Inductive Reasoning In Addition To The Philosophy Of Science

I've but finished reading Sharon Bertsch McGrayne's majority on Bayesian statistics,  The Theory That Would Not Die: How Bayes...

I've but finished reading Sharon Bertsch McGrayne's majority on Bayesian statistics, The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, as well as Emerged Triumphant from Two Centuries of Controversy. McGrayne presents a real interesting story of the advancement of a scientific thought over a real long menstruum (1740s through the 1950s). As she demonstrates at length, the thought that "subjective prior beliefs" could heighten our noesis well-nigh causation as well as the hereafter was regarded equally paradoxical as well as irrational past times mathematicians as well as statisticians for good over a century.

McGrayne's majority does a real goodness task of highlighting the scientific controversies that receive got arisen amongst honor to Bayesian methods, as well as the majority likewise makes a powerful instance for the value of the methods inwards many of import contemporary problems. But it isn't real detailed well-nigh the logic as well as mathematics of the field. She gives a unmarried illustration of applied Bayesian reasoning inwards appendix b, using the illustration of thorax cancer as well as mammograms. This is worth reading carefully, since it makes clear how the conditional probabilities of a Bayesian calculation work.

As McGrayne demonstrates amongst many examples, Bayesian reasoning permits a real substantial might to pull novel conclusions based on piecemeal observations as well as but about provisional assumptions well-nigh mechanisms inwards the messy world of complex causation. Examples tin last establish inwards epidemiology (the drive of lung cancer), climate science, as well as ecology. And she documents how Bayesian ideas receive got been used to heighten search processes for missing things -- for example, lost hydrogen bombs as well as nuclear submarines. Here is an of import illustration of the might of Bayesian reasoning to lay causal linkages to lung cancer, including especially cigarette smoking.

In 1951 Cornfield used Bayes’ dominion to assist response the puzzle. As his prior hypothesis he used the incidence of lung cancer inwards the full general population. Then he combined that amongst NIH’s latest information on the prevalence of smoking amid patients amongst as well as without lung cancer. Bayes’ dominion provided a business solid theoretical link, a bridge, if you lot will, betwixt the remove chances of affliction inwards the population at large as well as the remove chances of affliction inwards a subgroup, inwards this instance smokers. Cornfield was using Bayes equally a philosophy-free mathematical statement, equally a footstep inwards calculations that would yield useful results. He had non however embraced Bayes equally an all-encompassing philosophy. Cornfield’s newspaper stunned research epidemiologists. 

More than anything else, it helped advance the hypothesis that cigarette smoking was a drive of lung cancer. Out of necessity, but without whatever theoretical justification, epidemiologists had been using instance studies of patients to betoken to possible causes of problems. Cornfield’s newspaper showed clearly that nether surely atmospheric condition (that is, when subjects inwards a report were carefully matched amongst controls) patients’ histories could indeed assist stair out the forcefulness of the link betwixt a affliction as well as its possible cause. Epidemiologists could approximate affliction remove chances rates past times analyzing nonexperimental clinical information gleaned from patient histories. By validating research findings arising from case-control studies, Cornfield made much of modern epidemiology possible. In 1961, for example, case-control studies would assist lay the antinausea drug thalidomide equally the drive of serious nascency defects. (110-111)

One fairly specific thing that strikes me later reading the majority concerns the blindspots that existed inwards the neo-positivist tradition inwards the philosophy of scientific discipline that fix the damage for the champaign inwards the 1960s as well as 1970s (link). This tradition is largely focused on theories as well as theoretical explanation, to the relative exclusion of inductive methods. It reveals an underlying predilection for the thought that scientific noesis takes the cast of hypothetico-deductive systems describing unobservables. The hypothetico-deductive model of explanation as well as confirmation makes a lot of feel inwards the context of this perspective. But later reading McGrayne I'm retrospectively surprised at the relatively depression priority given inside touchstone philosophy of scientific discipline curriculum to probabilistic reasoning -- either frequentist or Bayesian. Many philosophers of scientific discipline receive got absorbed a score of disregard for "inductive logic", or the thought that nosotros tin discovery of import features of the world through careful observation as well as statistical analysis. The basic supposition seems to receive got been that statistical reasoning is like shooting fish in a barrel as well as Humean -- non actually capable of discovering novel things well-nigh nature or society. But in hindsight, this disregard for inductive reasoning is an strange distortion of the domain of scientific knowledge, and, in particular, of the projection of sorting out causes.

