Masticationpedia

Difference between revisions of "The logic of the probabilistic language"

The logic of the probabilistic language (view source)

Revision as of 10:50, 23 June 2024

12,879 bytes added ,  4 months ago
no edit summary
Line 12: Line 12:
The concept of probabilistic-causal analysis is then further explored, which seeks to quantify the relationship between events and random processes in clinical diagnosis. A detailed exposition is presented on how conditional probabilities can be interpreted and how causal relevance partitioning can be used to formulate a differential diagnosis.
The concept of probabilistic-causal analysis is then further explored, which seeks to quantify the relationship between events and random processes in clinical diagnosis. A detailed exposition is presented on how conditional probabilities can be interpreted and how causal relevance partitioning can be used to formulate a differential diagnosis.


Finally, the theme of interdisciplinarity in scientific research is addressed, highlighting the importance of an interdisciplinary approach to tackling complex problems. Fuzzy logic is also mentioned as a possible tool for managing uncertainty in medical contexts.<blockquote>
== Keywords ==


# '''Probabilistic Language in Medicine''' - Focuses on the application of probability and statistics to understand and manage uncertainties in medical diagnosis and treatment.
 
# '''Subjective vs. Objective Probability''' - Differentiates between personal belief systems and empirical data in medical practice.
Finally, the theme of interdisciplinarity in scientific research is addressed, highlighting the importance of an interdisciplinary approach to tackling complex problems. Fuzzy logic is also mentioned as a possible tool for managing uncertainty in medical contexts.
# '''Uncertainty in Medical Practice''' - Highlights the inherent uncertainties in medical diagnoses and the importance of managing these through probabilistic approaches.
 
# '''Causality and Randomness in Medicine''' - Discusses the challenges of identifying clear causal relationships in clinical conditions due to inherent randomness.
{{ArtBy|
# '''Interdisciplinary Approach in Medicine''' - Emphasizes the need for combining multiple scientific perspectives to tackle complex medical issues.
# '''Fuzzy Logic in Medicine''' - Suggests the use of fuzzy logic as a tool to handle uncertainty and variability in medical contexts.
# '''Probabilistic-Causal Analysis''' - Explores advanced techniques for quantifying relationships between different medical phenomena.
# '''Conditional Probabilities in Diagnosis''' - Examines how conditional probabilities are used to refine diagnoses and understand the probabilistic nature of medical outcomes.
</blockquote>{{ArtBy|
| autore = Gianni Frisardi
| autore = Gianni Frisardi
| autore2 = Riccardo Azzali
| autore2 = Riccardo Azzali
| autore3 = Flavio Frisardi
| autore3 = Flavio Frisardi
}}Every scientific idea—whether in medicine, architecture, engineering, chemistry, or any other field—when implemented, is prone to small errors and uncertainties. Mathematics, through the lens of probability theory and statistical inference, aids in precisely managing and thereby mitigating these uncertainties. It must always be considered that in all practical scenarios, "the outcomes also depend on many other external factors to the theory," be they initial and environmental conditions, experimental errors, or others.
}}
 
== Introduction to the Probabilistic Language ==
Every scientific idea—whether in medicine, architecture, engineering, chemistry, or any other field—when implemented, is prone to small errors and uncertainties. Mathematics, through the lens of probability theory and statistical inference, aids in precisely managing and thereby mitigating these uncertainties. It must always be considered that in all practical scenarios, "the outcomes also depend on many other external factors to the theory," be they initial and environmental conditions, experimental errors, or others.


