Connecting Tables by Allowing Negative Cell Counts
Abstract It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each table to be $$-1$$. In this p...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yoshida, Ruriko [verfasserIn] Barnhill, David [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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| Anmerkung: |
© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2024 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of statistical theory and practice - Springer International Publishing, 2007, 18(2024), 3 vom: 29. Mai |
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| Übergeordnetes Werk: |
volume:18 ; year:2024 ; number:3 ; day:29 ; month:05 |
| Links: |
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| DOI / URN: |
10.1007/s42519-024-00381-8 |
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| Katalog-ID: |
SPR056050208 |
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| 520 | |a Abstract It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each table to be $$-1$$. In this paper we show that if a subset of a Markov basis connects all tables in the fiber which contains a table with all ones, then moves in this subset connect tables in the fiber if we allow cell counts to be $$-1$$. In addition, we show that in some cases under the no-three-way interaction model, we can connect tables using all basic moves of $$2 \times 2 \times 2$$ minors by allowing $$X_{ijk} \ge -1$$. We then apply a Markov chain Monte Carlo (MCMC) scheme to an empirical data on Naval officer and enlisted population. Our computational experiments show it works well and we end with the conjecture on the no-three-way interaction model. | ||
| 650 | 4 | |a Discrete exponential family |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Lattice bases |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Markov bases |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Barnhill, David |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Journal of statistical theory and practice |d Springer International Publishing, 2007 |g 18(2024), 3 vom: 29. Mai |w (DE-627)771398247 |w (DE-600)2740991-0 |x 1559-8616 |7 nnns |
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10.1007/s42519-024-00381-8 doi (DE-627)SPR056050208 (SPR)s42519-024-00381-8-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ Yoshida, Ruriko verfasserin aut Connecting Tables by Allowing Negative Cell Counts 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2024 Abstract It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each table to be $$-1$$. In this paper we show that if a subset of a Markov basis connects all tables in the fiber which contains a table with all ones, then moves in this subset connect tables in the fiber if we allow cell counts to be $$-1$$. In addition, we show that in some cases under the no-three-way interaction model, we can connect tables using all basic moves of $$2 \times 2 \times 2$$ minors by allowing $$X_{ijk} \ge -1$$. We then apply a Markov chain Monte Carlo (MCMC) scheme to an empirical data on Naval officer and enlisted population. Our computational experiments show it works well and we end with the conjecture on the no-three-way interaction model. Discrete exponential family (dpeaa)DE-He213 Lattice bases (dpeaa)DE-He213 Markov bases (dpeaa)DE-He213 Barnhill, David verfasserin aut Enthalten in Journal of statistical theory and practice Springer International Publishing, 2007 18(2024), 3 vom: 29. Mai (DE-627)771398247 (DE-600)2740991-0 1559-8616 nnns volume:18 year:2024 number:3 day:29 month:05 https://dx.doi.org/10.1007/s42519-024-00381-8 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 18 2024 3 29 05 |
| spelling |
10.1007/s42519-024-00381-8 doi (DE-627)SPR056050208 (SPR)s42519-024-00381-8-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ Yoshida, Ruriko verfasserin aut Connecting Tables by Allowing Negative Cell Counts 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2024 Abstract It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each table to be $$-1$$. In this paper we show that if a subset of a Markov basis connects all tables in the fiber which contains a table with all ones, then moves in this subset connect tables in the fiber if we allow cell counts to be $$-1$$. In addition, we show that in some cases under the no-three-way interaction model, we can connect tables using all basic moves of $$2 \times 2 \times 2$$ minors by allowing $$X_{ijk} \ge -1$$. We then apply a Markov chain Monte Carlo (MCMC) scheme to an empirical data on Naval officer and enlisted population. Our computational experiments show it works well and we end with the conjecture on the no-three-way interaction model. Discrete exponential family (dpeaa)DE-He213 Lattice bases (dpeaa)DE-He213 Markov bases (dpeaa)DE-He213 Barnhill, David verfasserin aut Enthalten in Journal of statistical theory and practice Springer International Publishing, 2007 18(2024), 3 vom: 29. Mai (DE-627)771398247 (DE-600)2740991-0 1559-8616 nnns volume:18 year:2024 number:3 day:29 month:05 https://dx.doi.org/10.1007/s42519-024-00381-8 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 18 2024 3 29 05 |