Some philosophers of scientific discipline receive got indeed given substantial attending to Bayesian reasoning. (Here is a goodness article on Bayesian epistemology past times Bill Talbott inwards the Stanford Encyclopedia of Philosophy; link.) Ian Hacking's textbook An Introduction to Probability as well as Inductive Logic provides a real accessible introduction to the basics of inductive logic as well as Bayesian reasoning, as well as his The Emergence of Probability: Influenza A virus subtype H5N1 Philosophical Study of Early Ideas well-nigh Probability, Induction as well as Statistical Inference provides an splendid handling of the history of the dependent champaign from a philosophy of scientific discipline betoken of view. Another philosopher of scientific discipline who has treated Bayesian reasoning inwards particular is Michael Strevens. Here Strevens provides a goodness brief handling of the dependent champaign from the betoken of persuasion of the philosophy of scientific discipline (link). And hither is a first-rate unpublished manuscript past times Strevens on the role of Bayesian ideas equally a theory of confirmation (link). Strevens' recent Tychomancy: Inferring Probability from Causal Structure is likewise relevant. And the research program on causal reasoning of Judea Pearl has led to a flourishing of Bayesian reasoning inwards the theory of causality (link).

What is the potential relevance of Bayesian reasoning inwards sociology as well as other areas of the social sciences? Can Bayesian reasoning Pb to novel insights inwards assessing social causation? Several features of the social world appear peculiarly distinctive inwards the context of a Bayesian approach. Bayesianism conforms real naturally to a scenario-based way of approaching the outcomes of a arrangement or a complicated process; as well as it provides an elegant as well as rigorous way of incorporating "best guesses" (subjective probability estimates) into the analysis of a given process. Both features are good suited to the social world. One argue for this is the relatively narrow limits of frequency-based estimates of probabilities of social events. The social sciences are oftentimes concerned amongst single-instance events -- the French Revolution, the Great Depression, the ascension of ISIS. In cases similar these frequency-based probabilities are non available. Second, at that topographic point is the employment of causal heterogeneity inwards many social causal relations. If nosotros are interested inwards the phenomenon of baby mortality, nosotros are led straightaway to the realization that at that topographic point are multiple social factors as well as atmospheric condition that influence this population characteristic; thus the overall baby mortality charge per unit of measurement of People's Republic of Bangladesh or French Republic is the composite trial of numerous social as well as demographic causes. This agency that at that topographic point is no unmarried underlying causal belongings X, where X tin last said to create differences inwards baby mortality rates inwards diverse countries. And this inwards plough implies that it is dubious to assume that at that topographic point are durable objective probabilities underlying the creation of a given charge per unit of measurement of baby mortality. This is inwards contrast to the province of affairs of earthquakes or hurricanes, where a pocket-size issue of physical factors are causally relevant to the occurrence of the outcome.

Both these factors advise that subjective probabilities based on expert-based assessment of the likelihood of diverse scenarios stand upwardly for a to a greater extent than plausible foundation for assigning probabilities to a given social outcome. This is the logic underlying Philip Tetlock's approach to reliable forecasting inwards link). Both points advise that Bayesian reasoning may receive got fifty-fifty to a greater extent than applicability inwards the social world than inwards the natural sciences.

The joining of Monte Carlo methods amongst Bayesian reasoning that McGrayne describes inwards the instance of the search for the missing nuclear submarine Thresher (199 ff.) is peculiarly relevant to social inquiry, it would seem. This is truthful because of the conjunctural nature of social causation as well as the complexity of typical causal intersections inwards the social domain. Consider a forecasting employment similar to those considered past times Tetlock -- for example, the likelihood that Russian Federation volition endeavor to occupy Republic of Latvia inwards the side past times side 5 years. One way of analyzing this employment is to lay a handful of political scenarios moving frontward from the acquaint that Pb to consideration of this policy choice past times Russian leadership; assign prior probabilities to the constituent steps of each scenario; as well as calculate a large issue of Monte Carlo "runs" of the scenarios, based on random assignment of values to the constituent steps of each of the diverse scenarios according to the prior probabilities assigned past times the experts. Outcomes tin as well as thus last classified equally "Russia attempts to occupy Latvia" as well as "Russia does non endeavor to occupy Latvia". The issue of outcomes inwards the begin jail cellphone allows an approximate of the overall likelihood of this outcome. The logic of this do is just parallel to the calculation that McGrayne describes for assigning probabilities to geographic cells of sea flooring for the in conclusion resting spot of the submarine, given the administration as well as speed scenarios considered. And the Bayesian contribution of updating of priors is illuminating inwards this analysis equally well: equally experts' judgments of the probabilities of the constituent steps alter given novel information, the overall probability of the outcome changes equally well.

Here is a real elementary illustration of a scenario analysis. The 4 stages of the scenario are:

A: NATO signals unity
B: LATVIA accepts anti-missile defense
C: USA signals lack of interest
D: KREMLIN inwards turmoil

Here is a diagram of the scenarios, along amongst hypothetical "expert judgments" well-nigh the likelihoods of outcomes of the branch points:

This analysis leads to a forecast of a 7.8% likelihood of business (O1, O10, O13). And an of import policy recommendation tin last derived from this analysis equally well: most of the remove chances of business falls on the lower one-half of the tree, stemming from a NATO signal of disunity. This remove chances tin last avoided past times NATO giving the signal of unity instead; as well as thus the remove chances of business falls to less than 1%.