The uncertainties surrounding these factors render the theory-observation relationship probabilistic. In medical practice, two types of uncertainty predominantly impact diagnoses: subjective uncertainty and causality.<ref>{{Cite book | autore = Vázquez-Delgado E | autore2 = Cascos-Romero J | autore3 = Gay-Escoda C | titolo = Myofascial pain associated with trigger points: a literature review. Part 2: Differential diagnosis and treatment | url = http://www.medicinaoral.com/pubmed/medoralv15_i4_pe639.pdf | volume = | opera = Med Oral Patol Oral Cir Bucal | anno = 2007 | editore = | città = | ISBN = | PMID = 20173729 | PMCID = | DOI = 10.4317/medoral.15.e639 | oaf = <!-- any value --> | LCCN = | OCLC = }}</ref><ref>{{Cite book | autore = Thoppay J | autore2 = Desai B | titolo = Oral burning: local and systemic connection for a patient-centric approach | url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6459460/ | volume = | opera = EPMA J | anno = 2019 | editore = | città = | ISBN = | PMID = 30984309 | PMCID = PMC6459460 | DOI = 10.1007/s13167-018-0157-3 | oaf = <!-- any value --> | LCCN = | OCLC = }}</ref> Therefore, in this context, it becomes crucial to differentiate between these two uncertainties and to demonstrate that the concept of probability assumes different meanings in these contexts. We will endeavor to elucidate these concepts by connecting each critical step to the clinical approach that has been documented in previous chapters, particularly focusing on the dental and neurological domains in vying for diagnostic supremacy for our dear Mary Poppins.
The uncertainties surrounding these factors render the theory-observation relationship probabilistic. In medical practice, two types of uncertainty predominantly impact diagnoses: subjective uncertainty and causality.<ref>{{Cite book | autore = Vázquez-Delgado E | autore2 = Cascos-Romero J | autore3 = Gay-Escoda C | titolo = Myofascial pain associated with trigger points: a literature review. Part 2: Differential diagnosis and treatment | url = http://www.medicinaoral.com/pubmed/medoralv15_i4_pe639.pdf | volume = | opera = Med Oral Patol Oral Cir Bucal | anno = 2007 | editore = | città = | ISBN = | PMID = 20173729 | PMCID = | DOI = 10.4317/medoral.15.e639 | oaf = <!-- any value --> | LCCN = | OCLC = }}</ref><ref>{{Cite book | autore = Thoppay J | autore2 = Desai B | titolo = Oral burning: local and systemic connection for a patient-centric approach | url = https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6459460/ | volume = | opera = EPMA J | anno = 2019 | editore = | città = | ISBN = | PMID = 30984309 | PMCID = PMC6459460 | DOI = 10.1007/s13167-018-0157-3 | oaf = <!-- any value --> | LCCN = | OCLC = }}</ref> Therefore, in this context, it becomes crucial to differentiate between these two uncertainties and to demonstrate that the concept of probability assumes different meanings in these contexts. We will endeavor to elucidate these concepts by connecting each critical step to the clinical approach that has been documented in previous chapters, particularly focusing on the dental and neurological domains in vying for diagnostic supremacy for our dear Mary Poppins.
----
===Subjective Uncertainty and Causality===
==Subjective Uncertainty and Causality==
Let's imagine asking Mary Poppins which of the two medical colleagues—the dentist or the neurologist—is correct.
Let's imagine asking Mary Poppins which of the two medical colleagues—the dentist or the neurologist—is correct.


Line 47: Line 42:


In clinical cases—precisely because patients rarely possess advanced notions of medicine—subjective uncertainty must be considered. Living with uncertainty requires us to adopt a probabilistic approach.
In clinical cases—precisely because patients rarely possess advanced notions of medicine—subjective uncertainty must be considered. Living with uncertainty requires us to adopt a probabilistic approach.
======Causality ======
====Causality ====
Causality indicates the lack of a certain connection between cause and effect. The uncertainty of a close union between the source and the phenomenon is among the most challenging problems in determining a diagnosis.
Causality indicates the lack of a certain connection between cause and effect. The uncertainty of a close union between the source and the phenomenon is among the most challenging problems in determining a diagnosis.