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10.1007/s42519-024-00381-8 doi (DE-627)SPR056050208 (SPR)s42519-024-00381-8-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ Yoshida, Ruriko verfasserin aut Connecting Tables by Allowing Negative Cell Counts 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2024 Abstract It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each table to be $$-1$$. In this paper we show that if a subset of a Markov basis connects all tables in the fiber which contains a table with all ones, then moves in this subset connect tables in the fiber if we allow cell counts to be $$-1$$. In addition, we show that in some cases under the no-three-way interaction model, we can connect tables using all basic moves of $$2 \times 2 \times 2$$ minors by allowing $$X_{ijk} \ge -1$$. We then apply a Markov chain Monte Carlo (MCMC) scheme to an empirical data on Naval officer and enlisted population. Our computational experiments show it works well and we end with the conjecture on the no-three-way interaction model. Discrete exponential family (dpeaa)DE-He213 Lattice bases (dpeaa)DE-He213 Markov bases (dpeaa)DE-He213 Barnhill, David verfasserin aut Enthalten in Journal of statistical theory and practice Springer International Publishing, 2007 18(2024), 3 vom: 29. Mai (DE-627)771398247 (DE-600)2740991-0 1559-8616 nnns volume:18 year:2024 number:3 day:29 month:05 https://dx.doi.org/10.1007/s42519-024-00381-8 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 18 2024 3 29 05 |
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10.1007/s42519-024-00381-8 doi (DE-627)SPR056050208 (SPR)s42519-024-00381-8-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ Yoshida, Ruriko verfasserin aut Connecting Tables by Allowing Negative Cell Counts 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2024 Abstract It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each table to be $$-1$$. In this paper we show that if a subset of a Markov basis connects all tables in the fiber which contains a table with all ones, then moves in this subset connect tables in the fiber if we allow cell counts to be $$-1$$. In addition, we show that in some cases under the no-three-way interaction model, we can connect tables using all basic moves of $$2 \times 2 \times 2$$ minors by allowing $$X_{ijk} \ge -1$$. We then apply a Markov chain Monte Carlo (MCMC) scheme to an empirical data on Naval officer and enlisted population. Our computational experiments show it works well and we end with the conjecture on the no-three-way interaction model. Discrete exponential family (dpeaa)DE-He213 Lattice bases (dpeaa)DE-He213 Markov bases (dpeaa)DE-He213 Barnhill, David verfasserin aut Enthalten in Journal of statistical theory and practice Springer International Publishing, 2007 18(2024), 3 vom: 29. Mai (DE-627)771398247 (DE-600)2740991-0 1559-8616 nnns volume:18 year:2024 number:3 day:29 month:05 https://dx.doi.org/10.1007/s42519-024-00381-8 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 18 2024 3 29 05 |
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Yoshida, Ruriko ddc 510 misc Discrete exponential family misc Lattice bases misc Markov bases Connecting Tables by Allowing Negative Cell Counts |
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510 VZ Connecting Tables by Allowing Negative Cell Counts Discrete exponential family (dpeaa)DE-He213 Lattice bases (dpeaa)DE-He213 Markov bases (dpeaa)DE-He213 |
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connecting tables by allowing negative cell counts |
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Connecting Tables by Allowing Negative Cell Counts |
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Abstract It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each table to be $$-1$$. In this paper we show that if a subset of a Markov basis connects all tables in the fiber which contains a table with all ones, then moves in this subset connect tables in the fiber if we allow cell counts to be $$-1$$. In addition, we show that in some cases under the no-three-way interaction model, we can connect tables using all basic moves of $$2 \times 2 \times 2$$ minors by allowing $$X_{ijk} \ge -1$$. We then apply a Markov chain Monte Carlo (MCMC) scheme to an empirical data on Naval officer and enlisted population. Our computational experiments show it works well and we end with the conjecture on the no-three-way interaction model. © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2024 |
| abstractGer |
Abstract It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each table to be $$-1$$. In this paper we show that if a subset of a Markov basis connects all tables in the fiber which contains a table with all ones, then moves in this subset connect tables in the fiber if we allow cell counts to be $$-1$$. In addition, we show that in some cases under the no-three-way interaction model, we can connect tables using all basic moves of $$2 \times 2 \times 2$$ minors by allowing $$X_{ijk} \ge -1$$. We then apply a Markov chain Monte Carlo (MCMC) scheme to an empirical data on Naval officer and enlisted population. Our computational experiments show it works well and we end with the conjecture on the no-three-way interaction model. © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2024 |
| abstract_unstemmed |
Abstract It is well-known that computing a Markov basis for a discrete loglinear model is very hard in general. Thus, we focus on connecting tables in a fiber via a subset of a Markov basis and in this paper, we consider connecting tables if we allow cell counts in each table to be $$-1$$. In this paper we show that if a subset of a Markov basis connects all tables in the fiber which contains a table with all ones, then moves in this subset connect tables in the fiber if we allow cell counts to be $$-1$$. In addition, we show that in some cases under the no-three-way interaction model, we can connect tables using all basic moves of $$2 \times 2 \times 2$$ minors by allowing $$X_{ijk} \ge -1$$. We then apply a Markov chain Monte Carlo (MCMC) scheme to an empirical data on Naval officer and enlisted population. Our computational experiments show it works well and we end with the conjecture on the no-three-way interaction model. © This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2024 |
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2024-08-24T04:51:00.895Z |
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