the case. Whether you watch a movie, and whether you like it are confounded by a number of factors, many of which you cannot model or observe. The method does apply to this case, and it does better than their but the results lack the punch I was hoping to see.
My approach in therapy is like my view on my life, it will be what I make of it. I want every session to be as productive as possible. Realizing that 80% of the session is the therapeutic alliance, meaning the relationship between the therapist and the client, it my my belief that I can only help my clients reach optimum mental health if I also work on my own health. Self care and reflection are a part of my daily life, as they need to be for my clients.
I use several different theories in my practice because no two clients will respond the same, but my favorites are Gottman, Emotion Focused, Imago, and Internal Family Systems. A few of the techniques I use are EMDR, BrainSpotting, letter writing, guided imagery and empty chair (Gestalt) and of course, good old fashion listening. I find that by asking curious questions, it causes my clients to think and resolve problems on their own. Which in turn empowers them and give them tools to endure whatever struggles come their way.
The 1917 code contained 145 canons (cc. 1999- 2144) on causes of canonization, and mandated that an episcopal process and an apostolic process be conducted. The episcopal process consisted of the local bishop verifying the reputation of the person, ensuring that a biography existed, collecting eye witness testimony and the person's written works. All of this was then forwarded to the Congregation for Sacred Rites. The apostolic process consisted of reviewing the evidence submitted, collecting more evidence, studying the cause, investigating any alleged miracles and ultimately forwarding the cause to the Pope for his approval. This process remained in effect until 1983 with the promulgation of the 1983 Code of Canon Law and new norms for causes of canonization: Divinus Perfectionis Magister, Normae Servandae in Inquisitionibus ab Episcopis Faciendis in Causis Sanctorum and Sanctorum Mater (2007). This revised process for causes of canonization is still in force and is detailed below.
No precise count exists of those who have been proclaimed saints since the first centuries. However, in 1988, to mark its 4th centenary, the Congregation for the Causes of Saints published the first "Index ac Status Causarum." This book and its subsequent supplements, written entirely in Latin, are considered the definitive index of all causes that have been presented to the Congregation since its institution.
we shall be satisfied with the goodness of thy house;
even all that are like this man, chosen by the grace of God, redeemed by the blood of Christ, brought into the house of God, and have a place and a name there, better than that of sons and daughters of men: by "the house" of God we are to understand the church of God; and by "the goodness" of it the provisions of grace in it, the word and ordinances, and the blessings of grace held forth in them, and especially Christ the bread of life, whose flesh is meat indeed, and whose blood is drink indeed; of which true believers may eat, and do to full satisfaction; and blessed are they that have such food, and appetites for it, and are filled with it. The Targum paraphrases it,
We present here the results of our inter-disciplinary examination of the mummified heart of Blessed Anne-Madeleine Remuzat (1696-1730). This organ has been examined in the context of a canonization process. This analysis is related to important aspects of the early history of anatomy in Europe, that of "Holy autopsies", and to the relationship between anatomical investigations, Catholic theology, and religious/medical customs. According to anatomical, genetic, toxicological, and palynological analyses, it has been shown that this organ has not been naturally ("miraculously") conserved but embalmed using myrtle, honey, and lime. Moreover, a right ventricle dilatation has been diagnosed, that may represent a post-tuberculosis condition and may have played a role in the cause of death of this religious figure.
Today God's minister has blessed your prayer, and he has invoked upon you the blessings of heaven, so that every one of you may be worthy of this flag and may defend it against every attack.
Because this flag, young people, represents in a symbolic way a divine doctrine, given by Jesus Christ for our redemption.
Young people, I see on your flag the motto "Prayer, Action and Sacrifice." These are three words which summarize a very vast program whose implementation requires our energies and those of generations to come.
Prayer is the noble supplication which we lift up to the throne of God. It is the most efficient means to obtain from God the graces which we need, and especially the strength of persevering in these times, in which the hatred of the sons of the devil is breaking out violently against the sheep who are faithful to the fold.
In recommending heartfelt prayer to you, I am including all the practices of piety, first of all the most Holy Eucharist.
And remembering that apostle of the Holy Eucharist, the Holy Father Pius X2 of venerable memory, I urge you with all the strength of my soul to approach the Eucharistic Table as often as possible. Feed on this Bread of the Angels from which you will draw the strength to fight inner struggles, the struggles against passions and against all adversities, because Jesus Christ has promised to those who feed themselves with the most Holy Eucharist, eternal life and the necessary graces to obtain it.
And when you become totally consumed by this Eucharistic Fire, then you will be able to thank with greater awareness the Lord God who has called you to be part of his flock and you will enjoy that peace which those who are happy according to the world have never tasted. Because true happiness, young people, does not consist in the pleasures of the world and in earthly things, but in peace of conscience which we can have only if we are pure in heart and in mind.
After having fortified our spirit by applying ourselves with great diligence to works of mercy, and after having intensely studied the questions which are troubling us, then we can throw ourselves into the apostolate. And there are three distinct apostolates.
First of all there is the apostolate of good example. We Catholics must strive to have our whole life guided by Christian moral law. Then there is the apostolate of charity by going among those who suffer and comforting them, among the unfortunate and saying a comforting word to them, because the Catholic religion is based on charity which is nothing other than the most perfect Love.
The Apostle St. Paul says, "The charity of Christ needs us," and without this fire, which little by little must destroy our personality so that our heart beats only for the sorrows of others, we would not be Christians, much less Catholics.
Finally there is the apostolate of persuasion. This is one of the most beautiful and necessary. Young people, approach your colleagues at work who live their lives away from the Church and spend their free time not in healthy pastimes, but in vices. Persuade those unfortunate people to follow the ways of God, strewn with many thorns, but also many roses.
But if every one of you were to possess these gifts to the highest degree, and did not have the spirit of sacrifice in abundance, you would not be a good Catholic. We must sacrifice everything for everything: our ambitions, indeed our entire selves, for the cause of the Faith.
In order for our life to be Christian, it must be a continual renunciation, a continual sacrifice which however is not burdensome when only we think about what these few years passed in sorrow are, compared with a happy eternity, where joy will have no measure nor end, and where we will enjoy a peace beyond anything we could imagine. And so, young people, learn how to sacrifice from our Lord Jesus Christ. In order to atone for our horrible sins, He sacrificed Himself as an Innocent Victim on Calvary, and He renews this wonderful Sacrifice every day in every part of the world during Holy Mass.
From this day forward you have become part of the great family of the "Italian Catholic Youth." Hold high the place that the Lord in His Goodness has wanted to award you.
The times which we are going through are difficult, because persecution against the Church rages as cruelly as ever. But you fearless and good young people, do not be afraid because of this small problem. Bear in mind the fact that the Church is a divine institution that cannot end and will endure until the end of the world, and "the gates of hell will not prevail against her." Therefore keep this beautiful white flag immaculate, and if the occasion should present itself tomorrow, defend it, because from now on it is sacred: it not only represents your club, it also represents the most beautiful patrimony of our Italy and of the civilized world.
And in order to bring these poor words of mine to an end, let me cry out with you: Long live Jesus Christ! Long live the Pope!
Pier Giorgio Frassati
From: "Pier Giorgio Frassati, Letters to his Friends and Family"
ST PAULS/Alba House, 2009 2351a5e196
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