In a clinical case, a phenomenon <math>A(x)</math> (such as a malocclusion, a crossbite, an openbite, etc.) is randomly associated with another phenomenon <math>B(x)</math> (such as TMJ bone degeneration); when there are exceptions for which the logical proposition <math>A(x) \rightarrow B(x)</math> is not always true (but it is most of the time), we will say that the relation <math>A(x) \rightarrow B(x)</math> is not always true but it is probable.{{q2|<!--30-->We are moving from a deterministic condition to a stochastic one.|}}
In a clinical case, a phenomenon <math>A(x)</math> (such as a malocclusion, a crossbite, an openbite, etc.) is randomly associated with another phenomenon <math>B(x)</math> (such as TMJ bone degeneration); when there are exceptions for which the logical proposition <math>A(x) \rightarrow B(x)</math> is not always true (but it is most of the time), we will say that the relation <math>A(x) \rightarrow B(x)</math> is not always true but it is probable.{{q2|<!--30-->We are moving from a deterministic condition to a stochastic one.|}}
==Subjective and Objective Probability==
===Subjective and Objective Probability===
In this chapter, we revisit some topics previously discussed in the insightful book by Kazem Sadegh-Zadeh<ref>{{cita libro
In this chapter, we revisit some topics previously discussed in the insightful book by Kazem Sadegh-Zadeh<ref>{{cita libro
|autore=Sadegh-Zadeh Kazem
|autore=Sadegh-Zadeh Kazem
Line 69: Line 64:
#Mary Poppins is more likely to have TMDs than neuropathic OP (comparative term: the number of diagnosed cases of TMDs vs. neuropathic OP).
#Mary Poppins is more likely to have TMDs than neuropathic OP (comparative term: the number of diagnosed cases of TMDs vs. neuropathic OP).
#The probability that Mary Poppins has TMDs is 0.15 (quantitative term, relative to the population).
#The probability that Mary Poppins has TMDs is 0.15 (quantitative term, relative to the population).
=== Subjective Probability===
==== Subjective Probability====
In contexts of human subjective uncertainty, probabilistic, qualitative, comparative, and/or quantitative data can be interpreted by clinicians as measures of subjective uncertainty, to make 'states of conviction' numerically representable.
In contexts of human subjective uncertainty, probabilistic, qualitative, comparative, and/or quantitative data can be interpreted by clinicians as measures of subjective uncertainty, to make 'states of conviction' numerically representable.


For instance, stating "the probability that Mary Poppins is affected by TMDs is 0.15 of the cases" is akin to saying "with a 15% degree of belief, I think that Mary Poppins is affected by TMDs"; indicating that the degree of conviction corresponds to the degree of subjective probability.
For instance, stating "the probability that Mary Poppins is affected by TMDs is 0.15 of the cases" is akin to saying "with a 15% degree of belief, I think that Mary Poppins is affected by TMDs"; indicating that the degree of conviction corresponds to the degree of subjective probability.
===Objective Probability===
====Objective Probability====
Conversely, events and random processes cannot be accurately described by deterministic processes in the form 'if A then B'. Statistics are utilized to quantify the frequency of the association between A and B, representing their relationship as a degree of probability, which introduces the concept of objective probability.
Conversely, events and random processes cannot be accurately described by deterministic processes in the form 'if A then B'. Statistics are utilized to quantify the frequency of the association between A and B, representing their relationship as a degree of probability, which introduces the concept of objective probability.


