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These theses that change life: Estimation of semi-Markov chains and hidden semi-Markov chains for applications in reliability assessment and in biology

The chances of a machine break­ing down, or a patient relaps­ing into dis­or­der … prob­a­bil­i­ties of such events are an inte­gral part of our dai­ly lives with­out our always being aware of this. As sta­tis­ti­cal analy­sis sci­ences and prob­a­bil­i­ty the­o­ry progress they pro­vide bet­ter keys today to under­stand­ing phe­nom­e­na that appear strange indeed to the ‘man in the street’. 

Vlad Ste­fan Bar­bu – who read math­e­mat­ics and sta­tis­tics at Bucharest (Ruma­nia) — con­tact­ed the UTC-LMAC (applied maths) lab­o­ra­to­ry in Com­pieg­ne and did his PhD and pre­sent­ed his the­sis there in 2005. 

Under­pin­ning the title above, there are algo­rithms that help sim­pli­fy work for research sci­en­tists. “In the field of biol­o­gy, the appli­ca­tion aspects of my the­sis help sci­en­tists to move around on a genome map”, he explains. When geneti­cists are look­ing for the caus­es of a dis­or­der, they in fact are look­ing for areas in the DNA chain where genes are affect­ed. The algo­rithms Vlad Ste­fan Bar­bu pro­pos­es allow them to detect code-car­ry­ing seg­ments from non-cod­ed parts which con­sti­tutes a first sort­ing process that helps ori­ent the geneti­cist in a huge mass of data. 

The sec­ond part of his the­sis work relat­ed to esti­ma­tions of the para­me­ters that, for exam­ple, impact the reli­a­bil­i­ty of a machine or the sur­vival expec­ta­tions for of a patient. 

Giv­en that we are liv­ing in a com­plex world, machine do not direct­ly change over from a cor­rect oper­a­tional mode to being bro­ken down. Like­wise, the human body does not change bru­tal­ly – except for a few col­lapse type cas­es — from being in good health to being seri­ous­ly ill. Vlad Ste­fan Barbu’s work helps sci­en­tists and engi­neers bet­ter under­stand the inter­me­di­ate states. 

Mak­ing use of Markov hypothe­ses to ascer­tain what is going to take place tomor­row, we must also know what is hap­pen­ing today: the past is not tak­en into account. 

“By study­ing semi-Markov chains, you can atten­u­ate the ini­tial hypoth­e­sis and take ele­ments from a past peri­od into account too”. The idea, schemat­i­cal­ly, is to inte­grate for exam­ple the break-down his­to­ry of a giv­en machine in ser­vice. “If we aim at inte­grat­ing all the past data, this proves impos­si­ble, giv­en the num­ber of para­me­ters involved. Notwith­stand­ing, a study of semi-Markov chains allows the time-scale of the mod­els to be widened”. The the­sis enables prac­ti­tion­ers to deter­mine bet­ter the time-to-heal for some dis­or­ders or the risks of a relapse in the case of an illness. 

As of 2006, Vlad Ste­fan Bar­bu has been appoint­ed senior lec­tur­er in sta­tis­tics at the Uni­ver­si­ty of Rouen. 

Le magazine

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