<mods:mods xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" ID="etd989" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd">
	<mods:titleInfo>
		<mods:title>Large Deviations Rate Functions for the Empirical Measure: Explicit Formulas and an Application to Monte Carlo</mods:title>
	</mods:titleInfo><mods:name type="personal">
		<mods:namePart>Liu, Yufei </mods:namePart>
	<mods:role>
		<mods:roleTerm type="text">creator</mods:roleTerm>
	</mods:role>
	</mods:name>
<mods:originInfo>
	<mods:copyrightDate>2013</mods:copyrightDate>
</mods:originInfo>
<mods:physicalDescription>
        <mods:extent>xiii, 114 p.</mods:extent>
        <mods:digitalOrigin>born digital</mods:digitalOrigin>
</mods:physicalDescription>
<mods:note>Thesis (Ph.D. -- Brown University (2013)</mods:note>
<mods:name type="personal">
<mods:namePart>Dupuis, Paul</mods:namePart>
<mods:role>
<mods:roleTerm type="text">Director</mods:roleTerm>
</mods:role>
</mods:name>

<mods:name type="personal">
<mods:namePart>Doll, Jimmie</mods:namePart>
<mods:role>
<mods:roleTerm type="text">Reader</mods:roleTerm>
</mods:role>
</mods:name>

<mods:name type="personal">
<mods:namePart>Ramanan, Kavita</mods:namePart>
<mods:role>
<mods:roleTerm type="text">Reader</mods:roleTerm>
</mods:role>
</mods:name>
<mods:name type="corporate">
		<mods:namePart>Brown University. Applied Mathematics</mods:namePart>
		<mods:role>
			<mods:roleTerm type="text">sponsor</mods:roleTerm>
		</mods:role>
		</mods:name>
	<mods:genre authority="aat">theses</mods:genre>
	<mods:abstract>In this thesis, we use the large deviations principle to characterize the rate of convergence of the empirical measures of Markov processes. An explicit formula of the large deviations rate function is very useful for this purpose. The main result in this aspect is the Donsker-Varadhan formula for the reversible, continuous time Markov processes. However, it is not applicable to the Markov jump processes, and establishing such a formula is our goal in the first part of this thesis. In the second part, we apply such a formula to a Markov chain Monte Carlo algorithm, the parallel tempering algorithm. By examining the rate function, we arrive at a new class of MCMC

algorithm, the infinite swapping algorithm. We then devote the rest of this thesis into the study of infinite swapping algorithm, for both of its

theoretical properties and its implementation challenges and solutions.</mods:abstract>

    <mods:subject>
        <mods:topic>empirical measure</mods:topic>
    </mods:subject>

    <mods:subject>
        <mods:topic>Markov jump process</mods:topic>
    </mods:subject>

    <mods:subject>
        <mods:topic>Markov chain Monte Carlo</mods:topic>
    </mods:subject>

	<mods:subject xmlns:xlink="http://www.w3.org/1999/xlink" authority="FAST" authorityURI="http://id.worldcat.org/fast" valueURI="http://id.worldcat.org/fast/992659"><mods:topic>Large deviations</mods:topic></mods:subject><mods:recordInfo>
		<mods:recordContentSource authority="marcorg">RPB</mods:recordContentSource>
		<mods:recordCreationDate encoding="iso8601">20131218</mods:recordCreationDate>        
	</mods:recordInfo>
<mods:language xmlns:xlink="http://www.w3.org/1999/xlink"><mods:languageTerm type="code" authority="iso639-2b">eng</mods:languageTerm><mods:languageTerm type="text">English</mods:languageTerm></mods:language><mods:identifier xmlns:xlink="http://www.w3.org/1999/xlink" type="doi">10.7301/Z0GB22DT</mods:identifier><mods:accessCondition xmlns:xlink="http://www.w3.org/1999/xlink" type="rights statement" xlink:href="http://rightsstatements.org/vocab/InC/1.0/">In Copyright</mods:accessCondition><mods:accessCondition type="restriction on access">Collection is open for research.</mods:accessCondition><mods:typeOfResource xmlns:xlink="http://www.w3.org/1999/xlink" authority="primo">dissertations</mods:typeOfResource></mods:mods>