Amid the increasing acknowledgment of the role of probabilization of uncertainty and randomness in medicine since the eighteenth century, the term "probability" has become an integral part of medical language, methodology, and epistemology. Unfortunately, the distinction between subjective and objective probability is not always clearly made in medicine, as is the case in other disciplines too. Nevertheless, the vital contribution of probability theory in medicine, especially in concepts of probability in etiology, epidemiology, diagnostics, and therapy, lies in its aid in understanding and representing biological causality.
Amid the increasing acknowledgment of the role of probabilization of uncertainty and randomness in medicine since the eighteenth century, the term "probability" has become an integral part of medical language, methodology, and epistemology. Unfortunately, the distinction between subjective and objective probability is not always clearly made in medicine, as is the case in other disciplines too. Nevertheless, the vital contribution of probability theory in medicine, especially in concepts of probability in etiology, epidemiology, diagnostics, and therapy, lies in its aid in understanding and representing biological causality.
----
==Probabilistic-Causal Analysis==
From these premises, it is evident that clinical diagnosis employs the so-called hypothetical-deductive method, known as DN<ref name=":1">{{Cite book
| autore = Sarkar S
| titolo = Nagel on Reduction
| url = https://pubmed.ncbi.nlm.nih.gov/26386529/
| volume =
| opera = Stud Hist Philos Sci
| anno = 2015
| editore =
| città =
| ISBN =
| PMID = 26386529
| PMCID =
| DOI = 10.1016/j.shpsa.2015.05.006
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref> ([[wikipedia:Deductive-nomological_model|deductive-nomological model]]<ref>''<!--52-->DN model of scientific explanation'', <!--53-->also known as ''<!--54-->Hempel's model'', ''Hempel–Oppenheim model'', ''Popper–Hempel model'', <!--55-->or ''<!--56-->covering law model''</ref>). However, this is not realistic, as the medical knowledge used in clinical decision-making rarely contains causal deterministic laws that allow for causal explanations and, consequently, the formulation of clinical diagnoses, among other things in the specialist context. Let us re-examine the case of Mary Poppins, this time adopting a probabilistic-causal approach.
Consider a number <math>n</math> of individuals, including those who report Orofacial Pain, who generally have bone degeneration of the Temporomandibular Joint. However, there might also be other apparently unrelated causes. We must mathematically translate the 'relevance' of these causal uncertainties in determining a diagnosis.
----
===The casual relevance===
To do this we consider the degree of causal relevance <math>(cr)</math> of an event <math>E_1</math> with respect to an event <math>E_2</math> where:
*<math>E_1</math> = patients with bone degeneration of the temporomandibular joint.
*<math>E_2</math> = patients reporting orofacial pain.
*<math>E_3</math> = patients without bone degeneration of the temporomandibular joint.
We will use the conditional probability <math>P(A \mid B)</math>, that is the probability that the <math>A</math> event occurs only after the event <math>B</math> has already occurred.
With these premises the causal relevance <math>cr</math> of the sample <math>n</math> of patients is:
<math>cr=P(E_2 \mid E_1)- P(E_2 \mid E_3)</math>
where
:<math>P(E_2 \mid E_1)</math> indicates the probability that some people (among <math>n</math> taken into consideration) suffer from Orofacial Pain caused by bone degeneration of the Temporomandibular Joint,
while
:<math>P(E_2 \mid E_3)</math> indicates the probability that other people (always among <math>n</math> taken into consideration) suffer from Orofacial Pain conditioned by something other than bone degeneration of the Temporomandibular Joint.
Since all probability suggest that <math>P(A \mid B)</math> is a value between <math>0 </math> and <math>1 </math>, the parameter <math>(cr)</math> will be a number that is between <math>-1 </math> and <math>1 </math>.
The meanings that we can give to this number are as follows:
*we have the extreme cases (which in reality never occur) which are:
:*<math>cr=1</math> indicating that the only cause of orofacial pain is bone degeneration of the TMJ,
:*<math>cr=-1</math> which indicates that the cause of orofacial pain is never bone degeneration of the TMJ but is something else,
:*<math>cr=0</math> indicating that the probability that orofacial pain is caused by bone degeneration of the TMJ or otherwise is exactly the same,
*and the intermediate cases (which are the realistic ones)
:*<math>cr>0</math> indicating that the cause of orofacial pain is more likely to be bone degeneration of the TMJ,
:*<math>cr<0</math> which indicates that the cause of orofacial pain is more likely not bone degeneration of the TMJ.
<center>
===Second Clinical Approach===
''(hover over the images)''
<gallery widths="350" heights="282" perrow="2" mode="slideshow">
