Richard C. Carrier‚ Ph.D. “Bayes’ Theorem for Beginners: Formal Logic and Its Relevance to Historical Method — Adjunct Materials and Tutorial” The Jesus Project Inaugural Conference “Sources of the Jesus Tradition: An Inquiry” 5-7 December 2008 (Amherst‚ NY) Table of Contents for Enclosed Document Handout Accompanying Oral Presentation of December 5...................................pp. 2-5 Adjunct Document Expanding on Oral Presentation.............................................pp. 6-26
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Bayes’ theorem describes the relationships that exist within an array of simple and conditional probabilities. For example: Suppose there is a certain disease randomly found in one-half of one percent (.005) of the general population. A certain clinical blood test is 99 percent (.99) effective in detecting the presence of this disease; that is‚ it will yield an accurate positive result in 99 percent of the cases where the disease is actually present. But it also yields false-positive results in 5
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Assignment 20 A 1- Which of the following oxidation numbers in the species given is incorrect? a) SO32−; S +4‚ O −2 b) ClO3−; Cl +5‚ O −2 c) H2C2O4; H 1+‚ C 3+‚ O 2− d) H2O2; H +1‚ O −1 e) Ca(ClO)2; Ca +2‚ Cl +2‚ O −2 f) Zn(NH3)6Cl2; Zn 2+‚ N 3−‚ H 1+‚ Cl 1− (Cl is +1 in this compound. Ca: 1 × (+2) = +2. O: 2 × (−2) = −4. Charge on the compound = 0; therefore‚ (+2) + (−4) + 2 × Cl = 0. The charge on Cl is 1+.) 2- A voltaic cell is constructed. One electrode compartment consists of a zinc strip placed
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Chapter 9 Na¨ve Bayes ı David J. Hand Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Algorithm Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Power Despite Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extensions of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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UNIT 2 THEOREMS Structure 2.1 Introduction Objectives PROBABILITY 2.2 Some Elementary Theorems 2.3 General Addition Rule 2.4 Conditional Probability and Independence 2.4.1 Conditional Probability 2.4.2 Independent Events and MultiplicationRule 2.4.3 Theorem of Total Probability and Bayes Theorem 2.5 Summary 2.1 INTRODUCTION You have already learnt about probability axioms and ways to evaluate probability of events in some simple cases. In this unit‚ we discuss ways to evaluate
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Chapter 20- List the functions of the lymphatic vessels. The function of the lymphatic vessels‚ or lymphatic’s‚ is an elaborate system of drainage vessels that collect the excess protein-containing interstitial fluid and return it to the bloodstream. Describe the structure and distribution of lymphatic vessels. The lymphatic collecting vessels have the same three tunics as veins‚ but the collecting vessels are thinner walled‚ have more internal valves‚ and anastomose more. The lymphatic
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PYTHAGOREAN THEOREM More than 4000 years ago‚ the Babyloneans and the Chinese already knew that a triangle with the sides of 3‚ 4 and 5 must be a right triangle. They used this knowledge to construct right angles. By dividing a string into twelve equal pieces and then laying it into a triangle so that one side is three‚ the second side four and the last side five sections long‚ they could easily construct a right angle. A Greek scholar named Pythagoras‚ who lived around 500 BC‚ was also fascinated
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170 CHAPTER 5. RECURSION AND RECURRENCES 5.2 The Master Theorem Master Theorem In the last section‚ we saw three different kinds of behavior for recurrences of the form aT (n/2) + n if n > 1 d if n = 1. T (n) = These behaviors depended upon whether a < 2‚ a = 2‚ and a > 2. Remember that a was the number of subproblems into which our problem was divided. Dividing by 2 cut our problem size in half each time‚ and the n term said that after we completed our recursive work‚ we had n
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n calculus‚ Rolle’s theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. ------------------------------------------------- Standard version of the theorem [edit] If a real-valued function f is continuous on a closed interval [a‚ b]‚ differentiable on the open interval (a‚ b)‚ and f(a) = f(b)‚ then there
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pressure dynamics specified by Bernoulli’s Principle to keep their rare wheels on the ground‚ even while zooming off at high speed. It is successfully employed in mechanism like the carburetor and the atomizer. The study focuses on Bernoulli’s Theorem in Fluid Application. A fluid is any substance which when acted upon by a shear force‚ however small‚ cause a continuous or unlimited deformation‚ but at a rate proportional to the applied force. As a matter of fact‚ if a fluid is moving horizontally
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