File:Spasmo emimasticatorio.jpg|'''<!--81-->Figure 1:''' Patient reporting "Orofacial pain in the right hemilateral"
File:Spasmo emimasticatorio ATM.jpg|'''<!--83-->Figure 2:''' Patient's TMJ Stratigraphy showing signs of condylar flattening and osteophyte
File:Atm1 sclerodermia.jpg|'''<!--85-->Figure 3:''' Computed Tomography of the TMJ
File:Spasmo emimasticatorio assiografia.jpg|'''<!--87-->Figure 4:''' Axiography of the patient showing a flattening of the chewing pattern on the right condyle
File:EMG2.jpg|'''<!--89-->Figure 5:''' EMG Interferential Pattern. Overlapping upper traces corresponding to the right masseter, lower to the left masseter.
</gallery>
</center>
So be it then <math>P(D)</math> the probability of finding, in the sample of our <math>n</math> people, individuals who present the elements belonging to the aforementioned set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math>
In order to take advantage of the information provided by this dataset, the concept of partition of causal relevance is introduced:
====The partition of causal relevance====
:Always be <math>n</math> the number of people we have to conduct the analyses upon, if we divide (based on certain conditions as explained below) this group into <math>k</math> subsets <math>C_i</math> with <math>i=1,2,\dots,k</math>, a cluster is created that is called a "partition set" <math>\pi</math>:
:<math>\pi = \{C_1, C_2,\dots,C_k \}  \qquad \qquad \text{with} \qquad \qquad C_i \subset n , </math>
where with the symbolism <math>C_i \subset n </math> it indicates that the subclass <math>C_i</math> is contained in <math>n</math>.
The partition <math>\pi</math>, in order for it to be defined as a partition of causal relevance, must have these properties:
#For each subclass <math>C_i</math> the condition must apply <math>rc=P(D \mid C_i)- P(D )\neq 0, </math> ie the probability of finding in the subgroup <math>C_i</math> a person who has the symptoms, clinical signs and elements belonging to the set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math>. A causally relevant partition of this type is said to be '''homogeneous'''.
#Each subset <math>C_i</math> must be 'elementary', i.e. it must not be further divided into other subsets, because if these existed they would have no causal relevance.
Now let us assume, for example, that the population sample <math>n</math>, to which our good patient Mary Poppins belongs, is a category of subjects aged 20 to 70. We also assume that in this population we have those who present the elements belonging to the data set <math>D=\{\delta_1,.....\delta_n\}</math> which correspond to the laboratory tests mentioned above and precisa in '[[The logic of the classical language|The logic of classical language]]'.
Let us suppose that in a sample of 10,000 subjects from 20 to 70 we will have an incidence of 30 subjects <math>p(D)=0.003</math> showing clinical signs <math>\delta_1</math> and <math>\delta_4
</math>. We preferred to use these reports for the demonstration of the probabilistic process because in the literature the data regarding clinical signs and symptoms for Temporomandibular Disorders have too wide a variation as well as too high an incidence in our opinion.<ref name=":2">{{Cite book
| autore = Pantoja LLQ
| autore2 = De Toledo IP
| autore3 = Pupo YM
| autore4 = Porporatti AL
| autore5 = De Luca Canto G
| autore6 = Zwir LF
| autore7 = Guerra ENS
| titolo = Prevalence of degenerative joint disease of the temporomandibular joint: a systematic review
| url = https://pubmed.ncbi.nlm.nih.gov/30311063/
| volume =
| opera = Clin Oral Investig
| anno = 2019
| editore =
| città =
| ISBN =
| PMID = 30311063
| PMCID =
| DOI = 10.1007/s00784-018-2664-y
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":3">{{Cite book
| autore = De Toledo IP
| autore2 = Stefani FM
| autore3 = Porporatti AL
| autore4 = Mezzomo LA
| autore5 = Peres MA
| autore6 = Flores-Mir C
| autore7 = De Luca Canto G
| titolo = Prevalence of otologic signs and symptoms in adult patients with temporomandibular disorders: a systematic review and meta-analysis
| url = https://www.ncbi.nlm.nih.gov/pubmed/27511214
| volume =
| opera = Clin Oral Investig
| anno = 2017
| editore =
| città =
| ISBN =
| PMID = 27511214
| PMCID =
| DOI = 10.1007/s00784-016-1926-9
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":4">{{Cite book
| autore = Bonotto D
| autore2 = Penteado CA
| autore3 = Namba EL
| autore4 = Cunali PA
| autore5 = Rached RN
| autore6 = Azevedo-Alanis LR
| titolo = Prevalence of temporomandibular disorders in rugby players
| url = https://www.ncbi.nlm.nih.gov/pubmed/31355769
| volume =
| opera = Gen Dent
| anno =
| editore =
| città =
| ISBN =
| PMID = 31355769
| PMCID =
| DOI =
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":5">{{Cite book
| autore = da Silva CG
| autore2 = Pachêco-Pereira C
| autore3 = Porporatti AL
| autore4 = Savi MG
| autore5 = Peres MA
| autore6 = Flores-Mir C
| autore7 = De Luca Canto G
| titolo = Prevalence of clinical signs of intra-articular temporomandibular disorders in children and adolescents: A systematic review and meta-analysis
| url = https://www.ncbi.nlm.nih.gov/pubmed/26552334
| volume =
| opera = Am Dent Assoc
| anno = 2016
| editore =
| città =
| ISBN =
| PMID =
| PMCID = 26552334
| DOI = 10.1016/j.adaj.2015.07.017
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":6">{{Cite book
| autore = Gauer RL
| autore2 = Semidey MJ
| titolo = Diagnosis and treatment of temporomandibular disorders
| url = https://www.aafp.org/afp/2015/0315/afp20150315p378.pdf
| volume =
| opera = Am Fam Physician
| anno = 2015
| editore =
| città =
| ISBN =
| PMID = 25822556
| PMCID =
| DOI =
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref><ref name=":7">{{Cite book
| autore = Kohlmann T
| titolo = Epidemiology of orofacial pain
| url = https://www.ncbi.nlm.nih.gov/pubmed/12235497
| volume =
| opera = Schmerz
| anno = 2002
| editore =
| città =
| ISBN =
| PMID = 12235497
| PMCID =
| DOI = 10.1007/s004820200000
| oaf = <!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref>
An example of a partition with presumed probability in which TMJ degeneration (Deg.TMJ) occurs in conjunction with Temporomandibular Disorders (TMDs) would be the following:
{|
|+
|<math>P(D| Deg.TMJ  \cap TMDs)=0.95  \qquad \qquad \; </math>
|
|where
|
|
|<math>\C_1 \equiv Deg.TMJ  \cap TMDs</math>
|-
|<math>P(D| Deg.TMJ \cap noTMDs)=0.3  \qquad \qquad  \quad </math>
|
|where
|
|
|<math>C_2\equiv  Deg.TMJ  \cap noTMDs</math>
|-
|<math>P(D| no Deg.TMJ  \cap TMDs)=0.199  \qquad \qquad \; </math>
|
|where
|
|
|<math>C_3\equiv  no Deg.TMJ  \cap TMDs</math>
|-
|<math>P(D| noDeg.TMJ  \cap noTMDs)=0.001  \qquad \qquad \;</math>
|
|where
|
|
|<math> C_4\equiv noDeg.TMJ  \cap noTMDs</math>
|}
*{{q2|<!--107-->A homogeneous partition provides what we are used to calling Differential Diagnosis.|}}
====Clinical situations====
These conditional probabilities demonstrate that each of the partition's four subclasses is causally relevant to patient data <math>D=\{\delta_1,.....\delta_n\}</math> in the population sample <math>PO</math>. Given the aforementioned partition of the reference class, we have the following clinical situations:
*Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math>  Temporomandibular Disorders
*Mary Poppins <math>\in</math> degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders
*Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> Temporomandibular Disorders
*Mary Poppins <math>\in</math> no degeneration of the temporomandibular joint <math>\cap</math> no Temporomandibular Disorders
To arrive at the final diagnosis above, we conducted a probabilistic-causal analysis of Mary Poppins' health status whose initial data were <math>D=\{\delta_1,.....\delta_n\}</math>.
In general, we can refer to a logical process in which we examine the following elements:
*an individual: <math>a</math>
*its initial data set <math>D=\{\delta_1,.....\delta_n\}</math>
*a population sample <math>n</math> to which it belongs,
*a base probability <math>P(D)=0,003</math>
At this point we should introduce too specialized arguments that would take the reader off the topic but that have an high epistemic importance for which we will try to extract the most described logical thread of the Analysandum/Analysans concept.
The probabilistic-causal analysis of <math>D=\{\delta_1,.....\delta_n\}</math> is then a couple of the following logical forms (Analysandum / Analysans<ref>{{Cite book
| autore = Westmeyer H
| titolo = The diagnostic process as a statistical-causal analysis
| url = https://psycnet.apa.org/record/1976-01749-001
| volume =
| opera = APA
| anno = 1975
| editore =
| città =
| ISBN =
| PMID =
| PMCID =
| DOI = 10.1007/BF00139821
| oaf = CC BY<!-- qualsiasi valore -->
| LCCN =
| OCLC =
}}</ref>):
*'''Analysandum''' <math>  = \{P(D),a\}</math>: is a logical form that contains two parameters: ''probability'' <math>P(D)</math> to select a person who has the symptoms and elements belonging to the set <math>D=\{\delta_1,\delta_2,...,\delta_n\}</math>, and the ''generic individual'' <math>a</math> who is prone to those symptoms.
*'''Analysan <math>= \{\pi,a,KB\}</math>''': is a logical form that contains three parameters: the ''partition'' <math>\pi</math>, the ''generic individual'' <math>a</math> belonging to the population sample <math>n</math> and ''<math>KB</math> (Knowledge Base)'' which includes a set of <math>n>1</math> statements of conditioned probability.
For example, it can be concluded that the definitive diagnosis is the following:
<math>P(D| Deg.TMJ  \cap TMDs)=0.95</math> - this means that our Mary Poppins is 95% affected by TMDs, since she has a degeneration of the Temporomandibular Joint in addition to the positive data <math>D=\{\delta_1,.....\delta_n\}</math>
----


{{:Store:LPLen04}}
{{:Store:LPLen04}}


{{:Store:LPLen05}}
{{:Store:LPLen05}}
Gianni
Editor, Editors, USER, admin, Bureaucrats, Check users, dev, editor, founder, Interface administrators, oversight, Suppressors, Administrators, translator
10,782

edits

Retrieved from "https://www.masticationpedia.org/index.php/Special:MobileDiff/19254"